​Research

The Department of Electrical & Systems Engineering has a unique and long tradition of excellence in advancing basic science and solving cutting-edge engineering problems relevant to society. The second-oldest electrical engineering department in the country, it is dedicated to providing high-quality education and research.


 

 

ESE Seminar: Mathews Jacob https://engineering.wustl.edu/Events/Pages/ESE-Seminar-Mathews-Jacob-Ph-D.aspxESE Seminar: Mathews Jacob 12/14/2018 6:00:00 AM
ESE Seminar: Ari Stern Ph.Dhttps://engineering.wustl.edu/Events/Pages/ESE-Seminar-Ari-Stern.aspxESE Seminar: Ari Stern Ph.D12/13/2018 6:00:00 AM
Ph.D Defense: Srinath Nizampatnamhttps://engineering.wustl.edu/Events/Pages/Ph-D-Defense-Srinath-Nizampatnam.aspxPh.D Defense: Srinath Nizampatnam12/11/2018 6:00:00 AM


Research Highlights

 

 

 

https://engineering.wustl.edu/news/Pages/Yang-hosts-Nature-Communications-photonics-conference-at-WashU.aspx953Yang hosts Nature Communications photonics conference at WashU<img alt="" src="/Profiles/PublishingImages/Yang_Lan.jpg?RenditionID=2" style="BORDER:0px solid;" /><div id="__publishingReusableFragmentIdSection"><a href="/ReusableContent/36_.000">a</a></div><p>Nearly 100 of the world's leading experts in photonics, the technology involving the properties and transmission of photons, will converge on Washington University in St. Louis Nov. 11-13 to share the latest research and advances in topological photonics, from concepts to devices.</p><p>Lan Yang, the Edwin H. & Florence G. Skinner Professor in the School of Engineering & Applied Science, is hosting the <a href="https://www.nature.com/natureconferences/tpcd18/index.html">global conference</a>, sponsored by <em>Nature Communications</em>, a high-impact, peer-reviewed scientific journal that covers the natural sciences, such as physics, chemistry, biology <g class="gr_ gr_27 gr-alert gr_gramm gr_inline_cards gr_disable_anim_appear Punctuation only-ins replaceWithoutSep" id="27" data-gr-id="27">and</g> Earth sciences. In addition to photonics, the conference will include sessions on topological effects in 2D systems as well as lasers and devices.</p><p>Yang, a faculty member in the Preston M. Green Department of Electrical & Systems Engineering, is internationally renowned for her research in photonics and her Micro/Nano Photonics Research Group, which focuses on the silicon-chip-based, ultra-high-quality micro-resonators and their applications for sensing, lasing, nonlinear optics, environmental monitoring, biomedical research and communication.</p><p>Recently, Yang has published results of novel research in the loss-gain phenomenon. She and her team were able to provide new schemes and techniques to engineer a physical system by controlling loss. Further, she invented a new technique to control lasing emissions from an on-chip microlaser. In addition, her team demonstrated for the first time the transfer of chaos between two largely detuned optical fields mediated by <g class="gr_ gr_26 gr-alert gr_spell gr_inline_cards gr_disable_anim_appear ContextualSpelling ins-del multiReplace" id="26" data-gr-id="26">opto-mechanical</g> effects in a high-quality micro-resonator. </p><p>Yang's team works on fabrication, characterization and fundamental understanding of advanced nano/micro-photonic devices with outstanding optical properties or novel features for unconventional control of light flow. Her group has demonstrated the first on-chip micro-resonator-based particle sensors that can achieve not only detection but also size measurement of single nanoparticles one by one.</p><p>Yang has received numerous honors, including recently being named editor-in-chief of <em>Photonics Research</em>, a journal published by The Optical Society (OSA). During her three-year term, which begins Jan. 1, 2019, she will provide editorial oversight of the journal, which publishes fundamental and applied research progress in optics and photonics. She also joins the OSA Board of Editors. Yang was elected a Fellow of OSA in 2016.</p><p>In 2011, she was honored by President Barack Obama with a Presidential Early Career Award for Scientists and Engineers (PECASE), the highest honor bestowed by the United States government on science and engineering professionals in the early stages of their independent research careers. In 2010, she earned a National Science Foundation CAREER Award. She joined the Washington University in St. Louis faculty in 2007.<br/></p><SPAN ID="__publishingReusableFragment"></SPAN><p><br/></p><span> <div class="cstm-section"><h3>Lan Yang<br/></h3><div style="text-align: left;"><ul style="padding-left: 20px; caret-color: #343434; color: #343434;"><li>Edwin H. & Florence G. Skinner Professor</li><li>Expertise: Photonics, optical sensing, microresonators, lasers, non-Hermitian physics, parity-time symmetry in photonics<br/></li></ul></div><div style="text-align: center;"> <a href="/Profiles/Pages/Lan-Yang.aspx">>> ​View Bio</a></div><div style="text-align: center;"> <br/> </div><div style="text-align: center;"> <a href="https://ese.wustl.edu/Pages/default.aspx">>> Electrical & Systems Engineering</a>​<br/></div></div></span> <span> <div class="cstm-section"><h3>More research from Professor Lan Yang </h3><div><ul><li> <a href="/news/Pages/Breaking-the-laws-of-science.aspx"> <span style="font-size: 1em;">Breaking the laws of science</span></a></li><li> <span style="font-size: 1em;"> <a href="/news/Pages/Engineers-find-a-way-to-win-in-laser-performance-by-losing.aspx">Engineers find a way to win in laser performance by losing</a> </span></li><li> <span style="font-size: 1em;"><a href="/news/Pages/Engineers-develop-new-sensor-to-detect-tiny-individual-nanoparticles.aspx">Engineers develop new sensor to detect tiny individual nanoparticles</a></span></li></ul></div></div></span><br/>Beth Miller 2018-10-30T05:00:00ZLan Yang will host a global conference on photonics at WashU Nov. 11-13.<p>Named editor-in-chief of Photonics Research<br/></p>
https://engineering.wustl.edu/news/Pages/Unlocking-dynamic-information-in-complex-systems-focus-of-newly-funded-research.aspx936Unlocking dynamic information in complex systems <img alt="" src="/news/PublishingImages/Li%20research%209.18.png?RenditionID=1" style="BORDER:0px solid;" /><div id="__publishingReusableFragmentIdSection"><a href="/ReusableContent/36_.000">a</a></div><p> With fall in full swing, our bodies naturally adjust to fewer daylight hours thanks to our circadian rhythm. Engineering researchers at Washington University in St. Louis want to determine how the brain network allows this to happen using a system-theoretic and computational approach.<br/></p><p>Jr-Shin Li, the Das Family Career Development Distinguished Professor and an applied mathematician in the School of Engineering & Applied Science, has received a four-year, $1.6 million grant from the National Institutes of Health (NIH) to create a unified methodology that helps researchers infer dynamic topology and control spatiotemporal structures of complex networks, for example, the connectivity among the brain network that controls circadian rhythm, an important biological process that manages sleep, body temperature <g class="gr_ gr_64 gr-alert gr_gramm gr_inline_cards gr_disable_anim_appear Punctuation only-ins replaceWithoutSep" id="64" data-gr-id="64">and</g> digestion.<br/></p><p>In addition, Li received two grants from the National Science Foundation (NSF) totaling $625,000 to create model-based and data-driven methods for better understanding complex population and networked systems.  <br/></p><p>With the NIH funding, Li will use biological data derived from experiments performed by collaborators Erik Herzog, a WashU professor of biology, and Istvan Kiss, professor of chemistry at Saint Louis University, to build a framework that enables efficient and reliable inference of information about how the environment, such as changing seasons or changing time zones during travel, changes the circadian rhythm. They seek to overcome a significant mathematical challenge by creating a data-driven approach to decode dynamic network topology representing complex dynamic processes, as well as to understand the interaction of circadian rhythms. The researchers say the results of the work will give new insight into the circadian network and how repeated daily disruptions can reorganize the network and impact behavior.<br/></p><p>Kiss builds networks of chemical oscillators — populations of neurons that repeatedly fire together, go silent, then fire together again — that behave like circadian cells.  He will create a test bed on which Li can test his algorithms.<br/></p><p>"It's still far away from being realistic, but the oscillators can mimic the oscillatory behavior of real cells," Li said. "If everything works in these chemical oscillator networks, we will test it on real circadian cells."<br/></p><p>Herzog, who studies the cellular and molecular basis of circadian rhythms in mammals, will test Li's method on circadian cells of mice.<br/></p><p>The trio is part of a larger team who have already done some groundwork for this newly funded research. They began several years ago after they received a pilot grant from the Keck Foundation. Since then, they've gone on to test Li's method with an early group of chemical oscillators and with mice. That work was recently published in <em>PNAS</em>.<br/></p><p>Li will use a three-year, $325,000 grant from the NSF to develop mathematical tools to sort through a large amount of time-series data from a dynamical system. Li equated this work to dynamic learning.<br/></p><blockquote>"In machine learning, it is generally required to have a lot of data — often static data — for an algorithm to output useful information and the performance of the algorithm may be highly sensitive to different data sets of the same sort," Li said. "There could be situations where an algorithm works for a particular data set, but not for another. In this project, we aim to take a rigorous mathematical treatment to look into and resolve these issues."<br/></blockquote><p>Li will develop novel data-driven methods for inference and learning of complex dynamical systems. Specifically, inspired by the ideas of geometry and topology and tools of computational algebra, Li will construct principled and computational methods to learn how a dynamical or a networked system propagates in time and to characterize the dynamical modes of this system using its time-series data. In this new research, he seeks to decode the complex dynamics of large-scale nonlinear systems and networks and use this decoding to facilitate the control and computational tasks for these systems.<br/></p><p>"If I have a huge amount of data, I want to extract the important information and throw away the unwanted information," Li said. "I want to develop a universal method for simplifying complex data sets so that I can still gain the same amount of information I need from a reduced amount of data. In many cases, more data may not necessarily give you more information."<br/></p><p>In parallel with this data-inspired research, Li received another grant from the NSF to conduct theoretical work with co-investigator Shen Zeng, assistant professor of electrical & systems engineering. The three-year, $300,000 grant will allow them to learn how best to control and manipulate population systems, which are prevalent in nature, engineered infrastructure and human society, such as neurons in the brain, power grids, robot swarms or social networks. But it is a daunting task, the researchers said.<br/></p><p>"When you try to manipulate such populations, you have many systems, and it's virtually impossible to individually address a particular system," Zeng said. "When we do something like this, every other system in the population receives the same signal. Having to orchestrate this population of a bunch of systems and only having one voice is a very difficult coordination task."<br/></p><p>Li and Zeng will build on their preliminary work in ensemble control to build a unified theoretical framework that is able to describe and tackle this set of related problems in populations in a coherent way.<br/></p><p>"Our approach is an abstract one that tries to leverage the unified mathematical framework to bring into these vastly different fields," Zeng said. "If we could get insight into the fundamentals, understanding a specific case in one field could develop a strategy that could apply to another."<br/></p><SPAN ID="__publishingReusableFragment"></SPAN><p><br/></p><p><br/></p> <span> <div class="cstm-section"><h3>Jr-Shin Li<br/></h3><div><p style="text-align: center;"> <a href="/Profiles/Pages/Jr-Shin-Li.aspx"> <img src="/Profiles/PublishingImages/Li_Jr-Shin.jpg?RenditionID=3" class="ms-rtePosition-4" alt="" style="margin: 5px;"/></a> <br/></p><div style="text-align: center;"><div style="text-align: center;"> Professor Jr-Shin Li’s research group has extensive and close collaboration with biologists, chemists and applied physicists.</div> <br/> <a href="/Profiles/Pages/Jr-Shin-Li.aspx">View Bio</a><br/></div></div></div></span>Targeted excitation of a vast number of spin particles using radiofrequency-pulse sequences is a classical broadcast coordination task for dynamic populations, which is at the core of the principle of MRI.Beth Miller 2018-09-27T05:00:00ZJr-Shin Li and collaborators want to determine how the brain network controls circadian rhythm, among other theoretical work.<p>​NIH funding will allow the creation of model-based and data-driven methods<br/></p>
https://engineering.wustl.edu/news/Pages/Estimating-electrical-current-from-uterus-muscle-may-provide-clues-to-preterm-birth.aspx934Estimating electrical current from uterus muscle may provide clues to preterm birth<div class="youtube-wrap"><div class="iframe-container"> <iframe width="560" height="315" src="https://www.youtube.com/embed/HM2-94Pf21U"></iframe> <br/> <br/><br/></div></div><img alt="" src="/news/PublishingImages/Nehorai%20research.jpg" style="BORDER:0px solid;" /><div id="__publishingReusableFragmentIdSection"><a href="/ReusableContent/36_.000">a</a></div><p>Preterm birth, or birth before 37 weeks, affects one in 10 babies born nationally and globally, leading to a variety of complications and even death. While the causes are not well understood, researchers at Washington University in St. Louis and collaborating institutions are the first working to estimate electrical source currents in the uterus during real contractions to determine their potential impact on labor.</p><p>Building on earlier work, Arye Nehorai, the Eugene & Martha Lohman Professor of Electrical Engineering in the School of Engineering & Applied Science at WashU, and collaborators developed a method to estimate electrical current in the uterus during contractions from magnetomyography, a noninvasive technique that maps muscle activity by recording the abdominal magnetic fields that electrical currents in muscles produce. The results, published in <em>PLoS One</em> Aug. 23, could have clinical applications in better understanding pre- and post-term birth and dysfunctional labor.<br/></p><p>The team collected data from two pregnant women at the University of Arkansas for Medical Sciences using a device that allows the women to lean forward into a concave space. Within the SARA device are 151 primary magnetic sensors placed 3 centimeters apart that measure electrophysiological signals from the patient's abdomen. They divided the uterus into 25 contiguous regions.<br/></p><p>Through the studies, they were able to estimate the underlying source currents in the smooth muscle of the uterus and predicted the pressure within the uterus, which is currently used to measure contractions.<br/></p><p>"This is only the beginning," Nehorai said. "Our work is potentially important as a starting point for helping to characterize underlying activities of uterine contractions during pregnancy and future diagnosis of contractile dysfunction."<br/></p><p>The team's next steps are to use the estimated currents in the uterus to predict labor and early labor. They plan to develop efficient algorithms that would be made available to clinicians through software. <br/></p><SPAN ID="__publishingReusableFragment"></SPAN><p><br/></p> <span> <div class="cstm-section"><h3>Arye Nehorai</h3><div style="text-align: center;"> <img src="/Profiles/PublishingImages/Nehorai_2017.jpg?RenditionID=3" class="ms-rtePosition-4" alt="" style="margin: 5px;"/> <br/> </div><div style="text-align: center;"><ul style="padding-left: 20px; caret-color: #343434; color: #343434;"><li>The Eugene & Martha Lohman Professor of Electrical Engineering<br/></li><li>Research: Mathematical modeling of complex systems, statistical signal processing, machine learning, and imaging for information inference and decision making.<br/></li></ul></div><div style="text-align: center;"> <a href="/Profiles/Pages/Arye-Nehorai.aspx">>> ​View Bio</a></div><div style="text-align: center;"> <br/> </div><div style="text-align: center;"> <a href="http://ese.wustl.edu/Pages/default.aspx">>> Department of Electrical & Systems Engineering​</a>​</div></div></span><br/>The SARA device used to non-invasively take MMG measurements of uterine activities. Beth Miller 2018-09-26T05:00:00ZNew research by Arye Nehorai and collaborators could have clinical applications in better understanding pre- and post-term birth. <p>​Non-invasive technique could provide a useful tool for clinicians<br/></p>
https://engineering.wustl.edu/news/Pages/Shen-leads-team-seeking-to-improve-quantum-computation.aspx932Shen leads team seeking to improve quantum computation<img alt="two-photon controlled-phase logic gate" src="/news/PublishingImages/Shen_WashU.jpg?RenditionID=2" style="BORDER:0px solid;" /><div id="__publishingReusableFragmentIdSection"><a href="/ReusableContent/36_.000">a</a></div><p>Quantum technology is expected to play a decisive role in enhancing national security and bolstering further scientific discovery. A team of scientists, led by J.T. Shen at Washington University in St. Louis, is seeking to boost quantum information science and technology, particularly in the emerging areas of quantum computation and communication.</p><p>Shen, the Das Family Career Development Distinguished Associate Professor in the Preston M. Green Department of Electrical & Systems Engineering in the School of Engineering & Applied Science, has received a three-year, $1 million grant from the National Science Foundation, to develop a two-photon controlled-phase logic gate, an elementary building block of a full-fledged quantum photonic circuit for optical quantum information. To date, this type of photonic logic gate has been elusive because of the difficulty of working with photons.</p><p>Shen and two doctoral students in his lab, Zihao Chen and Yao Zhou, will develop the theory for the work, which lays the foundation for experiments performed by colleagues Pei-Cheng Ku associate professor, and Duncan Steel, the Robert J. Hiller Professor, both at the University of Michigan. The theory is based on Shen's previous work in which he found how to make photons interact with each other and bind together to become a quantum photonic dimer. Photons, or particles that represent a quantum of light, travel very quickly and don't carry a charge, so it is difficult to get them to interact with each other and manipulate them. Shen, however, overcame that difficulty.</p><blockquote>"Several years ago, we figured out how to make photons know each other and form a quantum mechanical bound state," Shen said. "That capability provided the missing link for optical quantum computation, which is the enabling feature for a two-qubit photonic logic gate," Shen said.</blockquote><p>While he has already made progress over the past five years, Shen said this work is still challenging.</p><p>"There are many obstacles for optical quantum computation, so we do not claim that the realization of this will bring a quantum computer immediately," Shen said. "In the end, people will need to make up to 1,000 of these logic gates and put them together in a quantum mechanical way. But now, we don't even have one. If we succeed, then we provide a fundamental two-qubit logic gate for photons. In principle, they provide a complete possibility for photonic quantum computation."<br/></p><p>The work is part of $31 million awarded by the NSF for fundamental quantum research aimed at enabling the United States to lead a new quantum technology revolution. <br/></p><p>"The quantum revolution is about expanding the definition of what's possible for the technology of tomorrow," said NSF Director France Córdova. "NSF-supported researchers are working to deepen our understanding of quantum mechanics and apply that knowledge to create world-changing applications. These new investments will position the U.S. to be a global leader in quantum research and development and help train the next generation of quantum researchers." <br/></p><SPAN ID="__publishingReusableFragment"></SPAN><p><br/></p><style type="text/css"> p.p1 {margin: 0.0px <span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd31336" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd84230" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="white-space: <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd80308" class="ms-spellcheck-error ms-rtegenerate-skip">nowrap</span></span>;"><span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd26834" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd87414" class="ms-spellcheck-error ms-rtegenerate-skip">rtestate</span></span>-read <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd41247" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd5956" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd35590" class="ms-spellcheck-error ms-rtegenerate-skip">contenteditable</span></span>="false" style="font-size: 8pt;"><a class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd95869" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd14942" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip"><<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd98722" class="ms-spellcheck-error ms-rtegenerate-skip">img</span></span> <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd50774" class="ms-spellcheck-error ms-rtegenerate-skip">src</span></span>="/_layouts/images/blank.gif" alt="Misspelled Word" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd47766" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd94676" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="width: 0px;"></a></span><span id="rnd27189" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd5930" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-spellcheck-error <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd31766" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd77078" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip">0.0px</span></span> <span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd69733" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd43332" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="white-space: <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd58042" class="ms-spellcheck-error ms-rtegenerate-skip">nowrap</span></span>;"><span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd44239" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd84615" class="ms-spellcheck-error ms-rtegenerate-skip">rtestate</span></span>-read <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd41996" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd56056" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd55374" class="ms-spellcheck-error ms-rtegenerate-skip">contenteditable</span></span>="false" style="font-size: 8pt;"><a class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd51959" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd95687" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip"><<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd47805" class="ms-spellcheck-error ms-rtegenerate-skip">img</span></span> <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd31372" class="ms-spellcheck-error ms-rtegenerate-skip">src</span></span>="/_layouts/images/blank.gif" alt="Misspelled Word" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd22267" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd8274" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="width: 0px;"></a></span><span id="rnd66727" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd80065" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-spellcheck-error <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd35371" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd52347" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip">0.0px</span></span> <span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd92691" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd4267" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="white-space: <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd18825" class="ms-spellcheck-error ms-rtegenerate-skip">nowrap</span></span>;"><span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd57396" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd70620" class="ms-spellcheck-error ms-rtegenerate-skip">rtestate</span></span>-read <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd41481" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd38234" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd59165" class="ms-spellcheck-error ms-rtegenerate-skip">contenteditable</span></span>="false" style="font-size: 8pt;"><a class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd96786" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd36123" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip"><<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd8232" class="ms-spellcheck-error ms-rtegenerate-skip">img</span></span> <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd49560" class="ms-spellcheck-error ms-rtegenerate-skip">src</span></span>="/_layouts/images/blank.gif" alt="Misspelled Word" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd8273" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd4174" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="width: 0px;"></a></span><span id="rnd34504" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd75912" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-spellcheck-error <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd54662" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd60439" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip">0.0px</span></span>; font: 12.0px Helvetica; min-height: 14.0px} p.p2 {margin: 0.0px <span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd83628" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd6011" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="white-space: <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd64921" class="ms-spellcheck-error ms-rtegenerate-skip">nowrap</span></span>;"><span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd77445" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd16633" class="ms-spellcheck-error ms-rtegenerate-skip">rtestate</span></span>-read <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd13011" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd47432" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd52758" class="ms-spellcheck-error ms-rtegenerate-skip">contenteditable</span></span>="false" style="font-size: 8pt;"><a class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd46491" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd78683" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip"><<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd79683" class="ms-spellcheck-error ms-rtegenerate-skip">img</span></span> <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd2021" class="ms-spellcheck-error ms-rtegenerate-skip">src</span></span>="/_layouts/images/blank.gif" alt="Misspelled Word" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd90045" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd89117" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="width: 0px;"></a></span><span id="rnd13921" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd39025" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-spellcheck-error <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd59529" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd47169" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip">0.0px</span></span> <span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd24483" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd14358" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="white-space: <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd79214" class="ms-spellcheck-error ms-rtegenerate-skip">nowrap</span></span>;"><span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd1507" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd2098" class="ms-spellcheck-error ms-rtegenerate-skip">rtestate</span></span>-read <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd53914" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd60362" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd12834" class="ms-spellcheck-error ms-rtegenerate-skip">contenteditable</span></span>="false" style="font-size: 8pt;"><a class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd87209" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd94159" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip"><<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd56449" class="ms-spellcheck-error ms-rtegenerate-skip">img</span></span> <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd7491" class="ms-spellcheck-error ms-rtegenerate-skip">src</span></span>="/_layouts/images/blank.gif" alt="Misspelled Word" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd28124" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd51095" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="width: 0px;"></a></span><span id="rnd64054" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd8492" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-spellcheck-error <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd1995" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd88793" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip">0.0px</span></span> <span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd77936" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd19973" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="white-space: <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd35314" class="ms-spellcheck-error ms-rtegenerate-skip">nowrap</span></span>;"><span class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd65362" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd54907" class="ms-spellcheck-error ms-rtegenerate-skip">rtestate</span></span>-read <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd95443" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd29127" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd27901" class="ms-spellcheck-error ms-rtegenerate-skip">contenteditable</span></span>="false" style="font-size: 8pt;"><a class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd65474" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd42751" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip"><<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd66557" class="ms-spellcheck-error ms-rtegenerate-skip">img</span></span> <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd27067" class="ms-spellcheck-error ms-rtegenerate-skip">src</span></span>="/_layouts/images/blank.gif" alt="Misspelled Word" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd17878" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd37257" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip" style="width: 0px;"></a></span><span id="rnd3217" class="<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd87836" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-spellcheck-error <span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd80599" class="ms-spellcheck-error ms-rtegenerate-skip">ms</span></span>-<span class="ms-rtegenerate-skip" style="white-space: nowrap;"><span class="ms-rtestate-read ms-rtegenerate-skip" contenteditable="false" style="font-size: 8pt;"><a class="ms-rtegenerate-skip"><img src="/_layouts/images/blank.gif" alt="Misspelled Word" class="ms-rtegenerate-skip" style="width: 0px;"></a></span><span id="rnd3817" class="ms-spellcheck-error ms-rtegenerate-skip">rtegenerate</span></span>-skip">0.0px</span></span>; font: 11.5px Helvetica; color: #3b3b3b} span.s1 {font: 12.0px Helvetica; color: #000000} </style><span> <div class="cstm-section"><h3>Professor J.T. Shen</h3><div style="text-align: center;"> <img src="/Profiles/PublishingImages/Shen_JT.jpg?RenditionID=3" class="ms-rtePosition-4" alt="" style="margin: 5px;"/> <br/> </div><div style="text-align: center;"><ul style="padding-left: 20px; caret-color: #343434; color: #343434;"><li>Das Family Career Development Distinguished Associate Professor<br/></li><li>Expertise: Exploiting the unique properties of quantum nano-photonics for applications in quantum communication, computation, and biomedical imaging<br/></li></ul></div><div style="text-align: center;"> <a href="/Profiles/Pages/Jung-Tsung-Shen.aspx">>> ​View Bio</a></div><div style="text-align: center;"> <br/> </div><div style="text-align: center;"> <a href="http://ese.wustl.edu/Pages/default.aspx">>> Department of Electrical & Systems Engineering​</a>​<br/></div></div></span><br/><span> <div class="cstm-section"><h3>Media Coverage<br/></h3><div> <strong>Michigan Engineering News Center:</strong><a href="https://news.engin.umich.edu/2018/09/it-takes-two-photonic-qubits-to-make-quantum-computing-possible/"> It takes two photonic qubits to make quantum computing possible</a><br/></div></div></span> <p> <br/> </p>J.T. Shen is leading a team developing a two-photon controlled-phase logic gate that could boost quantum information science and technology.Beth Miller 2018-09-24T05:00:00ZJ.T. Shen is leading a team developing a way to boost quantum information science and technology.<p>Research aims to develop the elusive "two-photon controlled-phase logic gate" <br/></p>

Research Areas

Applied Physics
  • Nano-photonics
  • Quantam Optics
  • Engineered Materials
  • Electrodynamics
Devices & Circuits
  • Computer Engineering
  • Integrated Circuits
  • Radiofrequency Circuits
  • Sensors
Systems Science
  • Optimization
  • Applied Mathematics
  • Control
  • Financial Engineering
Signals & Imaging
  • Computational Imaging
  • Signal Processing
  • Optical Imaging
  • Data Sciences