<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
</head>
<body>
Уважаемые коллеги,<br>
<br>
На заседании Ученого совета в пятницу 22 января будут заслушаны:<br>
<br>
1) М.В. Фейгельман<br>
<font size="+1"><b>Отчет сектора квантовой мезоскопики</b></font><br>
<br>
<br>
2) Л.Ю. Бараш (короткий доклад)<br>
<font size="+1"><b>Эффективное вычисление разделенных разностей
экспоненциальной функции для использования в методе квантового
Монте-Карло</b></font><br>
<br>
<div class="abstract tex"> Разработан метод вычисления разделенных
разностей экспоненциальной функции путем добавления и удаления
элементов из входного списка элементов. В нашем методе
используется новое тождество, связанное с разделенными разностями,
недавно полученное в работе F. Zivcovich [Dolomites Research Notes
on Approximation 12, 28-42 (2019)]. Мы показываем, что после
добавления элемента или удаления элемента из входного списка,
повторное вычисление разделенных разностей может быть выполнено
при помощи всего лишь <span class="MathJax"
id="MathJax-Element-1-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo
stretchy="false">(</mo><mi>s</mi><mi>n</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-1" style="width: 2.347em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.628em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1002.53em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-2"><span class="mi"
id="MathJax-Span-3" style="font-family:
MathJax_Math; font-style: italic;">O</span><span
class="mo" id="MathJax-Span-4" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-5" style="font-family:
MathJax_Math; font-style: italic;">s</span><span
class="mi" id="MathJax-Span-6" style="font-family:
MathJax_Math; font-style: italic;">n</span><span
class="mo" id="MathJax-Span-7" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span>операций
с плавающей запятой и <span class="MathJax"
id="MathJax-Element-2-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo
stretchy="false">(</mo><mi>s</mi><mi>n</mi><mo
stretchy="false">)</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-8" style="width: 2.347em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 2.628em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1002.53em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-9"><span class="mi"
id="MathJax-Span-10" style="font-family:
MathJax_Math; font-style: italic;">O</span><span
class="mo" id="MathJax-Span-11" style="font-family:
MathJax_Main;">(</span><span class="mi"
id="MathJax-Span-12" style="font-family:
MathJax_Math; font-style: italic;">s</span><span
class="mi" id="MathJax-Span-13" style="font-family:
MathJax_Math; font-style: italic;">n</span><span
class="mo" id="MathJax-Span-14" style="font-family:
MathJax_Main;">)</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span> байт
памяти, где <span class="MathJax" id="MathJax-Element-3-Frame"
tabindex="0" style="position: relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mo
stretchy="false">[</mo><msub><mi>z</mi><mn>0</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>z</mi><mi>n</mi></msub><mo
stretchy="false">]</mo></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-15" style="width: 4.052em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 4.616em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1004.5em,
2.736em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-16"><span class="mo"
id="MathJax-Span-17" style="font-family:
MathJax_Main;">[</span><span class="msubsup"
id="MathJax-Span-18"><span style="display:
inline-block; position: relative; width: 0.894em;
height: 0px;"><span style="position: absolute;
clip: rect(3.322em, 1000.47em, 4.201em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-19"
style="font-family: MathJax_Math; font-style:
italic;">z<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.003em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.465em;"><span class="mn" id="MathJax-Span-20"
style="font-size: 70.7%; font-family:
MathJax_Main;">0</span><span style="display:
inline-block; width: 0px; height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-21" style="font-family:
MathJax_Main;">,</span><span class="mo"
id="MathJax-Span-22" style="font-family:
MathJax_Main; padding-left: 0.167em;">…</span><span
class="mo" id="MathJax-Span-23" style="font-family:
MathJax_Main; padding-left: 0.167em;">,</span><span
class="msubsup" id="MathJax-Span-24"
style="padding-left: 0.167em;"><span style="display:
inline-block; position: relative; width: 0.964em;
height: 0px;"><span style="position: absolute;
clip: rect(3.322em, 1000.47em, 4.201em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-25"
style="font-family: MathJax_Math; font-style:
italic;">z<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.003em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.465em;"><span class="mi" id="MathJax-Span-26"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">n</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-27" style="font-family:
MathJax_Main;">]</span></span><span style="display:
inline-block; width: 0px; height: 2.273em;"></span></span></span><span
style="display: inline-block; overflow: hidden;
vertical-align: -0.283em; border-left: 0px solid; width:
0px; height: 1.005em;"></span></span></nobr></span> -
значения на входе, а <span class="MathJax"
id="MathJax-Element-4-Frame" tabindex="0" style="position:
relative;" data-mathml="<math
xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>∝</mo><munder><mo
movablelimits="true"
form="prefix">max</mo><mrow
class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi></mrow></munder><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow><msub><mi>z</mi><mi>i</mi></msub><mo>−</mo><msub><mi>z</mi><mi>j</mi></msub><mrow
class="MJX-TeXAtom-ORD"><mo
stretchy="false">|</mo></mrow></math>"
role="presentation"><nobr aria-hidden="true"><span class="math"
id="MathJax-Span-28" style="width: 7.106em; display:
inline-block;"><span style="display: inline-block; position:
relative; width: 8.026em; height: 0px; font-size: 88%;"><span
style="position: absolute; clip: rect(1.31em, 1007.91em,
2.78em, -1000em); top: -2.273em; left: 0em;"><span
class="mrow" id="MathJax-Span-29"><span class="mi"
id="MathJax-Span-30" style="font-family:
MathJax_Math; font-style: italic;">s</span><span
class="mo" id="MathJax-Span-31" style="font-family:
MathJax_Main; padding-left: 0.278em;">∝</span><span
class="munderover" id="MathJax-Span-32"
style="padding-left: 0.278em;"><span style="display:
inline-block; position: relative; width: 2.668em;
height: 0px;"><span style="position: absolute;
clip: rect(3.316em, 1001.85em, 4.201em,
-1000em); top: -3.977em; left: 0em;"><span
class="mo" id="MathJax-Span-33"
style="font-family: MathJax_Main;">max</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
1.861em;"><span class="texatom"
id="MathJax-Span-34"><span class="mrow"
id="MathJax-Span-35"><span class="mi"
id="MathJax-Span-36" style="font-size:
70.7%; font-family: MathJax_Math;
font-style: italic;">i</span><span
class="mo" id="MathJax-Span-37"
style="font-size: 70.7%; font-family:
MathJax_Main;">,</span><span class="mi"
id="MathJax-Span-38" style="font-size:
70.7%; font-family: MathJax_Math;
font-style: italic;">j</span></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="texatom" id="MathJax-Span-39"
style="padding-left: 0.167em;"><span class="mrow"
id="MathJax-Span-40"><span class="mo"
id="MathJax-Span-41" style="font-family:
MathJax_Main;">|</span></span></span><span
class="msubsup" id="MathJax-Span-42"><span
style="display: inline-block; position: relative;
width: 0.784em; height: 0px;"><span
style="position: absolute; clip: rect(3.322em,
1000.47em, 4.201em, -1000em); top: -3.977em;
left: 0em;"><span class="mi"
id="MathJax-Span-43" style="font-family:
MathJax_Math; font-style: italic;">z<span
style="display: inline-block; overflow:
hidden; height: 1px; width: 0.003em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.465em;"><span class="mi" id="MathJax-Span-44"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">i</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="mo" id="MathJax-Span-45" style="font-family:
MathJax_Main; padding-left: 0.222em;">−</span><span
class="msubsup" id="MathJax-Span-46"
style="padding-left: 0.222em;"><span style="display:
inline-block; position: relative; width: 0.831em;
height: 0px;"><span style="position: absolute;
clip: rect(3.322em, 1000.47em, 4.201em,
-1000em); top: -3.977em; left: 0em;"><span
class="mi" id="MathJax-Span-47"
style="font-family: MathJax_Math; font-style:
italic;">z<span style="display: inline-block;
overflow: hidden; height: 1px; width:
0.003em;"></span></span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span><span
style="position: absolute; top: -3.827em; left:
0.465em;"><span class="mi" id="MathJax-Span-48"
style="font-size: 70.7%; font-family:
MathJax_Math; font-style: italic;">j</span><span
style="display: inline-block; width: 0px;
height: 3.977em;"></span></span></span></span><span
class="texatom" id="MathJax-Span-49"><span
class="mrow" id="MathJax-Span-50"><span class="mo"
id="MathJax-Span-51" style="font-family:
MathJax_Main;">|</span></span></span></span><span
style="display: inline-block; width: 0px; height:
2.273em;"></span></span></span><span style="display:
inline-block; overflow: hidden; vertical-align: -0.321em;
border-left: 0px solid; width: 0px; height: 1.044em;"></span></span></nobr></span>.
Мы демонстрируем способность нашего алгоритма работать со входными
списками, которые на порядки длиннее, чем максимально возможные до
настоящего времени. Мы обсуждаем одно из практических применений
нашего метода: эффективное вычисление весов в алгоритме квантового
Монте-Карло, построенном на основе недиагонального разложения. <br>
По работе: L. Gupta, L. Barash, I. Hen, "Calculating the divided
differences of the exponential function by addition and removal of
inputs", Computer Physics Communications 254, 107385 (2020). <br>
</div>
<div class="abstract tex"> <br>
<br>
</div>
Доклады будут сопровождаться онлайн-трансляцией в Zoom. ID и пароль
те же, что и для предыдущих трансляций:<a
class="moz-txt-link-freetext"
href="https://zoom.us/j/93947383544?pwd=QnU4VGVuYVBlSlJSeHBkTlp4QW9HZz09"><br>
</a><a class="moz-txt-link-freetext"
href="https://zoom.us/j/96899364518?pwd=MzBsR2lYT0lYL2x2b1oyNU9LeWlWUT09">https://zoom.us/j/96899364518?pwd=MzBsR2lYT0lYL2x2b1oyNU9LeWlWUT09</a><br>
Meeting ID: 968 9936 4518<br>
Пароль: 250319<br>
<br>
</body>
</html>