BEGIN:VCALENDAR
VERSION:2.0
PRODID:IEEE vTools.Events//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:America/New_York
BEGIN:DAYLIGHT
DTSTART:20270314T030000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
RRULE:FREQ=YEARLY;BYDAY=2SU;BYMONTH=3
TZNAME:EDT
END:DAYLIGHT
BEGIN:STANDARD
DTSTART:20261101T010000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
RRULE:FREQ=YEARLY;BYDAY=1SU;BYMONTH=11
TZNAME:EST
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20260928T021357Z
UID:64E6467A-626C-4CA4-88D9-200F953FA0B1
DTSTART;TZID=America/New_York:20261120T120000
DTEND;TZID=America/New_York:20261120T140000
DESCRIPTION:Abstract: The binary reflected Gray code\, patented by Frank Gr
 ay in 1953\, is a permutation of the sequence ⟨0\, 1\, …\, n-1⟩\, wh
 ere n is a power of 2\, with the property that the binary representation o
 f each number in the sequence differs from that of the preceding number in
  exactly one bit. The binary reflected Gray code is also cyclic\, in that 
 the last and first numbers also differ in only one bit.\n\nWhat if n is no
 t a power of 2? How can we create a dense Gray code: a permutation of ⟨0
 \, 1\, …\, n-1⟩ with the Gray-code property for any integer n &gt; 1? The
  answer turns out to be surprisingly simple\, but not obvious at first why
  it should work. When can we create a dense Gray code with the cyclic Gray
 -code property\, and how do we do it? The answer here is a bit more obviou
 s—once you have already seen it.\n\nBecause Gray codes apply to non-bina
 ry integer representations as well\, I will also touch on Gray codes for r
 adices other than 2 and for mixed radices.\n\nAll results are joint work w
 ith my senior thesis students\, Jessica Fan ’17\, D\n\nSpeaker(s): Thoma
 n Cormen\, \n\nAgenda: \n1 - Gather - 12 noon\n\n2 - Introduction - 12:05\
 n\n3 - Presentation -12:10\n\n4 - Q&amp;A 12:55\n\n5 - Conversation over pizza
  1 pm\n\nRoom: PL128B\, Bldg: School of Engineering\, Technology and Aeron
 autics\, 2500 North River Rd\, Manchester\, New Hampshire\, United States\
 , 03106
LOCATION:Room: PL128B\, Bldg: School of Engineering\, Technology and Aerona
 utics\, 2500 North River Rd\, Manchester\, New Hampshire\, United States\,
  03106
ORGANIZER:bbancroft@ieee.org
SEQUENCE:37
SUMMARY:Dense and Cyclic Gray Codes 
URL;VALUE=URI:https://events.vtools.ieee.org/m/580342
X-ALT-DESC:Description: &lt;br /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;tab-stops: .5in 1
 .0in 1.5in 2.0in 2.5in 3.0in 3.5in 4.0in 4.5in 5.0in 5.5in 6.0in\; mso-lay
 out-grid-align: none\; text-autospace: none\;&quot;&gt;&lt;strong style=&quot;mso-bidi-fon
 t-weight: normal\;&quot;&gt;&lt;span style=&quot;mso-bidi-font-size: 16.0pt\; font-family:
  &#39;Verdana&#39;\,sans-serif\; color: #a8d08d\; mso-themecolor: accent6\; mso-th
 emetint: 153\;&quot;&gt;Abstract:&lt;/span&gt;&lt;/strong&gt;&lt;span style=&quot;mso-bidi-font-size: 
 16.0pt\; font-family: &#39;Verdana&#39;\,sans-serif\; color: #a8d08d\; mso-themeco
 lor: accent6\; mso-themetint: 153\;&quot;&gt; &lt;/span&gt;&lt;span style=&quot;font-size: 10.0p
 t\; font-family: &#39;Verdana&#39;\,sans-serif\; mso-bidi-font-family: Helvetica\;
 &quot;&gt;The binary reflected Gray code\, patented by Frank Gray in 1953\, is a p
 ermutation of the sequence &lt;/span&gt;&lt;span style=&quot;font-size: 10.0pt\; font-fa
 mily: &#39;Cambria Math&#39;\,serif\; mso-bidi-font-family: &#39;Cambria Math&#39;\;&quot;&gt;⟨&lt;
 /span&gt;&lt;span style=&quot;font-size: 10.0pt\; font-family: &#39;Verdana&#39;\,sans-serif\
 ; mso-bidi-font-family: Helvetica\;&quot;&gt;0\, 1\, &amp;hellip\;\, &lt;em&gt;n&lt;/em&gt;-1&lt;/spa
 n&gt;&lt;span style=&quot;font-size: 10.0pt\; font-family: &#39;Cambria Math&#39;\,serif\; ms
 o-bidi-font-family: &#39;Cambria Math&#39;\;&quot;&gt;⟩&lt;/span&gt;&lt;span style=&quot;font-size: 10
 .0pt\; font-family: &#39;Verdana&#39;\,sans-serif\; mso-bidi-font-family: Helvetic
 a\;&quot;&gt;\, where &lt;em&gt;n&lt;/em&gt; is a power of 2\, with the property that the bina
 ry representation of each number in the sequence differs from that of the 
 preceding number in exactly one bit.&lt;span style=&quot;mso-spacerun: yes\;&quot;&gt;&amp;nbs
 p\; &lt;/span&gt;The binary reflected Gray code is also cyclic\, in that the las
 t and first numbers also differ in only one bit.&lt;/span&gt;&lt;/p&gt;\n&lt;p class=&quot;Mso
 Normal&quot; style=&quot;tab-stops: .5in 1.0in 1.5in 2.0in 2.5in 3.0in 3.5in 4.0in 4
 .5in 5.0in 5.5in 6.0in\; mso-layout-grid-align: none\; text-autospace: non
 e\;&quot;&gt;&lt;span style=&quot;font-size: 10.0pt\; font-family: &#39;Verdana&#39;\,sans-serif\;
  mso-bidi-font-family: Helvetica\;&quot;&gt;What if &lt;em&gt;n&lt;/em&gt; is not a power of 2
 ?&lt;span style=&quot;mso-spacerun: yes\;&quot;&gt;&amp;nbsp\; &lt;/span&gt;How can we create a dens
 e Gray code: a permutation of &lt;/span&gt;&lt;span style=&quot;font-size: 10.0pt\; font
 -family: &#39;Cambria Math&#39;\,serif\; mso-bidi-font-family: &#39;Cambria Math&#39;\;&quot;&gt;
 ⟨&lt;/span&gt;&lt;span style=&quot;font-size: 10.0pt\; font-family: &#39;Verdana&#39;\,sans-se
 rif\; mso-bidi-font-family: Helvetica\;&quot;&gt;0\, 1\, &amp;hellip\;\, &lt;em&gt;n&lt;/em&gt;-1&lt;
 /span&gt;&lt;span style=&quot;font-size: 10.0pt\; font-family: &#39;Cambria Math&#39;\,serif\
 ; mso-bidi-font-family: &#39;Cambria Math&#39;\;&quot;&gt;⟩&lt;/span&gt;&lt;span style=&quot;font-size
 : 10.0pt\; font-family: &#39;Verdana&#39;\,sans-serif\; mso-bidi-font-family: Helv
 etica\;&quot;&gt; with the Gray-code property for any integer n &amp;gt\; 1?&lt;span styl
 e=&quot;mso-spacerun: yes\;&quot;&gt;&amp;nbsp\; &lt;/span&gt;The answer turns out to be surprisi
 ngly simple\, but not obvious at first why it should work.&lt;span style=&quot;mso
 -spacerun: yes\;&quot;&gt;&amp;nbsp\; &lt;/span&gt;When can we create a dense Gray code with
  the cyclic Gray-code property\, and how do we do it?&lt;span style=&quot;mso-spac
 erun: yes\;&quot;&gt;&amp;nbsp\; &lt;/span&gt;The answer here is a bit more obvious&amp;mdash\;o
 nce you have already seen it.&lt;/span&gt;&lt;/p&gt;\n&lt;p class=&quot;MsoNormal&quot; style=&quot;tab-
 stops: .5in 1.0in 1.5in 2.0in 2.5in 3.0in 3.5in 4.0in 4.5in 5.0in 5.5in 6.
 0in\; mso-layout-grid-align: none\; text-autospace: none\;&quot;&gt;&lt;span style=&quot;f
 ont-size: 10.0pt\; font-family: &#39;Verdana&#39;\,sans-serif\; mso-bidi-font-fami
 ly: Helvetica\;&quot;&gt;Because Gray codes apply to non-binary integer representa
 tions as well\, I will also touch on Gray codes for radices other than 2 a
 nd for mixed radices.&lt;/span&gt;&lt;/p&gt;\n&lt;p class=&quot;MsoNormal&quot; style=&quot;text-align: 
 justify\; background: white\;&quot;&gt;&lt;span style=&quot;font-size: 10.0pt\; font-famil
 y: &#39;Verdana&#39;\,sans-serif\; mso-bidi-font-family: Helvetica\; color: black\
 ; mso-color-alt: windowtext\;&quot;&gt;All results are joint work with my senior t
 hesis students\, Jessica Fan &amp;rsquo\;17\, D&lt;/span&gt;&lt;/p&gt;&lt;br /&gt;&lt;br /&gt;Agenda: 
 &lt;br /&gt;&lt;p&gt;1 - Gather - 12 noon&lt;/p&gt;\n&lt;p&gt;2 - Introduction - 12:05&lt;/p&gt;\n&lt;p&gt;3 -
  Presentation -12:10&lt;/p&gt;\n&lt;p&gt;4 - Q&amp;amp\;A&amp;nbsp\; 12:55&lt;/p&gt;\n&lt;p&gt;5 - Convers
 ation over pizza 1 pm&lt;/p&gt;
END:VEVENT
END:VCALENDAR