`
`Mike Korenberg
`
`From:
`"Mike Korenberg" <korenber@queensu.ca>
`To:
`"Sunny Gupta" <sunny@phasespacesystems.com>
`Sent:
`March 2, 2011 12:01 PM
`Subject: More on noiselessly differentiating the linear combinations of siine & cosines
`Sunny,
`
`
`There's a couple of points about the low-energy component (made from the last, say, 100 terms found by
`FOS) that are interesting. The 1st I already mentioned to you, namely that we can find noiselessly the
`derivative of this component, since it is a linear combination of sine and cosine terms, and this derivative
`can be useful to distinguish the shocked from the non-shocked ICD patients and to view in X, Y, Z space.
`In addition, there are some useful ratios to consider. Thus suppose that u(t), v(t), and w(t) are respectively
`the X, Y, and Z coordinates of the low-energy component and let u'(t), v'(t), w'(t) be their 1st derivatives.
`Then the ratios:
`
`(u'(t)/u(t)), (v'(t)/v(t)), and (w'(t)/w(t))
`
`
`are like Lyapunov exponents and can indicate instability when positive. Consider the regions when the
`ratios are positive, especially when all are. In such regions, the magnitudes of u, v, w will increase. For
`example, if u is then positive, it will grow to a larger positive value because its derivative u' is positive, and
`if instead u is negative it will move downward to a negative value of larger magnitude because u' is
`negative. So these regions will indicate instability, and timing when they occur, and for how long, can be
`good ways of distinguishing shocked from non-shocked ICD patients. Of course, the same discussion
`applies when exponentially-decaying sines and cosines are used, since these can also be noiselessly
`differentiated.
`
`
`Mike
`
`25/03/2011
`
`1
`
`Analytics For Life, Inc. v. 8825319 Canada Limited
`IPR-01742, X2012
`
`
Accessing this document will incur an additional charge of $.
After purchase, you can access this document again without charge.
Accept $ Charge
Still Working On It
This document is taking longer than usual to download. This can happen if we need to contact the court directly to obtain the document and their servers are running slowly.
Give it another minute or two to complete, and then try the refresh button.
A few More Minutes ... Still Working
It can take up to 5 minutes for us to download a document if the court servers are running slowly.
Thank you for your continued patience.
This document could not be displayed.
We could not find this document within its docket. Please go back to the docket page and check the link. If that does not work, go back to the docket and refresh it to pull the newest information.
Your account does not support viewing this document.
You need a Paid Account to view this document. Click here to change your account type.
Your account does not support viewing this document.
Set your membership
status to view this document.
With a Docket Alarm membership, you'll
get a whole lot more, including:
- Up-to-date information for this case.
- Email alerts whenever there is an update.
- Full text search for other cases.
- Get email alerts whenever a new case matches your search.
One Moment Please
The filing “” is large (MB) and is being downloaded.
Please refresh this page in a few minutes to see if the filing has been downloaded. The filing will also be emailed to you when the download completes.
Your document is on its way!
If you do not receive the document in five minutes, contact support at support@docketalarm.com.
Sealed Document
We are unable to display this document, it may be under a court ordered seal.
If you have proper credentials to access the file, you may proceed directly to the court's system using your government issued username and password.
Access Government Site
