RENSSELAER POLYTECHNIC INSTITUTE  
 
 

Program in Architectural Acoustics

 

The Graduate Program in Architectural Acoustics offers an intense curriculum in acoustics for effectively shaping sonic environments to achieve optimum acoustic performance and sound quality. The Program offers studies toward both Master of Science and Ph.D. degrees. This unique program in architectural acoustics provides the knowledge for next-generation acousticians involved in room acoustics, psychoacoustics, acoustic and vibration measurement techniques, and sound reinforcement.

The Program offers the knowledge and skills needed for advanced practice and applied research. Fieldwork develops the experience of sensitive perception of sound environments and musical performance, and industry relations give access to advanced techniques and materials used in acoustical practice.

 

Latest News

Cameron Fackler Receives Leo Beranek Student Medal (May 2014)

Our Ph.D. candidate, Cameron Fackler, received the prestigious Leo Beranek Student Medal for excellence in noise control studies at the 2014 School of Architecture spring awards ceremony. This award recognizes Cameron's work in designing multilayer microperforated panel sound absorbers, which have the potential to provide broadband noise control in demanding situations where traditional materials may fail. Congratulations Cameron!

Jeffrey Parkman Carter Receives Schultz Grant Award (2014)

Jeffrey Parkman Carter, a doctoral student of the Graduate Program in Architectural Acoustics, has won the prestigious Schultz Grant Award from the Newman Foundation. "The Theodore John Schultz Grant for Advancement of Acoustical Education provides support for the development of improved teaching methods, new curricula, or research in architectural acoustics education." Jeff's project is specifically for helping architects visualize acoustic surface reflections using existing 3D models and light rendering available in SketchUp. Congratulations Jeff!

Robert Connick Receives Newman Medal (Oct 2013)

This year's Robert Bradford Newman Student Medal has been bestowed upon Robert Connick, a M.S. student from the Graduate Program in Architectural Acoustics. This award is given once a year for meritorious student-conducted research in Architectural Acoustics. The Newman Student Medal program recognizes excellence in the study of acoustics and its application to architecture and honors outstanding students at schools of architecture and architectural engineering throughout the world. Congratulations Bob!

Sam Clapp Receives Prestigious Leo L. Beranek Award (May 2013)

At the Spring semester School of Architecture awards ceremony, the prestigious Leo L. Beranek Student Award from the Institute of Noise Control Engineering was bestowed upon our very own doctoral candidate, Sam Clapp. Well done! Congratulations Sam!

Visit from Dr. David Griesinger

Dr. David Griesinger (famous for his Lexicon reverb unit and his electronic room acoustics enhancement system LARES) delivere a lecture entitled "Something is Missing or Clarity, Presence, and Source Separation."¯ The afternoon's lecture continued the themes of the first lecture and included a question and answer session with demonstrations.

Wesley Henderson Receives Newman Medal (Dec. 2012)

This year's Robert Bradford Newman Student Medal has been bestowed upon Wesley Henderson, a M.S. student from the Graduate Program in Architectural Acoustics. This award is given once a year for meritorious student-conducted research in Architectural Acoustics. The Newman Student Medal program recognizes excellence in the study of acoustics and its application to architecture and honors outstanding students at schools of architecture and architectural engineering throughout the world. During his graduate study and research in the Graduate Program in Architectural Acoustics, School of Architecture, Wesley’s research resulted in two international conference papers (International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering held in Munich, July 2012, and the International Conference on Noise Control Engineering, held in New York City Aug. 2012), as well as one paper presentation at the 164th Acoustical Society of America Meeting in Kansas City, MO. Congratulations Wesley!

Hugo Fastl lectures at RPI (Sept. 2012)

Following Internoise 2012 in New York City, Prof. Dr. Hugo Fastl delived an introductory lecture series on sound quality and psychoacoustics to the Program in Architectural Acoustics. Dr. Fastl is Professor of Technical Acoustics in the Faculty of Electrical Engineering and Information Technology at the Technical University München, Germany, well known for his foundational text in the field of sound perception, Psychoacoustics: Facts and Models, co-authored with Eberhard Zwicker.

Cameron Fackler receives ASA and I-INCE honors

Cameron Fackler, a Ph.D. student in the Graduate Program in Architectural Acoustics, was recently appointed to the Acoustical Society of America Student Council. He will serve as the student representative from the Technical Committee on Noise from May 2012 to May 2014.

Cameron was also recently awarded the International Institute of Noise Control Engineering Young Scientist Grant for Inter-Noise 2012. This grant recognizes his research into the acoustical properties of aerogels and will support his attendance at the International Congress and Exposition on Noise Control Engineering.

Dr. Klaus Genuit Lectures at RPI

Dr. Klaus Genuit, the CEO of HEAD acoustics GmbH visited the Graduate Program in Architectural Acoustics at Rensselaer on Feb. 20th. Dr. Genuit delivered a series of lectures on psychoacoustics applications in industrial noise evaluations, on sound quality, sound design, and soundscape.

Two students awarded prestigious Newman Medal

The prestigious Robert Bradford Newman Student Medal, this year (2011) has been bestowed upon Cameron Fackler and Vanessa Li, M.S. students of the Graduate Program in Architectural Acoustics for merit of their study and research in Architectural Acoustics.

Congratulations!

The Newman Student Medal program recognizes excellence in the study of acoustics and its application to architecture and honors outstanding students at schools of architecture and architectural engineering throughout the world.


Christopher Jaffe to receive the Wallace Clement Sabine Award

J. Christopher Jaffe, the founding director, distinguished visiting professor of our program, is to receive the Wallace Clement Sabine Award from the Acoustical Society of America. The Sabine Medal is presented to an individual of any nationality who has furthered the knowledge of architectural acoustics, as evidenced by contributions to professional journals and periodicals or by other accomplishments in the field of architectural acoustics. Jaffe receives this honor “for innovative acoustical solutions in performance hall design and for architectural acoustics education.” The award will be presented in November 2011 at the ASA’s 162nd meeting in San Diego, CA.

Dr. Yun Jing Appointed Assistant Professor

Dr. Yun Jing, a PhD. Graduate of our program, has been appointed an Assistant Professor in the Department of Mechanical and Aerospace Engineering at North Carolina State University. He will begin with this academic duty in late August 2011. Congratulations!

Dr. Yun Jing enrolled in the Fall of 2006 in the Graduate Program in Architectural Acoustics, Rensselaer Polytechnic Institute. He obtained his B.S. Degree in acoustics at Nanjing University, China in 2006. In Summer 2009, Yun has received a Ph.D. degree in Architectural Sciences from RPI School of Architecture. After obtaining his Ph.D. degree, he worked with Harvard Medical School as a research fellow before this academic appointment.

Since 2007 Dr. Jing has accumulated a long list of peer-reviewed journal publications in the Journal of the Acoustical Society of America and IEEE Transactions. Furthermore, he was awarded the Robert B. Newman award in 2007. Through his attending at the acoustical society of America meetings, he was awarded the Young Presenter Award in 2007, Naval Research Office Traveling Grant in 2008, and Young Investigator Travel Grants in 2010.

Prof. Jens Blauert Receives Lifetime Achievement Award From EAA

Prof. Jens Blauert, distinguished visiting Professor of the RPI Graduate Program in Architectural Acoustics, has been awarded Lifetime Achievement Award from the European Acoustics Association.

The name "Professor Dr. Dr. Jens Blauert" stands for a great variety of different acoustical disciplines. Starting with his research at the RWTH Aachen University at the Institute for Electrical Communications Engineering in the field of spatial hearing, wherupon he detected and scientifically described the "trend-setting" decisive bands, his book "Spatial Hearing" was developed in the early 70s, which worldwide is the basis for binaural signal processing and was published in several languages apart from German and English - also in Japanese and Russian.

Professor Blauert's scientific work covers several fields of acoustics, including building-, room-, and architectural acoustics; speech and signal processing; psychoacoustics; sound quality; and sound design. During his time as Director of the Institute of Electrical Engineering and Acoustics at the University in Bochum, he took care of more than 50 dissertations which cover a broad range of topics in acoustics. Many of his doctoral candidates successfully established themselves as professors all over the world.

One can congratulate the EAA for their choice to honor Professor Dr. Dr. Jens Blauert with the award, "Lifetime Achievement in Acoustics." His scientific work in numerous fields in acoustics, his visionary approaches, his constructive lateral thinking, and his active life and commitment to the acoustical communitiy all set him apart in a special way.

ThinkSwiss Research Scholarship Bestowed upon SoA Graduate Student

Philip Robinson, a Ph.D. student of the Graduate Program in Architectural Acoustics has been awarded the 2011 ThinkSwiss Research Scholarship. ThinkSwiss offers scholarships for a research stay in Switzerland. It supports highly motivated and qualified U.S. undergraduate and graduate students to do research at a public Swiss university or research institute for 2 to 3 months.

Prestigious Robert Bradford Newman Student Medal

This year (2010), the Robert Bradford Newman Student Medal has been bestowed upon Isaac Old, a MS. student of the Graduate Program in Architectural Acoustics for Merit of his study and research in Architectural Acoustics. The Newman Student Medal program recognizes excellence in the study of acoustics and its application to architecture and honors outstanding students at schools of architecture and architectural engineering throughout the world.

Philip Robinson Awarded Fulbright Grant

Philip Robinson, a Ph.D. student of the Graduate Program in Architectural Acoustics, has been awarded a Fulbright award for an international research stay at the Aalto University of Science and Technology in Helsinki.

The Fulbright Program is a program of competitive, merit-based grants for international educational exchange for students, scholars, teachers, professionals, scientists and artists, founded by United States Senator J. William Fulbright in 1946. The Fulbright Program is one of the most prestigious awards programs worldwide, operating in over 155 countries. Forty-three Fulbright alumni have won Nobel Prizes and seventy-eight have won Pulitzer Prizes. The program was established to increase mutual understanding between the people of the United States and other countries through the exchange of persons, knowledge, and skills. The program is active in over 155 countries in all world regions.

Philip W. Robinson has been awarded a Fulbright grant for study in Helsinki, Finland to investigate the effects of architectural enclosures on listeners' perception of sound. Philip received an M.Sc. in Architectural Acoustics from Rensselaer Polytechnic Institute in Troy, NY in 2009 and is continuing studies towards a Ph.D. Collaborating with instructors from the Aalto University of Science and Technology in Helsinki, Philip's project will further knowledge that will be used in acoustic applications from concert halls to telecomunication systems.

Samuel Clapp

Ph.D. student in the Graduate Program in Architectural Acoustics, has been appointed the Student Council Representative for the Technical Committee on Architectural Acoustics of the Acoustical Society of America. Sam will serve from May 2011 to May 2013.

International Computer Music Conference Best Paper Award

Professor Jonas Braasch in collaboration with Pauline Oliveros and Doug Van Nort won the award for best paper at the International Computer Music Conference (ICMC) in New York City and Stony Brook, NY, June 1-5, 2010. They presented "Developing Systems for Improvisation based on Listening," a paper reporting the results of an NSF CreativeIT grant.

Leo Beranek lectures at RPI

Dr. Leo Beranek visited the Program in Architectural Acoustics on April 1-2, 2010. He met with students, toured classrooms and labs, and delivered two lectures: "Some Important Contributions to Acoustics" and "The History of Music in Concert Halls."

Leo Beranek donates professional library to RPI

Dr. Leo Beranek will present his personal library to the Graduate Program in Architectural Acoustics and RPI Libraries on April 1, 2010. More information can be found at the following link: http://news.rpi.edu/update.do?artcenterkey=2701

Red Wetherill visits RPI

Renowned architectural acoustician Red Wetherill lectured at the Graduate Program in Architectural Acoustics on Mar. 25th and 26th 2010. He spoke to RPI acoustics graduate students on topics "Acoustics in Buildings", "Worship Spaces" and "Acoustical Experiments."

Dr. Peter D'Antonio of RPG delivers guest lecture

Dr. Peter D'Antonio, CEO of RPG Inc. delivered a guest lecture to RPI Graduate Students on "Sound insulations/Vibration Isolations - Fundamentals and Applications" on March 17th, 2010. Dr. D'Antonio also visited the Architectural Acoustics Labs LASIP (Lab of Acoustics Sensing and Information Processing) and CARL (Communication Acoustics and Aural Architecture Research Laboratory) in Greene Building and Gurley Lab at RPI.

Dr. Jason Summers visits RPI

Dr. Jason Summers delivered a guest lecture to RPI Graduate Students on "Acoustics in Coupled-Volume Systems" on Mar.24th 2010.

John Storyk: Critical Listening Environments

Mr. John Storyk, a renowned Architectural Acoustician, highly recognized though his work in recording studio designs, delivered a guest lecture "Critical Listening Environment in Recording Studios" on Mar. 4th, 2010 to RPI Architectural Acoustics graduate students at the School of Architecture.

Prof. Jens Blauert visits RPI

Prof. Jens Blauert, Distinguished Adjunct Professor of the Graduate Program in Architectural Acoustics, Rensselaer Polytechnic Institute (RPI) delivered a series of lectures during his 9-days stay at RPI between Feb.23rd and Mar.5th 2010, in addition to interaction with RPI MS. Degree Students and Ph.D. students. His lectures included:
   Room-Related Presentations of Auditory Scenes via Loudspeakers
   From Binaural Technology to Virtual Reality
   Perception & Measurement: Some Basics
   Aural Precedence Effect


Uday Trivedi and Philip Robinson receive Newman Award

The Robert Bradford Newman Student Medal, this year (2009) has been bestowed upon both Philip Robinson and Uday Trivedi, students of the Graduate Program in Architectural Acoustics for Merit of their study and research in Architectural Acoustics.
The Newman Student Medal program recognizes excellence in the study of acoustics and its application to architecture and honors outstanding students at schools of architecture and architectural engineering throughout the world. Congratulations!.

Philip Robinson receives award from Institute of Noise Control Engineering

Philip Robinson, a PhD student in RPI's Graduate Program in Architectural Acoustics, won a student paper award in the Institute of Noise Control Engineering's Student Paper Competition. The award, including a $1000 prize, is based on the merit of both the written article and the oral presentation. The presentation, co-authored by Prof. Ning Xiang, and Dr. Peter D'Antonio of RPG Diffusor Systems Inc., titled "A synthesized aperture gonoimeter for diffusion coefficient measurements." was presented at the 38th International Congress and Exposition on Noise Control Engineering (INTER-NOISE 2009), in Ottawa, Canada, Aug. 26th 2009.

Dr. Jens Blauert Lectures at RPI

12/1/08- During the first 2 weeks of December 2008, adjunct distinguished professor Dr. Jens Blauert gave a series of lectures to the students in RPI's Graduate Program in Architectural Acoustics. His lectures included, "Binaural Hearing and Human Sound Localisation," "From Binaural Technology to Virtual Reality," and "Room-Related Presentation of Auditory Scenes via Loudspeakers."

RPI Students Win Student Paper Awards in Paris

08/21/08- Anne Guthrie and Yun Jing, PhD students in RPI's Graduate Program in Architectural Acoustics, placed first and second, respectively, in the Best Student Paper Competition sponsored by the ASA's Technical Committee on Architectural Acoustics at the Acoustics '08 meeting in Paris. Anne's presentation, co-authored by Prof. Jonas Braasch, was titled "Relevance of acoustic parameters for musician communication," and Yun's, co-authored with Prof. Ning Xiang, was titled "Modeling and analysis of acoustically coupled spaces using a diffusion equation model."

RPI Team Wins the 2008 ASA Student Design Competition

08/01/08- Kathleen Stetson, Alex Bockman, and Arthur van der Harten, students in RPI's Graduate Program in Architectural Acoustics, won First Honors in the Student Design Competition judged at the Acoustics' 08 Conference in Paris. A second RPI team, with members Stephen Secules, Douglas Malora, and Benjamin Markham, won a Commendation Award (one of four). Four RPI teams were among a total of 17, representing Chalmers University of Technology (Sweden), the Technical University of Denmark, Pennsylvania State University, the University of Nebraska, the University of Kansas, Johns Hopkins University, the University of Hartford, and the University of Florida. Additional details about the compeition can be found on the website of the Robert Bradford Newman Fund.

Students Visit Boston Symphony Hall

04/29/08- A group of students from the Graduate Program in Architectural Acoustics made a field trip to Boston Symphony Hall on April 29, 2008. After finishing a series of room-acoustic measurements in the Hall, Dr. Leo Beranek led the RPI students on a tour of the hall, and told many legendary stories about the hall design and Wallace Clement Sabine, the pioneer of the modern architectural acoustics. Following the measurements and the tour, the RPI students visited Acentech and met with Acentech consultants along with Dr. Leo Beranek, Dr. David Griesinger, and a group of MIT students to discuss their on-going research projects at RPI and Acentech.

3 Students Receive the Prestigious Newman Medal

11/25/07- Joseph Digerness, Yun Jing, and Dorea Ruggles each received the Robert Bradford Newman Student Medal for Merit in Architectural Acoustics, given by the Robert Bradford Newman Student Award Fund and the Acoustical Society of America. The medal is in recognition of excellence in the study of acoustics and its application to architecture. Additional details can be found at the Newman Fund's website.

Paul Calamia and Yun Jing receive ICA Young Scientist Grants

05/01/07- Prof. Paul Calamia and Yun Jing have each received a Young Scientist Grant from the International Congress on Acoustics for their research to be presented at ICA 2007 in Madrid in September:

"Culling insignificant diffraction components for interactive acoustic simulations," Paul Calamia and Peter Svensson (Norwegian Univ. of Science and Technology);

"Investigation on higher orders of spherical harmonics equations for efficient room-acoustic predictions," Yun Jing and Ning Xiang.

Dorea Ruggles receives an NSF Graduate Research Fellowship

03/25/07- Dorea Ruggles, a graduate student in RPI's Graduate Program in Architectural Acoustics, is a 2007 recipient of a National Science Foundation (NSF) Graduate Research Fellowship. This prestigious fellowship is awarded to outstanding graduate students who demonstrate the potential to become knowledge experts and who can contribute significantly to research, teaching, and innovations in science and engineering. Dorea's area of research is speech intelligibility. With NSF fellowship support she is going to pursue her Ph.D. research in the area of binaural room-acoustics evaluation in the Ph.D. Program of Architectural Sciences in the School of Architecture. She is a 2006 graduate of Gustavus Adolphus College, where she studied physics and music.

Distance and Intimacy: Musicians Transcend Distance to Join Voices Over the Internet

03/22/07- On Thursday, March 22, 2007, four ensembles located across the States came together via Internet2 for a co-located performance of improvisational music. Tintinnabulate, an ensemble helmed by pioneering composer Pauline Oliveros and co-run with Jonas Braasch's CARL group at Rensselaer Polytechnic Institute in Troy NY, joined Chris ChafeĀ’s SoundWire ensemble at CCRMA Stanford University, Cynthia PayneĀ’s DANM group from UC Santa Cruz, and Sarah WeaverĀ’s Weave Soundpainting Orchestra at ChicagoĀ’s Loyola University. Together, the four groups performed original works by Pauline Oliveros and Else Olsen S., an improvisational celleto concerto featuring Chris Chafe and conducted by Sarah Weaver, and an improvisation with interactive visual art by Arthur van der Harten. The night featured a range of instruments from multi-channel celleto, laptop, harp, electronics, and live video manipulation. The ensembles were also joined by dancer Asimina Chremos. The event was not only attended by audiences at all locations, but also broadcast live to the public through the world wide web.

This project is a part of ongoing research in high quality internet transmission between artists across the globe. The performance was made possible by a technical collaboration between Jonas Braasch, Dan Valente, Juan Pablo Caceres, Lynne Sheehan, Jim Warner, Bob Vitale, Joe Owens, Terry Figel, Lyle Troxell, and Christopher Sorg, along with various members of all the ensembles.

Graduate students visit Acentech, Inc. for a round-table meeting with consultants and students from the University of Nebraska Acoustics Group.

03/16/07- Prof. Xiang and eight RPI graduate students visited the office of Acentech, Inc. in Cambridge, MA to take part in a round-table meeting on current projects and research with consultants as well as students from the University of Nebraska Acoustics Group. Each student made a short presentation on her/his thesis project. Dr. Leo Beranek was also present, and delivered a lecture on "Audience absorption in concert Halls".

Graduate students visit the Institute of Acoustics at Tongji University in Shanghai and the Institute of Acoustics at the Chinese Academy of Sciences in Beijing.

03/02/07 - 03/14/07- Prof. Xiang and five RPI graduate students visited the Institute of Acoustics at Tongji University in Shanghai and the Institute of Acoustics at the Chinese Academy of Sciences in Beijing during a two-week field trip to China. In Shanghai they worked ogether with Tongji acoustics graduate students, led by Prof. Shengwo Sheng, on a series of standard acoustics experiments using their acoustics facilities. In Beijing they met with Prof. Maa Dah You, Prof. K. Liu, and a large number of acoustics graduate students. They also toured various new performing arts centers, building sites, and acoustics laboratories in both cities.

Prof. JiQung Wang from the Institute of Acoustics at the TongJi University in Shanghai Lectures at RPI

02/06/07- Prof. Wang paid a visit to the Graduate Program in Architectural Acoustics at RPI on February 6 - 8, 2007 and delivered a lecture on the "Acoustics of Courtyard Theaters".

Dr. David Griesinger from the Harman Specialty Group Lectures at RPI

01/30/07- Dr. Griesinger delivered a guest lecture for the Graduate Program in Architectural Acoustics at RPI on January 30, 2007 about the "Perception of Concert Hall Acoustics when the Reflected Energy is Stronger than the Direct Energy".

An Institute-Wide Academic Minor in Architectural Acoustics is Now Available

10/27/06- The minor in Architectural Acoustics is open to all Rensselaer students. Please click here for details.

Dr. Thomas Rossing, World Renowned Expert in Musical Acoustics, Lectures at RPI

10/19/06- On Thursday, October 19, Dr. Thomas Rossing delivered a lecture entitled, "Acoustics of Percussion Instruments, Old and New". He discussed the modes of vibration of bars, membranes, and plates and the physics of several percussion instruments, including drums, cymbals, gongs, bells, stone chimes, and Caribbean steel pans.

RPI Students Win Student Design Competition at the ASA Conference in Providence, RI

6/6/06- Anthony McCreery, Indi Savitala, and Arthur VanDerHarten won first honors for their architectural design at the meeting of the Acoustical Society of America in Providence, RI. Their entry can be seen here. There were more than twenty entries from numerous schools. In addition two other groups from RPI, Matt Boyd and Dan Valente as well as Jarrod Whittington, Zühre Sü, and Gordon Rubin won commendations for their designs. More information on the competition can be found at www.newmanfund.org.

Graduate Student Wins Student-Paper Award

6/6/06- Graduate student Zühre Sü placed second in the Student Paper Competition in the area of the Architectural Acoustics during the Providence Meeting of the Acoustical Society of America in June 2006.

Former Graduate Students Win Awards

6/6/06- Former graduate students Courtney McGinnes and Ken Andria each received a 2006 Newman Student Award from the Acoustical Society of America, a prestigious award bestowed upon Architectural Acoustics students.

Acoustician Red Wetherill Gives Guest Lecture

6/1/06 Acoustician Red Wetherill visited RPI and gave a guest lecture on some of his experiences as an acoustics consultant. In the photo he is seen working with two acoustics graduate students, Indi Savitala and Anthony McCreery.

Wooster Theater Group Visits Gurley NYSTAR Sound-Field Composition Lab

5/25/06 The Wooster Experimental Theater Group visited the Gurley NYSTAR Soundfield Composition Lab to experience the multi-channel rendering of audio using Virtual Microphone Control.

RPI Student is Awarded Fellowship from AT&T

5/23/06 Gordon Rubin was awarded a three year fellowship from AT&T for his Ph.D. research in the Architectural Acoustics Program. Rubin, currently a Master's student, will be continuing his research in Laser Doppler Vibrometry.

Leo Beranek Gives Lecture on Sound Quality

4/19/06 Renowned acoustician and author Leo Beranek came to RPI and gave two lectures to the students and staff. He also had an open book signing for his book "Concert Halls and Opera Houses".

Jonas Braasch Receives Lothar Cremer Award

3/20/06 Jonas Braasch received the Lothar Cremer Award, the highest honor of the German Acoustical Society (DEGA) for a young career scientist.

Richard Lyon Gives Guest Lecture

3/09/06 Richard Lyon, former MIT professor and president of Lyon Associates, visited the RPI Graduate Program in Architectural Acoustics and delivered a guest lecture on Statistical Energy Analysis applied in vibration-control projects.

Wolfgang Ahnert Speaks on EASE Software

2/15/06 Wolfgang Ahnert of ADA came to RPI to speak with students about using EASE acoustic modeling software and other acoustic modeling techniques. Ahnert remains a regular visitng professor and more information about him and his software can be found in the Faculty and Staff page.

 

 

 

 



 
 
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