prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How many people attend the 233rd ACS national meeting?

Read the following text and answer briefly.

Context 1: The major actions taken by the board of directors and council during the national meeting in Chicago were reported in C&EN, April 30 (page 32) 
The Society Committee on Budget & Finance met on Saturday, March 24, to review the society's 2006 financial performance  The society ended 2006 with a net contribution from operations of $12 2 million, on revenues of $424 0 million and expenses of $411 8 million  This was $7 8 million favorable to the approved budget 
After including the results of the Member Insurance Program and new ventures, the society's overall net contribution for 2006 was $11 5 million, which was $7 4 million favorable to the approved budget  The favorable variance was primarily attributable to higher than budgeted electronic services revenue and investment income, as well as expense savings from lower than budgeted health care costs and reduced IT spending  In addition, the society ended the year in compliance with the board-established financial guidelines 
The Society Committee on Education (SOCED) received an update from President Catherine Hunt on the thematic programming featured in Chicago focusing on the sustainability of energy, food, and water  President-Elect Bruce Bursten solicited input from the committee pertaining to the central role of education in his agenda  SOCED received a presentation from the Membership Affairs Committee on its white paper on membership requirements 
Committee members strongly support the proposal to include undergraduates as members of the society, but they requested that financial arrangements be clearly spelled out in the petition to ensure that the highly successful Student Affiliates program remains intact  The committee discussed the Education Division programs that were reviewed in 2006 and those that will be reviewed in 2007, under the auspices of the Program Review Advisory Group  SOCED received an update from the Committee on Professional Training regarding the draft ACS guidelines for approval of bachelor's degree programs in chemistry 
Committee members discussed the report prepared by the Globalization Task Force, focusing on those sections relevant to education  The committee suggested initiatives related to the new ACS strategic plan, including a potential program that would engage retired chemists in the K-12 classroom  SOCED created a task force to consider the role of online, or "virtual," simulations in the chemistry laboratory, recognizing the value of online/virtual experiences as a supplement to, but not a replacement for, hands-on laboratory experiments 
The committee ratified two interim actions taken since the Dec  3, 2006, meeting: to remove the financial restriction of the ACS Petroleum Research Fund (ACS PRF) Supplement for Underrepresented Minority Research Programs (SUMR) and to contact nominators whose nominations for the Volunteer Service Award had expired and to invite them to reactivate their nomination packet for the 2008 Volunteer Service Award 
Acting under delegated authority, the committee voted to accept the recommendations of the ACS Petroleum Research Fund Advisory Board (February 2007 meeting) for funding grants totaling $5 2 million; voted to recommend to the board a screened list of six nominees (due to a two-way tie for fifth place) for the 2008 Priestley Medal; voted to recommend to the board a screened list of five nominees for the 2008 Award for Volunteer Service to ACS; on the recommendation of the ACS Committee on Frasch Foundation Grants, voted to recommend to the board that it recommend to the trustee (US Trust) of the Frasch Foundation 12 grants for research in agricultural chemistry for the period of 2007–12; voted to recommend to the ACS Board of Directors that a new national award be established, the "ACS Award for Affordable Green Chemistry," sponsored by Rohm and Haas; and voted to recommend to the ACS Board of Directors that a new endowment be established, the "Affordable Green Chemistry Endowment Fund," to support the award 
The committee also reviewed the final report from the Special Board Task Force on the Review of the ACS National Awards Program, chaired by Ronald Breslow; established a Canvassing & Selection Subcommittee; and reviewed a list of external awards for which ACS may want to nominate candidates  The committee agreed to include the list of significant external awards in the awards locator database that is being developed 
The committee was updated on efforts to reconcile ACS's technical divisions' desires to leverage national meeting content using the Internet with our journal editors' concerns about prior publication issues  A conference call on this issue was scheduled for April 21, 2007 
The committee received a presentation on the recent actions of the ACS Board of Directors International Strategy Group (ISG)  The group's charge is to develop recommendations for a short- and long-term international strategy for the society 
The committee was updated on the status of the activities of the Board Oversight Group on Leadership Development (BOG)  Potential solutions for the unexpectedly high cost of facilitator training and transitioning from the current Leaders Conference format to the newly designed curriculum were presented to the committee 
The committee reviewed plans for conducting the 2007 Membership Satisfaction Survey  Preliminary results are expected in May or June with a final report to be delivered to the board at the 2007 Boston national meeting 
The committee received a briefing on the status of the MORE Project: Multidisciplinary Opportunities though Resource Enhancement  Twenty-eight proposals were received, and a decision on which proposals to support will be made in early May 
The chair led a discussion on draft 2007 committee goals, and committee members offered several suggestions related to successfully meeting them  One suggestion was to modify a communications goal to make it more completely reflect the duties of the committee outlined in the board regulations  The chair and committee members will examine the suggestion and revisit the question after the board retreat where board committee duties will be examined 
ACS President Hunt discussed her 2007-08 Presidential Task Force on Enhancing Science & Technology, which is charged with developing advocacy best practices that can enhance ACS's attainment of its public policy priorities  The task force is composed of a diverse set of ACS members as well as former U S  Representative and chairman of the House Science Committee, Sherwood Boehlert, who will cochair the task force 
• Results of the 2007 Public Policy Priorities Survey, which resulted in a four-tiered ranking of ACS's 2007 public policies  The ranking will help focus staff resources in conducting outreach and advocacy on behalf of ACS members 
• The hiring of a communications consulting firm for 2007 to assist ACS in implementing the initial phase of the ACS Strategic Communications Plan 
• Creation of a pilot ACS state government affairs advocacy program  Committee members agreed to the creation of a pilot, and staff will propose an initial list of states, policy focus, and a budget to carry out the program 
The committee met in executive session on March 23 and in open session jointly with the Joint Board-Council Committee on Publications and the Division of Chemical Information on March 26 
The committee heard from Chemical Abstracts Service (CAS) management on a range of issues including a report on continuing database building efforts, product enhancements, and CAS's centennial celebration plans 
The Committee on Chemical Safety (CCS) provides advice on the handling of chemicals and seeks to ensure safe facilities, designs, and operations by calling attention to potential hazards and stimulating education in safe practices 
CCS has several publications (many downloadable), including the flagship publication, "Safety in Academic Chemistry Labs" (SACL)  Work has recently started on the translation of SACL into Arabic  This is in addition to the online Spanish version of SACL  Also online are the "Student Lab Code of Conduct for Secondary Science Programs" and a security vulnerability analysis checklist  A K-12 restricted hazardous substances list is under development  The third edition of the "Chemical Safety Manual for Small Businesses" will be ready soon 
The committee's Task Force on Laboratory Environment, Health & Safety is working on a new edition of "Laboratory Waste Management " Task force members also commented on the recent Environmental Protection Agency Proposed Rule for Hazardous Waste in Academic Laboratories  Our Video Safety Resources Task Force is developing video resources to be distributed over the Web 
CCS has been involved in collaborations for the updating of publications like "Prudent Practices in the Laboratory" and "ACS Guidelines for the Teaching of High School Chemistry " Along with other ACS units, CCS is exploring participating in the EPA's School Chemicals Cleanout Campaign 
The Committee on Chemists with Disabilities (CWD) met at the 233rd ACS national meeting, Chicago, on Monday, March 26  Judy Summers-Gates reported on the Joint Subcommittee on Diversity meeting  This subcommittee is made up of representatives of the five committees that support people in chemistry (as opposed to a category of the profession): CWD, Committee on Minority Affairs, Committee on Technician Affairs, Women Chemists Committee, and Younger Chemists Committee, and its goal is to develop ways to coordinate the efforts of the five groups 
The CWD Ambassador Program that was announced at CWD's 25th anniversary celebration at the Washington, D C , meeting was discussed  Zelda Wasserman reported on the status of the letter from CWD to the ACS Board regarding captioning of ACS video materials  Janelle Kasper-Wolf, of ACS staff, discussed adding new questions to the ACS annual employment salary survey to obtain information for the committee 
At the Chicago national meeting, the Committee on Community Activities (CCA) partnered with the ACS Education Division and the Office of the President to host "Chemistry In Action—It's Easy Being Green" at the Peggy Notebaert Nature Museum on Saturday, March 24  More than 250 children participated in the hands-on activities focused on recycling  ACS President Hunt presented a Salutes to Excellence plaque to the museum for its dedication to community outreach 
The Chemists Celebrate Earth Day celebration occurred in 120 local sections with 138 coordinators leading the efforts within their communities  This represents an increase of more than 30% in local section and coordinator participation from 2006 
CCA was featured in C&EN's April 16th issue on page 53  A shortcut to CCA's homepage was created: chemistry org/committees/cca html 
During the Boston national meeting, CCA and the Office of Community Activities will celebrate National Chemistry Week's 20th Anniversary and its theme, "The Many Faces of Chemistry " A special outreach event is being planned for Sunday, Aug  19  Hands-on activities will focus on health and wellness 
The Committee on Corporation Associates (CCA) advises and influences ACS to ensure that its products and services are of value to industrial members and their companies  CCA vice chair, Roslyn White (SC Johnson), provided an overview of recent interactions between Corporation Associates and the U K -based Society of Chemical Industry (SCI) 
CCA gave feedback to a recommendations report from the ACS Board Committee on Professional & Member Relations Task Force on Globalization  Presentations were also received from the ACS Green Chemistry Institute and SCI 
Staff reported on the Department of Industry Member Programs' activities since the San Francisco meeting  The report covered the Regional Industrial Innovation Awards, the World Congress on Industrial Biotechnology, the Analytical Pavilion sponsored by C&EN, and the ACS/Pharma Leaders Meeting 
The Awards/Finance & Grants Subcommittee reported that CCA received two funding proposals that total $7,500  Funding was provided to the following: The Committee on Economic & Professional Affairs at $3,000 for the Chicago symposium on "Benefits Trends for the Chemical Workforce" and the Office of Graduate Education and the Department of Career Development & Management at $4,500 for a workshop on "Preparing for Life after Graduate School," to be held in conjunction with the 39th Central Regional Meeting 
The subcommittee also requested that ACS staff provide CCA with an official annual statement of Corporation Associates' financial reserves as of Jan  1 of each year 
The Programs Subcommittee reported on planned programming activities in 2007 and beyond between CCA and SCI  The subcommittee gave an update on a Boston symposium cosponsored by Corporation Associates and the Medicinal Chemistry Division featuring past ACS Heroes of Chemistry from the pharmaceutical industry 
By request of the subcommittee, representatives from Chemical Abstracts Service gave an overview on AnaVist—a tool with potential applications for CCA's efforts to provide member companies with industry-relevant information and reports  The subcommittee also requested that CCA earmark approximately $20,000 of Corporation Associates funds in 2008 for its activities 
The Educational Outreach Subcommittee reported on its decision to collaborate with the Graduate Student Symposium Programming Committee of the Chemical Education Division on a graduate student industry roundtable program in Boston 
The subcommittee requested $5,000 in support of this effort  The subcommittee also discussed a request for corporate executive support of an American Association of Physics Teachers initiative to promote undergraduate research 
The Committee on Environmental Improvement (CEI) continues to be focused on the sustainability of the chemical enterprise  In Chicago, the committee introduced a multiyear effort to make ACS meetings more sustainable  This effort is designed to take advantage of the large size and diverse programs of the society to lead in the sustainability arena by "walking the talk "
The committee held a dialogue with representatives of the U S  Environmental Protection Agency who are trying to "green" federal conferences and work with the travel and tourism industry to change practices and shrink the environmental footprint of meetings  The committee also used advertising and student volunteers to engage individual meeting participants in a campaign to increase recycling by asking "Are you sustainable?" Moving forward, CEI looks forward to working closely with the Committee on Meetings & Expositions to advance this agenda 
CEI was also pleased to participate in the meeting theme on sustainability through the ACS presidential programming  CEI cohosted the Monday presidential luncheon to discuss sustainability issues with the Committee on Science and is leading the follow-up to that luncheon, which will include recommendations on advancing sustainability in the three focal areas of the meeting—energy, food, and water 
The committee also continued its dialogue with the Committee on Corporation Associates about a collaborative workshop  This activity, tentatively slated for the New Orleans meeting, will seek additional insights from chemical and allied products companies about public policy barriers that limit adoption of more sustainable products and practices as well as policy incentives that would lead to increased sustainability in the chemical enterprise 
At its Chicago meeting, the committee welcomed the president of the Jordanian Chemical Society and the past-president of the Arab Union of Chemists 
The committee was briefed on Pittcon 2007, where, with financial support from the Society of Analytical Chemists of Pittsburgh, ACS coordinated participation of a scientific delegation from Adriatic nations 
The committee heard reports on the 2007 Frontiers of Chemical Science III: Research & Education in the Middle East meeting; the 2007 Transatlantic Frontiers of Chemistry meeting, which was jointly sponsored by ACS, the German Chemical Society, and the Royal Society of Chemistry; planned workshops to engage U S  and Chinese early-career scientists in chemical biology, supramolecular, and new materials chemistry; and ACS Discovery Corps U S /Brazil Research Collaboration Project in Biomass Conversion to Biofuels, Biomaterials & Chemicals 
The committee discussed Latin American engagement opportunities created through Puerto Rico's involvement in three key chemical science events there: the 2009 ACS Southeast Regional Meeting, the 2008 Federation of Latin American Chemical Associations (FLAQ) meeting, and the proposed IUPAC 2011 Congress & General Assembly 
The committee heard reports on letter-writing efforts by the ACS president to government officials in Libya and Mexico expressing concerns about challenges to the scientific freedom and human rights of scientists there 
The Committee on Minority Affairs (CMA) approved new vision, mission, and values statements at the Chicago national meeting  The mission of CMA is to increase the participation of minority chemical scientists and influence policy on behalf of minorities in ACS and the chemical enterprise 
An aggressive new strategic plan was approved by CMA to guide its activities over the next three years  By the end of 2009, CMA will increase the number of ACS Scholars that graduate to 100 per year, add 100 new minorities to leadership positions in ACS, engage in several collaborations, and increase the number of minority members of ACS by 5,000  CMA will focus initially on increasing minorities in ACS leadership  In working toward this goal, CMA began work on two new leadership-development programs for minority chemists 
CMA continues to support the work of the Joint Subcommittee on Diversity (JSD) in developing programs, products, and services to ensure full participation of all members in ACS  In Chicago, JSD premiered a diversity booth at the meeting exposition hall and cosponsored symposia 
The Committee on Patents & Related Matters (CPRM) discussed proposed legislative and regulatory changes to the U S  patent system as well as open-access legislation and the potential effects such matters might have on industry and academia as well as on ACS 
CPRM also continued its work on several new educational tools to assist and inform members on patent issues and other intellectual property matters important to a successful career in the chemical enterprise  Many of these tools are now available on the committee's expanded website, membership acs org/C/CPRM/ 
At the March 2007 meeting, the Committee on Professional Training (CPT) reviewed 42 new and additional information reports from ACS-approved chemistry programs  CPT held conferences with four schools seeking approval, discussed three updates and five site visit reports, and approved three new schools  The total number of ACS-approved chemistry programs is now 642 
The committee released the full draft of the ACS guidelines for review and comment  Copies of the draft were distributed to the department chairs at all ACS-approved schools, the chairs of all ACS committees, and the chairs of all ACS technical divisions 
Several CPT members met with the ACS technical divisions during the Chicago meeting to present an overview of the draft and obtain feedback  The draft guidelines document is available on the CPT website, and the committee invites any comments to be sent to cpt@acs org 
In other business, the committee continued development of the two workshops with minority-serving institutions that will be held in 2007  The committee reviewed the editorial policies for the 2007 edition of the ACS Directory of Graduate Research, which is using a new protocol for retrieving research publication titles in an effort to improve the accuracy of the directory 
C&EN finished 2006 with an exceptionally strong editorial package  The first months of 2007 are proving to be equally successful in fulfilling the magazine's mission of keeping its readers informed  On the advertising side, revenues in 2006 increased for the second year in a row, and the early months of 2007 show continuing positive signs  The most significant editorial achievement was the successful launch of the redesign of the print edition of C&EN with the Oct  16, 2006, issue 
The Subcommittee on Copyright has successfully updated the Copyright Module on the ACS Publications website  The subcommittee is looking into the possibility of conducting copyright programs at future ACS national and regional meetings 
The final monitoring reports for Chemistry of Materials, Journal of Agricultural & Food Chemistry, and Molecular Pharmaceutics were presented and accepted by the committee  Journal of Chemical Information & Modeling, Organic Letters, Accounts of Chemical Research, and the Journal of Chemical Theory & Computation will be monitored next 
3  Examining the scientific basis of public policies related to the chemical sciences and making recommendations to the appropriate ACS units 
In the first of these areas, ComSci partnered with President Hunt and the Committee on Environmental Improvement in planning and hosting a sustainability luncheon that featured roundtable discussions centering on a key sustainability question  At the Boston national meeting, ComSci will deliver a full-day program on the subject of "Partnerships in Innovation & Competitiveness "
Regarding the second thrust, ComSci will present two programs in Boston: a box lunch that will feature two speakers taking opposing sides on the subject of "Genetic Screening & Diagnostic Testing: Do You Really Want to Know?" and a symposium titled "Creating & Sustaining International Research Collaborations "
In support of the last thrust, ComSci is planning two events for 2008: "Balancing Security & Openness" will gather data to determine if the recent emphasis on security is hindering scientific progress and "Transitioning Chemical Science to Commercially Successful Products "
The Women Chemists Committee (WCC) hosted more than 70 attendees at its open meeting recently in Chicago, where representatives from Iota Sigma Pi, Women in Science & Engineering, the Association of Women in Science, and the Chicago local section helped WCC celebrate the committee's 80th anniversary 
The Women in Industry Breakfast was also highly successful with a new format of speed networking  More than 100 participants had the opportunity to practice their elevator speeches and make several professional connections  A related workshop will be offered by WCC in Boston 
In Chicago, WCC sponsored two symposia, "Women Achieving Success: The ACS as a Platform in Leadership Development" in honor of Madeleine Joullié's 80th birthday and the ACS Award for Encouraging Women into Careers in the Chemical Sciences: Symposium in Honor of Bojan H  Jennings 
More than 225 ACS meeting attendees were present for the biannual WCC Luncheon and heard the keynote speaker Laura Kiessling, 2007 Francis P  Garvan-John Olin Medal Recipient  Twelve women presented their research at this meeting with funding by the WCC/Eli Lilly Travel Grant Award  WCC members also spent time educating expo attendees on programs offered by the ACS Office of Diversity Programs at its new booth 
In Chicago, the Younger Chemists Committee (YCC) welcomed its new committee members with an information session centered on YCC's charter as well as on its strategic plan: to make ACS relevant to younger chemists, to involve younger chemists in all levels of the society, and to integrate younger chemists into the profession 
In January, YCC again hosted a Leadership Development Workshop during the ACS Leaders Conference  There were more than 80 applications for the 15 awards, which covered travel and registration for the conference  YCC plans to again fund the travel awards and provide leadership training for young chemists in 2008  YCC also solicited applications and selected a new graduate student representative on the Graduate Education Advisory Board 
During the Chicago meeting, YCC programs included "Starting a Successful Research Program at a Predominantly Undergraduate Institution," "Career Experiences at the Interface of Chemistry & Biology," and "Chemistry Pedagogy 101 "
In addition to these programs, YCC cosponsored five programs with various committees and divisions  YCC continues to reach out to ACS committees and divisions and has initiated liaisonships with 11 technical divisions to encourage technical programming that highlights the contributions of younger chemists  Looking forward to Boston, YCC is planning symposia including "The Many Faces of Chemistry: International Opportunities for Chemists"; "Being a Responsible Chemist: Ethics, Politics & Policy"; and "Changing Landscapes of the Bio-Pharma Industry "
The Committee on Committees (ConC) conducted its annual training session for new national committee chairs at the ACS Leaders Conference in January 2007  ConC's interactive session for committee chairs in Chicago served as an opportune follow-on and a forum for informative interchange among seasoned and new chairs 
ConC began developing its recommendations for the 2008 committee chair appointments for consideration by the president-elect and chair of the board  ConC continues to focus efforts to identify members with the skills and expertise specified by the committee chairs using the councilor preference form 
The form will be sent to councilors in May  ConC also seeks the names of noncouncilor members for consideration for service on council-related committees, especially those with no prior appointment 
As part of ongoing activities with the joint CPC-Board Governance Review Task Force, ConC has collected data on committee liaisons to other committees  This information will be distributed to committee chairs  The number of liaisons indicates that unofficial but strong communication channels exist within the ACS committee structure 
On Sunday evening, the Committee on Nominations & Elections (N&E) sponsored its fifth successful Town Hall Meeting for President-Elect Nominees  An estimated 200 people attended this session  This forum facilitated communication among the 2008 president-elect nominees, councilors, and other members  N&E will hold another Town Hall Meeting featuring the candidates for director-at-large at the fall meeting in Boston 
Now that voting over the Internet has become an accepted procedure for ACS national elections, the ACS technical divisions and local sections have expressed strong interest in using this method for their elections  N&E has developed protocols for elections for local sections and divisions  This document will be forwarded to the appropriate committees for their review and distribution 
N&E is responsible for reviewing annually the distribution of member populations within the six electoral districts to ensure that the districts have equitable representation  According to bylaw V, section 4(a), the member population of each electoral district must be within 10% of the result of dividing by six the number of members whose addresses lie within these districts  The committee is happy to report that the six electoral districts are in compliance 
The committee has developed a petition on election procedures for president-elect and district director  The proposed election mechanism provides for a preferential (ranked) ballot and an "instant runoff " N&E continues to address the areas of campaigning and the timing of our national election process  Between the Chicago and Boston meetings, the committee plans to sponsor online forums for input from councilors and other interested members on these issues 
In response to member concerns regarding the collection of signatures for petition candidates, N&E reviewed the society's bylaws  The bylaws state that an endorsement is required, but does not stipulate the method of endorsement  N&E has determined that original or electronic signatures are acceptable and will establish appropriate procedures for receipt of electronic signatures 
The Committee on Constitution & Bylaws (C&B), acting for the council, issued new certified bylaws to the Corning Section, the Portland Section, the Division of Colloid & Surface Chemistry, and the Division of Chemical Education  The committee reviewed new proposed amendments for the Division of Medicinal Chemistry, the Columbus Section, the Detroit Section, and the Southern Arizona Section 
Three petitions were presented to council for action at this meeting  Regarding the "Petition on Election Procedures 2006," a motion to separate the petition was approved, and the petition was divided  Provisions affecting bylaw V, sec  2d, bylaw V, sec  3c, and bylaw V, sec  4f, which deal with election procedures and the timing of run-off elections, were approved by council and will become effective following confirmation by the board of directors 
The second part of the petition regarding bylaw V, sec  2c, and bylaw V, sec  3b, which deal with signature requirements for petition candidates for president-elect and director-at-large respectively, was recommitted to the Committee on Nominations & Elections, which has primary substantive responsibility for the petition 
The Committee on Nominations & Elections was asked to reconsider the signature requirements, procedures for acceptance of electronic signatures, and recommendations from the Governance Review Task Force on election procedures 
The second petition presented to council for action was the "Petition on Rules for Nominating Members of N&E for National Offices " This petition was not approved by council  The third petition, the "Petition on Multiyear Dues," was amended by incidental motion on the council floor, calling for the petition to become effective when technical components are instituted to track payments, but no later than Jan  1, 2010  Council approved the incidental motion and then approved the petition 
The committee reviewed one petition for consideration, the "Petition on Local Section Affiliations," which will be submitted to council for action at the fall 2007 meeting in Boston 
The committee met with representatives of the Committee on Membership Affairs and the Governance Review Task Force to continue discussions on proposals currently being formulated on membership requirements and student membership  In addition, the committee discussed election issues of concern to the Southern California Section 
We hope you enjoyed the presidential and division thematic program, "Sustainability of Energy, Food & Water" in Chicago  A small, dedicated group of volunteers and staff labored tirelessly to create and coordinate this programming; to them the Committee on Divisional Activities (DAC) offers sincere thanks 
DAC has committed to transfer the process of choosing and organizing future national meeting themes to a body that represents all divisions  We made substantial progress in Chicago, where division, secretariat, and committee representatives convened to discuss national meeting program concepts  They proposed themes for the 2008 Philadelphia national meeting as well as a framework for a future national programming group 
Divisions have successfully served their members fortunate enough to attend national meetings  To maximize benefits to division members, DAC encourages divisions to consider extending the reach of the content they deliver at national meetings through Internet-based distribution channels and will support worthy efforts in this direction via Innovative Program Grants 
The committee voted in Chicago to propose modifications to the division funding formula that will more greatly reward interdisciplinary programming  The new formula will also be simpler and more transparent to divisions  DAC will present the revised plan to council for action in Boston 
The Committee on Economic & Professional Affairs (CEPA), working with ACS staff in the Departments of Career Management & Development and Member Research & Technology, continues to update and implement its strategic plan to address the career needs of society members 
Specifically, the committee reviewed and revised existing workshops and materials to help ACS members get jobs  CEPA is developing new programs to address the needs of mid- and late-career chemists to ensure their continued competitiveness in the workplace and to ease their career transitions  New initiatives in these areas include the development of workshops, online training, surveys to assess member needs, suggested changes to public policies, and updates to professional and ethical workplace guidelines  As a result of discussions at the Public Policy Roundtable, which was held in San Francisco, a background paper is being developed on trends in health care issues 
The newly revised "Chemical Professional's Code of Conduct" was presented to council, which approved it  The Standards & Ethics Subcommittee is preparing a revision of the "Academic Professional Guidelines" to be presented to council for consideration in Boston 
CEPA reviewed the Globalization Task Force Report  As our science diffuses around the globe, we want to make sure that our members are aware of the economic and professional challenges they will face and that they have the tools they need to succeed  Therefore, CEPA made a commitment to work with other committees, divisions, and ACS staff to develop programs and policies that position our membership to compete in the global workforce 
CEPA heard and discussed a presentation on the proposal from the Membership Affairs Committee on broadening the requirements of membership  CEPA supports the spirit of this proposal and encourages further detailed studies to assess financial impacts on local sections and student affiliates chapters 
The Local Section Activities Committee (LSAC) recognized local sections celebrating significant anniversaries in 2007, including Savannah River (50 years), Northeast Tennessee (75 years), and the St  Louis and Syracuse local sections (both celebrating 100 years) 
LSAC hosted the local section leaders track in conjunction with the ACS Leaders Conference in Baltimore on Jan  26–28  A total of 135 delegates from 124 local sections participated in the weekend leadership conference 
LSAC also hosted a Local Section Summit on March 2–4 in Arlington, Va  The summit focused on practical operational issues that will support local sections' long-term success  Specific areas that were discussed include the development of a multiyear plan to expand or develop programming for local sections, opportunities to encourage innovation and experimentation within and among local sections, and capitalizing on existing opportunities to facilitate partnerships between local sections and other ACS groups 
Following the San Francisco national meeting, LSAC launched a local section Science Café minigrant program  Fifty-five local sections accepted LSAC invitation to host Science Cafés in 2007 
A DVD entitled "ACS Close to Home: Local Sections Connecting Chemistry & the Community" was released earlier this year  The video provides a seven-minute overview of the many outreach and educational programs sponsored by local sections and the critical role they play in positively influencing the public's perception of chemistry and its practitioners  Copies of the DVD were sent to all local section officers 
The Committee on Meetings & Expositions (M&E) reported that the 233rd ACS national meeting hosted 14,520 attendees  This included 7,152 chemical scientists, 5,059 students, 1,283 exhibitors, 119 precollege teachers, 573 exposition visitors, and 453 guests  The exposition had 424 booths with 268 companies 
The 10 2006 regional meetings set a new standard for excellence with attendance exceeding 8,000, a 30% increase in average meeting attendance compared to the 2005 meetings  A total of 4,717 abstracts were submitted  A region summit was held in February at which the final report of the ReACT study group was reviewed 
The practice of tracking the number of presenter no-shows continues  M&E will collaborate with the Committee on Divisional Activities to study options for addressing this problem  Suggestions will be presented at the Boston meeting for implementation in 2008 
It is the intent of M&E to pursue the goal of making our meetings "greener " We will communicate with staff and governance units to identify actions for both the short and long term 
The American Institute of Chemical Engineers (AIChE) and ACS will hold their 2008 spring meetings simultaneously in New Orleans  An ad hoc working group consisting of members from M&E, DAC, and AIChE are actively exploring joint programming opportunities for this meeting 
The Committee on Membership Affairs (MAC) met in executive session on Saturday and Sunday in Chicago and reported that the ACS closed 2006 with 160,491 members, our highest year-end membership count since 2002  Of the 17,857 applications processed in 2006, more than 1,000 came from the Member-Get-a-Member campaign in which many councilors participated  The society's retention rate in 2006 remained strong at 92%  The committee also reported that recruitment for the first two months of 2007 netted 2,844 new applications—729 more than for the same time period last year 
MAC continues to work with deliberate speed on the proposed new bylaw language for members, student members, and society affiliates-the three ways to connect to the society  The committee received input from the Governance Review Task Force and its action teams, the Council Policy Committee, the board of directors, the Committee on Constitution & Bylaws, and several other committees between the San Francisco and Chicago meetings  These interactions have resulted in the current bylaw change recommendations 
In Chicago, representatives from MAC attended several committee meetings and all seven councilor caucuses to summarize the current proposal for membership changes, answer questions, and seek input  In addition, all committee chairs were invited to have their respective committees review these bylaw changes and respond to MAC—if possible—before council met on Wednesday  MAC received 11 responses: eight supported the proposed changes as is, and three supported the proposed language with specified changes or considerations 
The comprehensive petition will likely represent the most significant and voluminous change in the ACS bylaws that has occurred in decades, and MAC is proud to be among the leaders in its development and in efforts to get it right the first time  Hundreds of individuals have contributed to this major effort, since MAC began such discussions at the spring 2004 national meeting 
The Committee on Ethics met in Chicago and discussed the possibility of organizing and scheduling a committee retreat in the near future to enable the committee to move from the current stage of exploring the needs and interests of ACS members to setting priorities for the next few years 
The Project SEED program offers summer research opportunities for high school students from economically disadvantaged families  Since its inception in 1968, the program has had a significant impact on the lives of more than 8,400 students  At the selection meeting in March, the committee approved research projects for 340 SEED I students and 98 SEED II students for this summer in more than 100 institutions 
The 2006 annual assessment surveys from 300 students indicate that 78% of the Project SEED participants are planning to major in a chemistry-related science, and 66% aspire to continue to graduate education  This program is made possible by contributions from industry, academia, local sections, ACS friends and members, the ACS Petroleum Research Fund, and the Project SEED Endowment 
The committee formally submitted a request to ConC to amend the Project SEED acronym and the committee duties described in the Supplementary Information of the "ACS Charter, Constitution, Bylaws & Regulations "
In Chicago, the committee's agenda focused on the ACS Strategic Plan and how Project SEED fits into it, the Program Review Advisory Group (PRAG) review of the Project SEED program, the committee's review of an online application form, and planning of the 40th anniversary celebration to be held at the Philadelphia meeting in the fall of 2008  The committee selected a task force to review the criteria for selection of the Project SEED ChemLuminary Award 
3  Making ACS relevant to technicians 
Last year, CTA, along with the Division of Chemical Technicians, the Committee on Economic & Professional Affairs, and ChemTechLinks, started the Equipping the 2015 Chemical Technology Workforce initiative  This year, the initiative awarded six $500 minigrants to activities and programs that support the educational and professional development of chemical technicians 
We are pleased to announce that the winners of the minigrants are the ACS Division of Environmental Chemistry; the Chemical Technician Program Chair for the 39th ACS Central Regional Meeting in Covington, Ky ; Delta College, University Center, Mich ; Grand Rapids Community College, in Michigan; Mount San Antonio College, Walnut, Calif ; and Southwestern College in Chula Vista, Calif 
The winners are collaborating with industry, academia, and ACS local sections on such activities as chemical technology career fairs for high school students, discussion panels on employability skills for technicians, and technical programming at regional and national meetings on the vital role technicians have in the chemical enterprise 
Because of the enthusiastic response to the minigrants, Equipping the 2015 Chemical Technology Workforce will be supporting another round of minigrants to be distributed in the fall  Details will be available on the website  For more information, go to www ChemTechLinks org and click on "Equipping the 2015 Chemical Technology Workforce "
CTA has also joined with the Joint Subcommittee on Diversity, formerly known as the Collaboration of Committees Working Group  Because this group is focused on increasing diversity in ACS and the chemical enterprise, we believe that this is an opportunity to raise awareness of the value of technicians  CTA looks forward to collaborating on the promotion of traditionally underrepresented chemical professionals 
In 2007, CTA will be placing renewed focus on distribution of the ACS Chemical Technology Student Recognition Award  The award recognizes academic excellence in students preparing for careers as chemical technicians  For more information on the award, please visit the CTA website at chemistry org/committees/cta 
Context 2: \section{Introduction}\label{S1}

The multiple access interferences (MAI) is the root of user
limitation in CDMA systems \cite{R1,R3}  The parallel least mean
square-partial parallel interference cancelation (PLMS-PPIC) method
is a multiuser detector for code division multiple access (CDMA)
receivers which reduces the effect of MAI in bit detection  In this
method and similar to its former versions like LMS-PPIC \cite{R5}
(see also \cite{RR5}), a weighted value of the MAI of other users is
subtracted before making the decision for a specific user in
different stages \cite{cohpaper}  In both of these methods, the
normalized least mean square (NLMS) algorithm is engaged
\cite{Haykin96}  The $m^{\rm th}$ element of the weight vector in
each stage is the true transmitted binary value of the $m^{\rm th}$
user divided by its hard estimate value from the previous stage  The
magnitude of all weight elements in all stages are equal to unity 
Unlike the LMS-PPIC, the PLMS-PPIC method tries to keep this
property in each iteration by using a set of NLMS algorithms with
different step-sizes instead of one NLMS algorithm used in LMS-PPIC 
In each iteration, the parameter estimate of the NLMS algorithm is
chosen whose element magnitudes of cancelation weight estimate have
the best match with unity  In PLMS-PPIC implementation it is assumed
that the receiver knows the phases of all user channels  However in
practice, these phases are not known and should be estimated  In
this paper we improve the PLMS-PPIC procedure \cite{cohpaper} in
such a way that when there is only a partial information of the
channel phases, this modified version simultaneously estimates the
phases and the cancelation weights  The partial information is the
quarter of each channel phase in $(0,2\pi)$ 

The rest of the paper is organized as follows: In section \ref{S4}
the modified version of PLMS-PPIC with capability of channel phase
estimation is introduced  In section \ref{S5} some simulation
examples illustrate the results of the proposed method  Finally the
paper is concluded in section \ref{S6} 

\section{Multistage Parallel Interference Cancelation: Modified PLMS-PPIC Method}\label{S4}

We assume $M$ users synchronously send their symbols
$\alpha_1,\alpha_2,\cdots,\alpha_M$ via a base-band CDMA
transmission system where $\alpha_m\in\{-1,1\}$  The $m^{th}$ user
has its own code $p_m( )$ of length $N$, where $p_m(n)\in \{-1,1\}$,
for all $n$  It means that for each symbol $N$ bits are transmitted
by each user and the processing gain is equal to $N$  At the
receiver we assume that perfect power control scheme is applied 
Without loss of generality, we also assume that the power gains of
all channels are equal to unity and users' channels do not change
during each symbol transmission (it can change from one symbol
transmission to the next one) and the channel phase $\phi_m$ of
$m^{th}$ user is unknown for all $m=1,2,\cdots,M$ (see
\cite{cohpaper} for coherent transmission)  According to the above
assumptions the received signal is
\begin{equation}
\label{e1} r(n)=\sum\limits_{m=1}^{M}\alpha_m
e^{j\phi_m}p_m(n)+v(n),~~~~n=1,2,\cdots,N,
\end{equation}
where $v(n)$ is the additive white Gaussian noise with zero mean and
variance $\sigma^2$  Multistage parallel interference cancelation
method uses $\alpha^{s-1}_1,\alpha^{s-1}_2,\cdots,\alpha^{s-1}_M$,
the bit estimates outputs of the previous stage, $s-1$, to estimate
the related MAI of each user  It then subtracts it from the received
signal $r(n)$ and makes a new decision on each user variable
individually to make a new variable set
$\alpha^{s}_1,\alpha^{s}_2,\cdots,\alpha^{s}_M$ for the current
stage $s$  Usually the variable set of the first stage (stage $0$)
is the output of a conventional detector  The output of the last
stage is considered as the final estimate of transmitted bits  In
the following we explain the structure of a modified version of the
PLMS-PIC method \cite{cohpaper} with simultaneous capability of
estimating the cancelation weights and the channel phases 

Assume $\alpha_m^{(s-1)}\in\{-1,1\}$ is a given estimate of
$\alpha_m$ from stage $s-1$  Define
\begin{equation}
\label{e6} w^s_{m}=\frac{\alpha_m}{\alpha_m^{(s-1)}}e^{j\phi_m} 
\end{equation}
From (\ref{e1}) and (\ref{e6}) we have
\begin{equation}
\label{e7} r(n)=\sum\limits_{m=1}^{M}w^s_m\alpha^{(s-1)}_m
p_m(n)+v(n) 
\end{equation}
Define
\begin{subequations}
\begin{eqnarray}
\label{e8} W^s&=&[w^s_{1},w^s_{2},\cdots,w^s_{M}]^T,\\
\label{e9}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!X^{s}(n)\!\!\!&=&\!\!\![\alpha^{(s-1)}_1p_1(n),\alpha^{(s-1)}_2p_2(n),\cdots,\alpha^{(s-1)}_Mp_M(n)]^T 
\end{eqnarray}
\end{subequations}
where $T$ stands for transposition  From equations (\ref{e7}),
(\ref{e8}) and (\ref{e9}), we have
\begin{equation}
\label{e10} r(n)=W^{s^T}X^{s}(n)+v(n) 
\end{equation}
Given the observations $\{r(n),X^{s}(n)\}^{N}_{n=1}$, in modified
PLMS-PPIC, like the PLMS-PPIC \cite{cohpaper}, a set of NLMS
adaptive algorithm are used to compute
\begin{equation}
\label{te1} W^{s}(N)=[w^{s}_1(N),w^{s}_2(N),\cdots,w^{s}_M(N)]^T,
\end{equation}
which is an estimate of $W^s$ after iteration $N$  To do so, from
(\ref{e6}), we have
\begin{equation}
\label{e13} |w^s_{m}|=1 ~~~m=1,2,\cdots,M,
\end{equation}
which is equivalent to
\begin{equation}
\label{e14} \sum\limits_{m=1}^{M}||w^s_{m}|-1|=0 
\end{equation}
We divide $\Psi=\left(0,1-\sqrt{\frac{M-1}{M}}\right]$, a sharp
range for $\mu$ (the step-size of the NLMS algorithm) given in
\cite{sg2005}, into $L$ subintervals and consider $L$ individual
step-sizes $\Theta=\{\mu_1,\mu_2,\cdots,\mu_L\}$, where
$\mu_1=\frac{1-\sqrt{\frac{M-1}{M}}}{L}, \mu_2=2\mu_1,\cdots$, and
$\mu_L=L\mu_1$  In each stage, $L$ individual NLMS algorithms are
executed ($\mu_l$ is the step-size of the $l^{th}$ algorithm)  In
stage $s$ and at iteration $n$, if
$W^{s}_k(n)=[w^s_{1,k},\cdots,w^s_{M,k}]^T$, the parameter estimate
of the $k^{\rm th}$ algorithm, minimizes our criteria, then it is
considered as the parameter estimate at time iteration $n$  In other
words if the next equation holds
\begin{equation}
\label{e17} W^s_k(n)=\arg\min\limits_{W^s_l(n)\in I_{W^s}
}\left\{\sum\limits_{m=1}^{M}||w^s_{m,l}(n)|-1|\right\},
\end{equation}
where $W^{s}_l(n)=W^{s}(n-1)+\mu_l \frac{X^s(n)}{\|X^s(n)\|^2}e(n),
~~~ l=1,2,\cdots,k,\cdots,L-1,L$ and
$I_{W^s}=\{W^s_1(n),\cdots,W^s_L(n)\}$, then we have
$W^s(n)=W^s_k(n)$, and therefore all other algorithms replace their
weight estimate by $W^{s}_k(n)$  At time instant $n=N$, this
procedure gives $W^s(N)$, the final estimate of $W^s$, as the true
parameter of stage $s$ 

Now consider $R=(0,2\pi)$ and divide it into four equal parts
$R_1=(0,\frac{\pi}{2})$, $R_2=(\frac{\pi}{2},\pi)$,
$R_3=(\pi,\frac{3\pi}{2})$ and $R_4=(\frac{3\pi}{2},2\pi)$  The
partial information of channel phases (given by the receiver) is in
a way that it shows each $\phi_m$ ($m=1,2,\cdots,M$) belongs to
which one of the four quarters $R_i,~i=1,2,3,4$  Assume
$W^{s}(N)=[w^{s}_1(N),w^{s}_2(N),\cdots,w^{s}_M(N)]^T$ is the weight
estimate of the modified algorithm PLMS-PPIC at time instant $N$ of
the stage $s$  From equation (\ref{e6}) we have
\begin{equation}
\label{tt3}
\phi_m=\angle({\frac{\alpha^{(s-1)}_m}{\alpha_m}w^s_m}) 
\end{equation}
We estimate $\phi_m$ by $\hat{\phi}^s_m$, where
\begin{equation}
\label{ee3}
\hat{\phi}^s_m=\angle{(\frac{\alpha^{(s-1)}_m}{\alpha_m}w^s_m(N))} 
\end{equation}
Because $\frac{\alpha^{(s-1)}_m}{\alpha_m}=1$ or $-1$, we have
\begin{eqnarray}
\hat{\phi}^s_m=\left\{\begin{array}{ll} \angle{w^s_m(N)} &
\mbox{if}~
\frac{\alpha^{(s-1)}_m}{\alpha_m}=1\\
\pm\pi+\angle{w^s_m(N)} & \mbox{if}~
\frac{\alpha^{(s-1)}_m}{\alpha_m}=-1\end{array}\right 
\end{eqnarray}
Hence $\hat{\phi}^s_m\in P^s=\{\angle{w^s_m(N)},
\angle{w^s_m(N)+\pi, \angle{w^s_m(N)}-\pi}\}$  If $w^s_m(N)$
sufficiently converges to its true value $w^s_m$, the same region
for $\hat{\phi}^s_m$ and $\phi_m$ is expected  In this case only one
of the three members of $P^s$ has the same region as $\phi_m$  For
example if $\phi_m \in (0,\frac{\pi}{2})$, then $\hat{\phi}^s_m \in
(0,\frac{\pi}{2})$ and therefore only $\angle{w^s_m(N)}$ or
$\angle{w^s_m(N)}+\pi$ or $\angle{w^s_m(N)}-\pi$ belongs to
$(0,\frac{\pi}{2})$  If, for example, $\angle{w^s_m(N)}+\pi$ is such
a member between all three members of $P^s$, it is the best
candidate for phase estimation  In other words,
\[\phi_m\approx\hat{\phi}^s_m=\angle{w^s_m(N)}+\pi \]
We admit that when there is a member of $P^s$ in the quarter of
$\phi_m$, then $w^s_m(N)$ converges  What would happen when non of
the members of $P^s$ has the same quarter as $\phi_m$? This
situation will happen when the absolute difference between $\angle
w^s_m(N)$ and $\phi_m$ is greater than $\pi$  It means that
$w^s_m(N)$ has not converged yet  In this case where we can not
count on $w^s_m(N)$, the expected value is the optimum choice for
the channel phase estimation, e g  if $\phi_m \in (0,\frac{\pi}{2})$
then $\frac{\pi}{4}$ is the estimation of the channel phase
$\phi_m$, or if $\phi_m \in (\frac{\pi}{2},\pi)$ then
$\frac{3\pi}{4}$ is the estimation of the channel phase $\phi_m$ 
The results of the above discussion are summarized in the next
equation
\begin{eqnarray}
\nonumber \hat{\phi}^s_m = \left\{\begin{array}{llll} \angle
{w^s_m(N)} & \mbox{if}~
\angle{w^s_m(N)}, \phi_m\in R_i,~~i=1,2,3,4\\
\angle{w^s_m(N)}+\pi & \mbox{if}~ \angle{w^s_m(N)}+\pi, \phi_m\in
R_i,~~i=1,2,3,4\\
\angle{w^n_m(N)}-\pi & \mbox{if}~ \angle{w^s_m(N)}-\pi, \phi_m\in
R_i,~~i=1,2,3,4\\
\frac{(i-1)\pi+i\pi}{4} & \mbox{if}~ \phi_m\in
R_i,~~\angle{w^s_m(N)},\angle
{w^s_m(N)}\pm\pi\notin R_i,~~i=1,2,3,4 \\
\end{array}\right 
\end{eqnarray}
Having an estimation of the channel phases, the rest of the proposed
method is given by estimating $\alpha^{s}_m$ as follows:
\begin{equation}
\label{tt4}
\alpha^{s}_m=\mbox{sign}\left\{\mbox{real}\left\{\sum\limits_{n=1}^{N}
q^s_m(n)e^{-j\hat{\phi}^s_m}p_m(n)\right\}\right\},
\end{equation}
where
\begin{equation} \label{tt5}
q^{s}_{m}(n)=r(n)-\sum\limits_{m^{'}=1,m^{'}\ne
m}^{M}w^{s}_{m^{'}}(N)\alpha^{(s-1)}_{m^{'}} p_{m^{'}}(n) 
\end{equation}
The inputs of the first stage $\{\alpha^{0}_m\}_{m=1}^M$ (needed for
computing $X^1(n)$) are given by
\begin{equation}
\label{qte5}
\alpha^{0}_m=\mbox{sign}\left\{\mbox{real}\left\{\sum\limits_{n=1}^{N}
r(n)e^{-j\hat{\phi}^0_m}p_m(n)\right\}\right\}



ground_truth: There are 14,520 attendees, including 7,152 chemical scientists, 5,059 students, 1,283 exhibitors, 119 precollege teachers, 573 exposition visitors, and 453 guests.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What algorithm is engaged in the PLMS-PPIC method?

Read the following text and answer briefly.

Context 2: 
\end{equation}
Assuming $\phi_m\in R_i$, then
\begin{equation}
\label{qqpp} \hat{\phi}^0_m =\frac{(i-1)\pi+i\pi}{4} 
\end{equation}
Table \ref{tab4} shows the structure of the modified PLMS-PPIC
method  It is to be notified that
\begin{itemize}
\item Equation (\ref{qte5}) shows the conventional bit detection
method when the receiver only knows the quarter of channel phase in
$(0,2\pi)$  \item With $L=1$ (i e  only one NLMS algorithm), the
modified PLMS-PPIC can be thought as a modified version of the
LMS-PPIC method 
\end{itemize}

In the following section some examples are given to illustrate the
effectiveness of the proposed method 

\section{Simulations}\label{S5}

In this section we have considered some simulation examples 
Examples \ref{ex2}-\ref{ex4} compare the conventional, the modified
LMS-PPIC and the modified PLMS-PPIC methods in three cases: balanced
channels, unbalanced channels and time varying channels  In all
examples, the receivers have only the quarter of each channel phase 
Example \ref{ex2} is given to compare the modified LMS-PPIC and the
PLMS-PPIC in the case of balanced channels 

\begin{example}{\it Balanced channels}:
\label{ex2}
\begin{table}
\caption{Channel phase estimate of the first user (example
\ref{ex2})} \label{tabex5} \centerline{{
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{6}{*}{\rotatebox{90}{$\phi_m=\frac{3\pi}{8},M=15~~$}} & N(Iteration) & Stage Number& NLMS & PNLMS  \\
&&&&\\
\cline{2-5} & \multirow{2}{*}{64}& s = 2 &  $\hat{\phi}^s_m=\frac{3 24\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 18\pi}{8}$ \\
\cline{3-5} & & s = 3 & $\hat{\phi}^s_m=\frac{3 24\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 18\pi}{8}$ \\
\cline{2-5} & \multirow{2}{*}{256}& s = 2 &  $\hat{\phi}^s_m=\frac{2 85\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 88\pi}{8}$ \\
\cline{3-5} & & s = 3 & $\hat{\phi}^s_m=\frac{2 85\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 88\pi}{8}$ \\
\cline{2-5} \hline
\end{tabular} }}
\end{table}
Consider the system model (\ref{e7}) in which $M$ users
synchronously send their bits to the receiver through their
channels  It is assumed that each user's information consists of
codes of length $N$  It is also assumd that the signal to noise
ratio (SNR) is 0dB  In this example there is no power-unbalanced or
channel loss is assumed  The step-size of the NLMS algorithm in
modified LMS-PPIC method is $\mu=0 1(1-\sqrt{\frac{M-1}{M}})$ and
the set of step-sizes of the parallel NLMS algorithms in modified
PLMS-PPIC method are
$\Theta=\{0 01,0 05,0 1,0 2,\cdots,1\}(1-\sqrt{\frac{M-1}{M}})$,
i e  $\mu_1=0 01(1-\sqrt{\frac{M-1}{M}}),\cdots,
\mu_4=0 2(1-\sqrt{\frac{M-1}{M}}),\cdots,
\mu_{12}=(1-\sqrt{\frac{M-1}{M}})$  Figure~\ref{Figexp1NonCoh}
illustrates the bit error rate (BER) for the case of two stages and
for $N=64$ and $N=256$  Simulations also show that there is no
remarkable difference between results in two stage and three stage
scenarios  Table~\ref{tabex5} compares the average channel phase
estimate of the first user in each stage and over $10$ runs of
modified LMS-PPIC and PLMS-PPIC, when the the number of users is
$M=15$ 
\end{example}

Although LMS-PPIC and PLMS-PPIC, as well as their modified versions,
are structured based on the assumption of no near-far problem
(examples \ref{ex3} and \ref{ex4}), these methods and especially the
second one have remarkable performance in the cases of unbalanced
and/or time varying channels 

\begin{example}{\it Unbalanced channels}:
\label{ex3}
\begin{table}
\caption{Channel phase estimate of the first user (example
\ref{ex3})} \label{tabex6} \centerline{{
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{6}{*}{\rotatebox{90}{$\phi_m=\frac{3\pi}{8},M=15~~$}} & N(Iteration) & Stage Number& NLMS & PNLMS  \\
&&&&\\
\cline{2-5} & \multirow{2}{*}{64}& s=2 &  $\hat{\phi}^s_m=\frac{2 45\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 36\pi}{8}$ \\
\cline{3-5} & & s=3 & $\hat{\phi}^s_m=\frac{2 71\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 80\pi}{8}$ \\
\cline{2-5} & \multirow{2}{*}{256}& s=2 &  $\hat{\phi}^s_m=\frac{3 09\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 86\pi}{8}$ \\
\cline{3-5} & & s=3 & $\hat{\phi}^s_m=\frac{2 93\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 01\pi}{8}$ \\
\cline{2-5} \hline
\end{tabular} }}
\end{table}
Consider example \ref{ex2} with power unbalanced and/or channel loss
in transmission system, i e  the true model at stage $s$ is
\begin{equation}
\label{ve7} r(n)=\sum\limits_{m=1}^{M}\beta_m
w^s_m\alpha^{(s-1)}_m c_m(n)+v(n),
\end{equation}
where $0<\beta_m\leq 1$ for all $1\leq m \leq M$  Both the LMS-PPIC
and the PLMS-PPIC methods assume the model (\ref{e7}), and their
estimations are based on observations $\{r(n),X^s(n)\}$, instead of
$\{r(n),\mathbf{G}X^s(n)\}$, where the channel gain matrix is
$\mathbf{G}=\mbox{diag}(\beta_1,\beta_2,\cdots,\beta_m)$  In this
case we repeat example \ref{ex2}  We randomly get each element of
$G$ from $[0,0 3]$  Figure~\ref{Figexp2NonCoh} illustrates the BER
versus the number of users  Table~\ref{tabex6} compares the channel
phase estimate of the first user in each stage and over $10$ runs of
modified LMS-PPIC and modified PLMS-PPIC for $M=15$ 
\end{example}

\begin{example}
\label{ex4} {\it Time varying channels}: Consider example \ref{ex2}
with time varying Rayleigh fading channels  In this case we assume
the maximum Doppler shift of $40$HZ, the three-tap
frequency-selective channel with delay vector of $\{2\times
10^{-6},2 5\times 10^{-6},3\times 10^{-6}\}$sec and gain vector of
$\{-5,-3,-10\}$dB  Figure~\ref{Figexp3NonCoh} shows the average BER
over all users versus $M$ and using two stages 
\end{example}


\section{Conclusion}\label{S6}

In this paper, parallel interference cancelation using adaptive
multistage structure and employing a set of NLMS algorithms with
different step-sizes is proposed, when just the quarter of the
channel phase of each user is known  In fact, the algorithm has been
proposed for coherent transmission with full information on channel
phases in \cite{cohpaper}  This paper is a modification on the
previously proposed algorithm  Simulation results show that the new
method has a remarkable performance for different scenarios
including Rayleigh fading channels even if the channel is
unbalanced 





ground_truth: The normalized least mean square (NLMS) algorithm.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the average magnetic moment per column in Ge$_{1-x}$Mn$_{x}$ films?

Read the following text and answer briefly.

Context 3: \section{introduction}
In the past few years, the synthesis of ferromagnetic semiconductors has become a major challenge for spintronics  Actually, growing a magnetic and semiconducting material could lead to promising advances like spin injection into non magnetic semiconductors, or electrical manipulation of carrier induced magnetism in magnetic semiconductors \cite{ohno00,Bouk02}  Up to now, major efforts have focused on diluted magnetic semiconductors (DMS) in which the host semiconducting matrix is randomly substituted by transition metal (TM) ions such as Mn, Cr, Ni, Fe or Co \cite{Diet02}  However Curie temperatures ($T_{C}$) in DMS remain rather low and TM concentrations must be drastically raised in order to increase $T_{C}$ up to room temperature  That usually leads to phase separation and the formation of secondary phases  It was recently shown that phase separation induced by spinodal decomposition could lead to a significant increase of $T_{C}$ \cite{Diet06,Fuku06}  For semiconductors showing $T_{C}$ higher than room temperature one can foresee the fabrication of nanodevices such as memory nanodots, or nanochannels for spin injection  Therefore, the precise control of inhomogeneities appears as a new challenge which may open a way to industrial applications of ferromagnetism in semiconductors 

The increasing interest in group-IV magnetic semiconductors can also be explained by their potential compatibility with the existing silicon technology  In 2002, carrier mediated ferromagnetism was reported in  MBE grown Ge$_{0 94}$Mn$_{0 06}$ films by Park \textit{et al } \cite{Park02}  The maximum critical temperature was 116 K  Recently many publications indicate a significant increase of $T_{C}$ in Ge$_{1-x}$Mn$_{x}$ material depending on growth conditions \cite{Pint05,Li05,tsui03}  Cho \textit{et al } reported a Curie temperature as high as 285 K \cite{Cho02}  
Taking into account the strong tendency of Mn ions to form intermetallic compounds in germanium, a detailed investigation of the nanoscale structure is required  Up to now, only a few studies have focused on the nanoscale composition in Ge$_{1-x}$Mn$_{x}$ films  Local chemical inhomogeneities have been recently reported by Kang \textit{et al } \cite{Kang05} who evidenced a micrometer scale segregation of manganese in large Mn rich stripes  Ge$_3$Mn$_5$ as well as Ge$_8$Mn$_{11}$ clusters embedded in a germanium matrix have been reported by many authors  However, Curie temperatures never exceed 300 K \cite{Bihl06,Morr06,Pass06,Ahle06}  Ge$_3$Mn$_5$ clusters exhibit a Curie temperature of 296 K \cite{Mass90}  This phase frequently observed in Ge$_{1-x}$Mn$_{x}$ films is the most stable (Ge,Mn) alloy  The other stable compound Ge$_8$Mn$_{11}$ has also been observed in nanocrystallites surrounded with pure germanium \cite{Park01}  Ge$_8$Mn$_{11}$ and Ge$_3$Mn$_5$ phases are ferromagnetic but their metallic character considerably complicates their potential use as spin injectors 
Recently, some new Mn-rich nanostructures have been evidenced in Ge$_{1-x}$Mn$_{x}$ layers  Sugahara \textit{et al } \cite{Sugh05} reported the formation of high Mn content (between 10 \% and 20 \% of Mn) amorphous Ge$_{1-x}$Mn$_x$ precipitates  in a Mn-free germanium matrix  Mn-rich coherent cubic clusters were observed by Ahlers \textit{et al } \cite{Ahle06} which exhibit a Curie temperatures below 200 K  Finally, high-$T_{C}$ ($>$ 400 K) Mn-rich nanocolumns have been evidenced \cite{Jame06} which could lead to silicon compatible room temperature operational devices \\
In the present paper, we investigate the structural and magnetic properties of Ge$_{1-x}$Mn$_x$ thin films for low growth temperatures ($<$ 200$^{\circ}$C) and low Mn concentrations (between 1 \% and 11 \%)  By combining TEM, x-Ray diffraction and SQUID magnetometry, we could identify different magnetic phases  We show that depending on growth conditions, we obtain either Mn-rich nanocolumns or Ge$_{3}$Mn$_{5}$ clusters embedded in a germanium matrix  We discuss the structural and magnetic properties of these nanostructures as a function of manganese concentration and growth temperature  We also discuss the magnetic anisotropy of nanocolumns and  
Ge$_3$Mn$_5$ clusters  

\section{Sample growth}

Growth was performed using solid sources molecular beam epitaxy (MBE) by co-depositing Ge and Mn evaporated from standard Knudsen effusion cells   Deposition rate was low ($\approx$ 0 2 \AA s$^{-1}$)  Germanium substrates were epi-ready Ge(001) wafers with a residual n-type doping and resistivity of 10$^{15}$ cm$^{-3}$ and 5 $\Omega cm$ respectively  After thermal desorption of the surface oxide, a 40 nm thick Ge buffer layer was grown at 250$^{\circ}$C, resulting in a 2 $\times$ 1 surface reconstruction as observed by reflection high energy electron diffraction (RHEED) (see Fig  1a)  Next, 80 nm thick Ge$_{1-x}$Mn$_{x}$ films were subsequently grown  at low substrate temperature (from 80$^{\circ}$C to 200$^{\circ}$C)  Mn content has been determined by x-ray fluorescence measurements performed on thick samples ($\approx$ 1 $\mu m$ thick) and complementary Rutherford Back Scattering (RBS) on thin Ge$_{1-x}$Mn$_{x}$ films grown on silicon  Mn concentrations range from 1 \% to 11\% Mn 

For Ge$_{1-x}$Mn$_{x}$ films grown at substrate temperatures below 180$^{\circ}$C, after the first monolayer (ML) deposition, the  2 $\times$ 1 surface reconstruction almost totally disappears  After depositing few MLs, a slightly diffuse 1 $\times$ 1 streaky RHEED pattern and a very weak 2 $\times$ 1 reconstruction (Fig  1b) indicate a predominantly two-dimensional growth  For growth temperatures above 180$^{\circ}$C additional spots appear in the RHEED pattern during the Ge$_{1-x}$Mn$_{x}$ growth (Fig  1c)  These spots may correspond to the formation of very small secondary phase crystallites  The nature of these crystallites will be discussed below 

Transmission electron microscopy (TEM) observations were performed using a JEOL 4000EX microscope with an acceleration voltage of 400 kV  Energy filtered transmission electron microscopy (EFTEM) was done using a JEOL 3010 microscope equipped with a Gatan Image Filter   Sample preparation was carried out by standard mechanical polishing and argon ion milling for cross-section investigations and plane views were prepared by wet etching with H$_3$PO$_4$-H$_2$O$_2$ solution \cite{Kaga82} 

\begin{figure}[htb]
    \center
    \includegraphics[width= 29\linewidth]{ /fig1a eps}
    \includegraphics[width= 29\linewidth]{ /fig1b eps}
    \includegraphics[width= 29\linewidth]{ /fig1c eps}
    \caption{RHEED patterns recorded during the growth of Ge$_{1-x}$Mn$_{x}$ films: (a) 2 $\times$ 1 surface reconstruction of the germanium buffer layer  (b) 1 $\times$ 1 streaky RHEED pattern obtained at low growth temperatures ($T_g<$180$^{\circ}$C)  (c) RHEED pattern of a sample grown at $T_g=$180$^{\circ}$C  The additional spots reveal the presence of Ge$_3$Mn$_5$ clusters at the surface of the film }
\label{fig1}
\end{figure}

\section{Structural properties \label{structural}}

\begin{figure}[htb]
    \center
	\includegraphics[width= 49\linewidth]{ /fig2a eps}
	\includegraphics[width= 49\linewidth]{ /fig2b eps}
	 \includegraphics[width= 49\linewidth]{ /fig2c eps}
	 \includegraphics[width= 49\linewidth]{ /fig2d eps}
    \caption{Transmission electron micrographs of a Ge$_{1-x}$Mn$_{x}$ film grown at 130$^{\circ}$C and containing 6 \% of manganese  (a) cross-section along the [110] axis : we clearly see the presence of nanocolumns elongated along the growth axis  (b) High resolution image of the interface between the Ge$_{1-x}$Mn$_{x}$ film and the Ge buffer layer  The Ge$_{1-x}$Mn$_{x}$ film exhibits the same diamond structure as pure germanium  No defect can be seen which could be caused by the presence of nanocolumns  (c) Plane view micrograph performed on the same sample confirms the columnar structure and gives the density and size distribution of nanocolumns  (d) Mn chemical map obtained by energy filtered transmission electron microcopy (EFTEM)  The background was carefully substracted from pre-edge images  Bright areas correspond to Mn-rich regions }
\label{fig2}
\end{figure}

In samples grown at 130$^{\circ}$C and containing 6 \% Mn, we can observe vertical elongated nanostructures \textit{i e } nanocolumns as shown in Fig  2a  Nanocolumns extend through the whole Ge$_{1-x}$Mn$_{x}$ film thickness  From the high resolution TEM image shown in Fig  2b, we deduce their average diameter around 3 nm  Moreover in Fig  2b, the interface between the Ge buffer layer and the Ge$_{1-x}$Mn$_{x}$ film is flat and no defect propagates from the interface into the film  The Ge$_{1-x}$Mn$_{x}$ film is a perfect single crystal in epitaxial relationship with the substrate  In Fig  2c is shown a plane view micrograph of the same sample confirming the presence of nanocolumns in the film  From this image, we can deduce the size and density of nanocolumns  The nanocolumns density is 13000 $\rm{\mu m}^{-2}$ with a mean diameter of 3 nm which is coherent with cross-section measurements  In order to estimate the chemical composition of these nanocolumns, we further performed chemical mapping using EFTEM  In Fig  2d we show a cross sectional Mn chemical map of the Ge$_{1-x}$Mn$_{x}$ film  This map shows that the formation of nanocolumns is a consequence of Mn segregation  Nanocolumns are Mn rich and the surrounding matrix is Mn poor  However, it is impossible to deduce the Mn concentration in Ge$_{1-x}$Mn$_{x}$ nanocolumns from this cross section  Indeed, in cross section observations, the columns diameter is much smaller than the probed film thickness and the signal comes from the superposititon of the Ge matrix and Mn-rich nanocolumns  In order to quantify Mn concentration inside the nanocolumns and inside the Ge matrix, EELS measurements (not shown here) have been performed in a plane view geometry \cite{Jame06}  These observations revealed that the matrix Mn content is below 1 \% (detection limit of our instrument)  Measuring the surface occupied by the matrix and the nanocolumns in plane view TEM images, and considering the average Mn concentration in the sample (6 \%), we can estimate the Mn concentration in the nanocolumns  The Mn concentration measured by EELS being between 0\% and 1\%, we can conclude that the Mn content in the nanocolumns is between 30 \% and 38 \% \\
For samples grown between 80$^\circ$C and 150$^\circ$C cross section and plane view TEM observations reveal the presence of Mn rich nanocolumns surrounded with a Mn poor Ge matrix  In order to investigate the influence of Mn concentration on the structural properties of Ge$_{1-x}$Mn$_{x}$ films, ten samples have been grown at 100$^\circ$C and at 150$^\circ$C with Mn concentrations of 1 3 \%, 2 3 \%, 4 \%, 7 \% and 11 3 \%  Their structural properties have been investigated by plane view TEM observations  

\begin{figure}[htb]
    \center
    \includegraphics[width= 98\linewidth]{ /fig3a eps}
	\includegraphics[width= 45\linewidth]{ /fig3b eps}
		\includegraphics[width= 45\linewidth]{ /fig3c eps}
    \caption{Nanocolumns size and density as a function of growth conditions  Samples considered have been grown at 100$^{\circ}$C and 150$^{\circ}$C respectively  (a) Mn concentration dependence of the size distribution  (b) columns density as a function of Mn concentration  (c) Volume fraction of the nanocolumns as a function of Mn concentration }
 \label{fig3}
\end{figure}

For samples grown at 100$^\circ$C with Mn concentrations below 5 \% the nanocolumns mean diameter is 1 8$\pm$0 2 nm  The evolution of columns density as a fonction of Mn concentration is reported in figure 3b  By increasing the Mn concentration from 1 3 \% to 4 \% we observe a significant increase of the columns density from 13000 to 30000 $\rm{\mu m}^{-2}$  For Mn concentrations higher than 5 \% the density seems to reach a plateau corresponding to 35000 $\rm{\mu m}^{-2}$ and their diameter slightly increases from 1 8 nm at 4 \% to 2 8 nm at 11 3 \%  By plotting the volume fraction occupied by the columns in the film as a function of Mn concentration, we observe a linear dependence for Mn contents below 5 \%  The non-linear behavior above 5 \% may indicate that the mechanism of Mn incorporation is different in this concentration range, leading to an increase of Mn concentration in the columns or in the matrix  For samples grown at 100$^\circ$C, nanocolumns are always fully coherent with the surrounding matrix (Fig  4a)  

Increasing the Mn content in the samples grown at 150$^\circ$C from 1 3 \% to 11 3 \% leads to a decrease of the columns density (fig 3b)  Moreover, their average diameter increases significantly and size distributions become very broad (see Fig  3a)  For the highest Mn concentration (11 3 \%) we observe the coexistence of very small columns with a diameter of 2 5 nm and very large columns with a diameter of 9 nm  In samples grown at 150$^\circ$C containing 11 3 \% of Mn, the crystalline structure of nanocolumns is also highly modified  In plane view TEM micrographs, one can see columns exhibiting several different crystalline structures  We still observe some columns which are fully coherent with the Ge matrix like in the samples grown at lower temperature  Nevertheless, observations performed on these samples grown at 150$^\circ$C and with 11 3\% Mn reveal some uniaxially \cite{Jame06} or fully relaxed columns exhibiting a misfit of 4 \% between the matrix and the columns and leading to misfit dislocations at the interface between the column and the matrix (see fig  4b)  Thus we can conclude that coherent columns are probably in strong compression and the surrounding matrix in tension  On the same samples (T$_g$=150$^{\circ}$C, 11 3\% Mn), we also observe a large number of highly disordered nanocolumns leading to an amorphous like TEM contrast(fig  4c) 

\begin{figure}[htb]
    \center
   \includegraphics[width= 31\linewidth]{ /fig4a eps}
	\includegraphics[width= 31\linewidth]{ /fig4b eps}
	\includegraphics[width= 31\linewidth]{ /fig4c eps}
    \caption{Plane view high resolution transmission electron micrographs of different types of nanocolumns : (a) typical structure of a column grown at 100$^{\circ}$C  The crystal structure is exactly the same as germanium   (b) Partially relaxed nanocolumn  One can see dislocations at the interface between the columns and the matrix leading to stress relaxation  (c) Amorphous nanocolumn  These columns are typical in samples grown at 150$^{\circ}$C with high Mn contents }
 \label{fig4}
\end{figure}

In conclusion, we have evidenced a complex mechanism of Mn incorporation in Mn doped Ge films grown at low temperature  In particular Mn incorporation is highly inhomogeneous  For very low growth temperatures (below 120$^\circ$C) the diffusion of Mn atoms leads to the formation of Mn rich, vertical nanocolumns  Their density mostly depends on Mn concentration and their mean diameter is about 2 nm  These results can be compared with the theoretical predictions of Fukushima \textit{et al } \cite{Fuku06}: they proposed a model of spinodal decomposition in (Ga,Mn)N and (Zn,Cr)Te based on layer by layer growth conditions and a strong pair attraction between Mn atoms which leads to the formation of nanocolumns  This model may also properly describe the formation of Mn rich nanocolumns in our samples  Layer by layer growth conditions can be deduced from RHEED pattern evolution during growth  For all the samples grown at low temperature, RHEED observations clearly indicate two-dimensional growth  Moreover, Ge/Ge$_{1-x}$Mn$_{x}$/Ge heterostructures have been grown and observed by TEM (see Fig  5)  Ge$_{1-x}$Mn$_{x}$/Ge (as well as Ge/Ge$_{1-x}$Mn$_{x}$) interfaces are very flat and sharp thus confirming a two-dimensional, layer by layer growth mode  Therefore we can assume that the formation of Mn rich nanocolumns is a consequence of 2D-spinodal decomposition 

\begin{figure}[htb]
    \center
	\includegraphics[width= 7\linewidth]{ /fig5 eps}
    \caption{Cross section high resolution micrograph of a Ge/Ge$_{1-x}$Mn$_{x}$/Ge/Ge$_{1-x}$Mn$_{x}$/Ge heterostructure  This sample has been grown at 130 $^{\circ}$C with 6\% Mn  Ge$_{1-x}$Mn$_{x}$ layers are 15 nm thick and Ge spacers 5 nm thick  We clearly see the sharpness of both Ge$_{1-x}$Mn$_{x}$/Ge and Ge/Ge$_{1-x}$Mn$_{x}$ interfaces  Mn segregation leading to the columns formation already takes place in very thin Ge$_{1-x}$Mn$_{x}$ films }
\label{fig5}
\end{figure}

For growth temperatures higher than 160$^\circ$C, cross section TEM and EFTEM observations (not shown here) reveal the coexistence of two Mn-rich phases: nanocolumns and Ge$_{3}$Mn$_{5}$ nanoclusters embedded in the germanium matrix  A typical high resolution TEM image is shown in figure 6  
Ge$_{3}$Mn$_{5}$ clusters are not visible in RHEED patterns for temperatures below 180$^\circ$C  To investigate the nature of these clusters, we performed x-ray diffraction in $\theta-2\theta$ mode  Diffraction scans were acquired on a high resolution diffractometer using the copper K$_\alpha$ radiation and on the GMT station of the BM32 beamline at the European Synchrotron Radiation Facility (ESRF)  Three samples grown at different temperatures and/or annealed at high temperature were investigated  The two first samples are Ge$_{1-x}$Mn$_{x}$ films grown at 130$^\circ$C and 170$^\circ$C respectively  The third one has been grown at 130$^\circ$C and post-growth annealed at 650$^\circ$C  By analysing x-ray diffraction spectra, we can evidence two different crystalline structures  For the sample grown at 130$^\circ$C, the $\theta-2\theta$ scan only reveals the (004) Bragg peak of the germanium crystal, confirming the good epitaxial relationship between the layer and the substrate, and the absence of secondary phases in the film in spite of a high dynamics of the order of 10$^7$  For both samples grown at 170$^\circ$C and annealed at 650$^\circ$C, $\theta-2\theta$ spectra are identical  In addition to the (004) peak of germanium, we observe three additional weak peaks  The first one corresponds to the (002) germanium forbidden peak which probably comes from a small distortion of the germanium crystal, and the two other peaks are respectively attributed to the (002) and (004) Bragg peaks of a secondary phase  The $c$ lattice parameter of Ge$_3$Mn$_5$ hexagonal crystal is 5 053 \AA \ \cite{Fort90} which is in very good agreement with the values obtained from diffraction data for both (002) and (004) lines assuming that the $c$ axis of Ge$_3$Mn$_5$ is along the [001] direction of the Ge substrate 

\begin{figure}[htb]
    \center
	\includegraphics[width= 7\linewidth]{ /fig6 eps}
	\caption{Cross section high resolution transmission electron micrograph of a sample grown at 170$^{\circ}$C  We observe the coexistence of two different Mn-rich phases: Ge$_{1-x}$Mn$_{x}$ nanocolumns and Ge$_3$Mn$_5$ clusters }
\label{fig6}
\end{figure}

In summary, in a wide range of growth temperatures and Mn concentrations, we have evidenced a two-dimensional spinodal decomposition leading to the formation of Mn-rich nanocolumns in Ge$_{1-x}$Mn$_{x}$ films  This decomposition is probably the consequence of: $(i)$ a strong pair attraction between Mn atoms, $(ii)$ a strong surface diffusion of Mn atoms in germanium even at low growth temperatures and $(iii)$ layer by layer growth conditions  We have also investigated the influence of growth parameters on the spinodal decomposition: at low growth temperatures (100$^{\circ}$C), increasing the Mn content leads to higher columns densities while at higher growth temperatures (150$^{\circ}$C), the columns density remains nearly constant whereas their size increases drastically  By plotting the nanocolumns density as a function of Mn content, we have shown that the mechanism of Mn incorporation in Ge changes above 5 \% of Mn  Finally, using TEM observations and x-ray diffraction, we have shown that Ge$_3$Mn$_5$ nanoclusters start to form at growth temperatures higher than 160$^\circ$C 

\section{Magnetic properties \label{magnetic}}

We have thoroughly investigated the magnetic properties of thin Ge$_{1-x}$Mn$_{x}$ films for different growth temperatures and Mn concentrations  In this section, we focus on Mn concentrations between 2 \% and 11 \%  We could clearly identify four different magnetic phases in Ge$_{1-x}$Mn$_{x}$ films : diluted Mn atoms in the germanium matrix, low $T_{C}$ nanocolumns ($T_{C}$ $\leq$ 170 K), high $T_{C}$ nanocolumns ($T_{C}$ $\geq$ 400 K) and Ge$_{3}$Mn$_{5}$ clusters ($T_{C}$ $\thickapprox$ 300 K)  The relative weight of each phase clearly depends on the growth temperature and to a lesser extend on Mn concentration  For low growth temperature ($<$ 120$^{\circ}$C), we show that nanocolumns are actually made of four uncorrelated superparamagnetic nanostructures  Increasing T$_{g}$ above 120$^{\circ}$C, we first obtain continuous columns exhibiting low $T_{C}$ ($<$ 170 K) and high $T_{C}$ ($>$ 400 K) for $T_{g}\approx$130$^{\circ}$C  The larger columns become ferromagnetic \textit{i e } $T_{B}>T_{C}$  Meanwhile Ge$_{3}$Mn$_{5}$ clusters start to form  Finally for higher $T_{g}$, the magnetic contribution from Ge$_{3}$Mn$_{5}$ clusters keeps increasing while the nanocolumns signal progressively disappears 

\begin{figure}[htb]
\center
   \includegraphics[width= 6\linewidth]{ /fig7a eps}
   \includegraphics[width= 3\linewidth]{ /fig7b eps}
\caption{(a) Temperature dependence of the saturation magnetization (in $\mu_{B}$/Mn) of Ge$_{0 93}$Mn$_{0 07}$ samples for different growth temperatures  The magnetic field is applied in the film plane  The inset shows the temperature dependence of a sample grown at 130$^{\circ}$C and annealed at 650$^{\circ}$C for 15 minutes  After annealing, the magnetic signal mostly arises from Ge$_{3}$Mn$_{5}$ clusters  (b) ZFC-FC measurements performed on Ge$_{0 93}$Mn$_{0 07}$ samples for different growth temperatures  The in-plane applied field is 0 015 T  The ZFC peak at low temperature ($\leq$150 K) can be attributed to the superparamagnetic nanocolumns  This peak widens and shifts towards high blocking temperatures when increasing growth temperature  The second peak above 150 K in the ZFC curve which increases with increasing growth temperature is attributed to superparamagnetic Ge$_{3}$Mn$_{5}$ clusters  The increasing ZFC-FC irreversibility at $\approx$ 300 K is due to the increasing contribution from large ferromagnetic Ge$_{3}$Mn$_{5}$ clusters  The nanocolumns signal completely vanishes after annealing at 650$^{\circ}$C for 15 minutes }
\label{fig7}
\end{figure}

In Fig  7a, the saturation magnetization at 2 Tesla in $\mu_{B}$/Mn of Ge$_{1-x}$Mn$_{x}$ films with 7 \% of Mn is plotted as a function of temperature for different growth temperatures ranging from $T_{g}$=90$^{\circ}$C up to 160$^{\circ}$C  The inset shows the temperature dependence of the magnetization at 2 Tesla after annealing at 650$^{\circ}$C during 15 minutes  Figure 7b displays the corresponding Zero Field Cooled - Field Cooled (ZFC-FC) curves recorded at 0 015 Tesla  In the ZFC-FC procedure, the sample is first cooled down to 5 K in zero magnetic field and the susceptibility is subsequently recorded at 0 015 Tesla while increasing the temperature up to 400 K (ZFC curve)  Then, the susceptibility is recorded under the same magnetic field while decreasing the temperature down to 5 K (FC curve)  Three different regimes can be clearly distinguished  \\
For $T_{g}\leq$120$^{\circ}$C, the temperature dependence of the saturation magnetization remains nearly the same while increasing growth temperature  The overall magnetic signal vanishing above 200 K is attributed to the nanocolumns whereas the increasing signal below 50 K originates from diluted Mn atoms in the surrounding matrix  The Mn concentration dependence of the saturation magnetization is displayed in figure 8  For the lowest Mn concentration (4 \%), the contribution from diluted Mn atoms is very high and drops sharply for higher Mn concentrations (7 \%, 9 \% and 11 3 \%)  Therefore the fraction of Mn atoms in the diluted matrix decreases with Mn concentration probably because Mn atoms are more and more incorporated in the nanocolumns  In parallel, the Curie temperature of nanocolumns increases with the Mn concentration reaching 170 K for 11 3 \% of Mn  This behavior may be related to different Mn compositions and to the increasing diameter of nanocolumns (from 1 8 nm to 2 8 nm) as discussed in section \ref{structural} 

\begin{figure}[htb]
\center
   \includegraphics[width= 7\linewidth]{ /fig8 eps}
    \caption{Temperature dependence of the saturation magnetization (in $\mu_{B}$/Mn) of Ge$_{1-x}$Mn$_{x}$ films grown at 100$^{\circ}$C plotted for different Mn concentrations: 4 1 \%; 7 \%; 8 9 \% and 11 3 \% }
\label{fig8}
\end{figure}

ZFC-FC measurements show that the nanocolumns are superparamagnetic  The magnetic signal from the diluted Mn atoms in the matrix is too weak to be detected in susceptibility measurements at low temperature  In samples containing 4 \% of Mn, ZFC and FC curves superimpose down to low temperatures  As we do not observe hysteresis loops at low temperature, we believe that at this Mn concentration nanocolumns are  superparamagnetic in the whole temperature range and the blocking temperature cannot be measured  For higher Mn contents, the ZFC curve exhibits a very narrow peak with a maximum at the blocking temperature of 15 K whatever the Mn concentration and growth temperature (see Fig  7b)  Therefore the anisotropy barrier distribution is narrow and assuming that nanocolumns have the same magnetic anisotropy, this is a consequence of the very narrow size distribution of the nanocolumns as observed by TEM  To probe the anisotropy barrier distribution, we have performed ZFC-FC measurements but instead of warming the sample up to 400 K, we stopped at a lower temperature $T_{0}$  

\begin{figure}[htb]
\center
   \includegraphics[width= 6\linewidth]{ /fig9 eps}
\caption{Schematic drawing of the anisotropy barrier distribution n($E_{B}$) of superparamagnetic nanostructures  If magnetic anisotropy does not depend on the particle size, this distribution exactly reflects their magnetic size distribution  In this drawing the blocking temperature ($T_{B}$) corresponds to the distribution maximum  At a given temperature $T_{0}$ such that 25$k_{B}T_{0}$ falls into the anisotropy barrier distribution, the largest nanostructures with an anisotropy energy larger than 25$k_{B}T_{0}$ are blocked whereas the others are superparamagnetic }
\label{fig9}
\end{figure}

If this temperature falls into the anisotropy barrier distribution as depicted in Fig  9, the FC curve deviates from the ZFC curve  Indeed the smallest nanostructures have become superparamagnetic at $T_{0}$ and when decreasing again the temperature, their magnetization freezes along a direction close to the magnetic field and the FC susceptibility is higher than the ZFC susceptibility  Therefore any irreversibility in this procedure points at the presence of superparamagnetic nanostructures  The results are given in Fig  10a  ZFC and FC curves clearly superimpose up to $T_{0}$=250 K thus the nanocolumns are superparamagnetic up to their Curie temperature and no Ge$_{3}$Mn$_{5}$ clusters could be detected  Moreover for low $T_{0}$ values, a peak appears at low temperature in FC curves which evidences strong antiferromagnetic interactions between the nanocolumns \cite{Chan00} 

\begin{figure}[htb]
\center
    \includegraphics[width= 35\linewidth]{ /fig10a eps}
    \includegraphics[width= 63\linewidth]{ /fig10b eps}
\caption{(a) ZFC-FC measurements performed on a Ge$_{0 887}$Mn$_{0 113}$ sample grown at 115$^{\circ}$C  The in-plane applied field is 0 015 T  Magnetization was recorded up to different T$_{0}$ temperatures: 30 K, 50 K, 100 K, 150 K, 200 K and 250 K  Curves are shifted up for more clarity  (b) ZFC-FC curves for in-plane and out-of-plane applied fields (0 015 T) }
\label{fig10}
\end{figure}

In order to derive the magnetic size and anisotropy of the Mn-rich nanocolumns embedded in the Ge matrix, we have fitted the inverse normalized in-plane (resp  out-of-plane) susceptibility: $\chi_{\parallel}^{-1}$ (resp  $\chi_{\perp}^{-1}$)  The corresponding experimental ZFC-FC curves are reported in Fig  10b  Since susceptibility measurements are performed at low field (0 015 T), the matrix magnetic signal remains negligible  In order to normalize susceptibility data, we need to divide the magnetic moment by the saturated magnetic moment recorded at 5 T  However the matrix magnetic signal becomes very strong at 5 T and low temperature so that we need to subtract it from the saturated magnetic moment using a simple Curie function  From Fig  10b, we can conclude that nanocolumns are isotropic  Therefore to fit experimental data we use the following expression well suited for isotropic systems or cubic anisotropy: $\chi_{\parallel}^{-1}= \chi_{\perp}^{-1}\approx 3k_{B}T/M(T)+\mu_{0}H_{eff}(T)$  $k_{B}$ is the Boltzmann constant, $M=M_{s}v$ is the magnetic moment of a single-domain nanostructure (macrospin approximation) where $M_{s}$ is its magnetization and $v$ its volume  The in-plane magnetic field is applied along $[110]$ or $[-110]$ crystal axes  Since the nanostructures Curie temperature does not exceed 170 K, the temperature dependence of the saturation magnetization is also accounted for by writting $M(T)$  Antiferromagnetic interactions between nanostructures are also considered by adding an effective field estimated in the mean field approximation \cite{Fruc02}: $\mu_{0}H_{eff}(T)$ 
The only fitting parameters are the maximum magnetic moment (\textit{i e } at low temperature) per nanostructure: $M$ (in Bohr magnetons $\mu_{B}$) and the maximum interaction field (\textit{i e } at low temperature): $\mu_{0}H_{eff}$ 

\begin{figure}[htb]
\center
   \includegraphics[width= 7\linewidth]{ /fig11 eps}
\caption{Temperature dependence of the inverse in-plane (open circles) and out-of-plane (open squares) normalized susceptibilities of a Ge$_{0 887}$Mn$_{0 113}$ sample grown at 115$^{\circ}$C  Fits were performed assuming isotropic nanostructures or cubic anisotropy  Dashed line is for in-plane susceptibility and solid line for out-of-plane susceptibility }
\label{fig11}
\end{figure}

In Fig  11, the best fits lead to $M\approx$1250 $\mu_{B}$ and $\mu_{0}H_{eff}\approx$102 mT for in-plane susceptibility and $M\approx$1600 $\mu_{B}$ and $\mu_{0}H_{eff}\approx$98 mT for out-of-plane susceptibility  It gives an average magnetic moment of 1425 $\mu_{B}$ per column and an effective interaction field of 100 mT  Using this magnetic moment and its temperature dependence, magnetization curves could be fitted using a Langevin function and $M(H/T)$ curves superimpose for $T<$100 K  However, from the saturated magnetic moment of the columns and their density (35000 $\rm{\mu m}^{-2}$), we find almost 6000 $\mu_{B}$ per column  Therefore, for low growth temperatures, we need to assume that nanocolumns are actually made of almost four independent elongated magnetic nanostructures  The effective field for antiferromagnetic interactions between nanostructures estimated from the susceptibility fits is at least one order of magnitude larger than what is expected from pure magnetostatic coupling  This difference may be due to either an additional antiferromagnetic coupling through the matrix which origin remains unexplained or to the mean field approximation which is no more valid in this strong coupling regime  As for magnetic anisotropy, the nanostructures behave as isotropic magnetic systems or exhibit a cubic magnetic anisotropy  First we can confirm that nanostructures are not amorphous otherwise shape anisotropy would dominate leading to out-of-plane anisotropy  We can also rule out a random distribution of magnetic easy axes since the nanostructures are clearly crystallized in the diamond structure and would exhibit at least a cubic anisotropy (except if the random distribution of Mn atoms within the nanostructures can yield random easy axes)  Since the nanostructures are in strong in-plane compression (their lattice parameter is larger than the matrix one), the cubic symmetry of the diamond structure is broken and magnetic cubic anisotropy is thus unlikely  We rather believe that out-of-plane shape anisotropy is nearly compensated by in-plane magnetoelastic anisotropy due to compression leading to a \textit{pseudo} cubic anisotropy  From the blocking temperature (15 K) and the magnetic volume of the nanostructures , we can derive their magnetic anisotropy constant using $Kv=25k_{B}T_{B}$: K$\approx$10 kJ m$^{-3}$ which is of the same order of magnitude as shape anisotropy 

\begin{figure}[htb]
\center
    \includegraphics[width= 35\linewidth]{ /fig12a eps}
    \includegraphics[width= 63\linewidth]{ /fig12b eps} 
\caption{(a) ZFC-FC measurements performed on a Ge$_{0 93}$Mn$_{0 07}$ sample grown at 122$^{\circ}$C  The in-plane applied field is 0 015 T  Magnetization was recorded up to different T$_{0}$ temperatures: 50 K, 100 K, 150 K, 200 K and 250 K  Curves are shifted up for more clarity  (b) ZFC-FC curves for in-plane and out-of-plane applied fields  (0 015 T) }
\label{fig12}
\end{figure}

For growth temperatures $T_{g}\geq$120$^{\circ}$C and Mn concentrations $\geq$ 7 \%, samples exhibit a magnetic signal above 200 K corresponding to Ge$_{3}$Mn$_{5}$ clusters (see Fig  7a)  As we can see, SQUID measurements are much more sensitive to the presence of Ge$_{3}$Mn$_{5}$ clusters, even at low concentration, than TEM and x-ray diffraction used in section \ref{structural}  We also observe a sharp transition in the ZFC curve (see Fig  7b, Fig  12a and 12b): the peak becomes very large and is shifted towards high blocking temperatures (the signal is maximum at $T=$23 K)  This can be easily understood as a magnetic percolation of the four independent nanostructures obtained at low growth temperatures into a single magnetic nanocolumn  Therefore the magnetic volume increases sharply as well as blocking temperatures  At the same time, the size distribution widens as observed in TEM  In Fig  12a, we have performed ZFC-FC measurements at different $T_{0}$ temperatures  The ZFC-FC irreversibility is observed up to the Curie temperature of $\approx$120 K meaning that a fraction of nanocolumns is ferromagnetic (\textit{i e } $T_{B}\geq T_{C}$) 
In Fig  12b, in-plane and out-of-plane ZFC curves nearly superimpose for $T\leq$150 K due to the isotropic magnetic behavior of the nanocolumns: in-plane magnetoelastic anisotropy is still compensating out-of-plane shape anisotropy  Moreover the magnetic signal above 150 K corresponding to Ge$_{3}$Mn$_{5}$ clusters that start to form in this growth temperature range is strongly anisotropic  This perpendicular anisotropy confirms the epitaxial relation: (0002) Ge$_{3}$Mn$_{5}$ $\parallel$ (002) Ge discussed in Ref \cite{Bihl06}  The magnetic easy axis of the clusters lies along the hexagonal $c$-axis which is perpendicular to the film plane 

\begin{figure}[ht]
\center
   \includegraphics[width= 35\linewidth]{ /fig13a eps}
   \includegraphics[width= 63\linewidth]{ /fig13b eps} 
\caption{(a) ZFC-FC measurements performed on a Ge$_{0 887}$Mn$_{0 113}$ sample grown at 145$^{\circ}$C  The in-plane applied field is 0 015 T  Magnetization was recorded up to different T$_{0}$ temperatures: 50 K, 100 K, 150 K, 200 K, 250 K and 300 K  Curves are shifted up for more clarity  (b) ZFC-FC curves for in-plane and out-of-plane applied fields (0 015 T) }
\label{fig13}
\end{figure}

For growth temperatures $T_{g}\geq$145$^{\circ}$C the cluster magnetic signal dominates (Fig  13b)  Superparamagnetic nanostructures are investigated performing ZFC-FC measurements at different $T_{0}$ temperatures (Fig  13a)  The first ZFC peak at low temperature \textit{i e } $\leq$ 150 K is attributed to  low-$T_{C}$ nanocolumns ($T_{C}\approx$130 K)  This peak is wider than for lower growth temperatures and its maximum is further shifted up to 30 K  These results are in agreement with TEM observations: increasing $T_{g}$ leads to larger nanocolumns (\textit{i e } higher blocking temperatures) and wider size distributions  ZFC-FC irreversibility is observed up to the Curie temperature due to the presence of ferromagnetic columns  The second peak above 180 K in the ZFC curve is attributed to Ge$_{3}$Mn$_{5}$ clusters and the corresponding ZFC-FC irreversibility persisting up to 300 K means that some clusters are ferromagnetic  We clearly evidence the out-of-plane anisotropy of Ge$_{3}$Mn$_{5}$ clusters and the isotropic magnetic behavior of nanocolumns (Fig  13b)  In this growth temperature range, we have also investigated the Mn concentration dependence of magnetic properties  

\begin{figure}[ht]
\center
    \includegraphics[width= 49\linewidth]{ /fig14a eps}
    \includegraphics[width= 49\linewidth]{ /fig14b eps} 
\caption{Temperature dependence of the saturation magnetization (in $\mu_{B}$/Mn) of Ge$_{1-x}$Mn$_{x}$ films grown at 150$^{\circ}$C plotted for different Mn concentrations: 2 3 \%; 4 \%; 7 \%; 9 \%; 11 3 \%  (b) ZFC-FC measurements performed on Ge$_{1-x}$Mn$_{x}$ films grown at 150$^{\circ}$C  The in-plane applied field is 0 025 T for 2 3 \% and 4 \% and 0 015 T for 8 \% and 11 3 \%  }
\label{fig14}
\end{figure}

In Fig  14a, for low Mn concentrations (2 3 \% and 4 \%) the contribution from diluted Mn atoms in the germanium matrix to the saturation magnetization is very high and nearly vanishes for higher Mn concentrations (7 \%, 9 \% and 13 \%) as observed for low growth temperatures  Above 7 \%, the magnetic signal mainly comes from nanocolumns and Ge$_{3}$Mn$_{5}$ clusters  We can derive more information from ZFC-FC measurements (Fig  14b)  Indeed, for 2 3 \% of Mn, ZFC and FC curves nearly superimpose down to low temperature meaning that nanocolumns are superparamagnetic in the whole temperature range  Moreover the weak irreversibility arising at 300 K  means that some Ge$_{3}$Mn$_{5}$ clusters have already formed in the samples even at very low Mn concentrations  For 4 \% of Mn, we can observe a peak with a maximum at the blocking temperature (12 K) in the ZFC curve  We can also derive the Curie temperature of nanocolumns: $\approx$45 K  The irresversibility arising at 300 K still comes from Ge$_{3}$Mn$_{5}$ clusters  Increasing the Mn concentration above 7 \% leads to: higher blocking temperatures (20 K and 30 K) due to larger nanocolumns and wider ZFC peaks due to wider size distributions in agreement with TEM observations (see Fig  3a)  Curie temperatures also increase (110 K and 130 K) as well as the contribution from Ge$_{3}$Mn$_{5}$ clusters \\
Finally when increasing $T_{g}$ above 160$^{\circ}$C, the nanocolumns magnetic signal vanishes and only Ge$_{3}$Mn$_{5}$ clusters and diluted Mn atoms coexist  The overall magnetic signal becomes comparable to the one measured on annealed samples in which only Ge$_{3}$Mn$_{5}$ clusters are observed by TEM (see Fig  7a) \\
The magnetic properties of high-$T_{C}$ nanocolumns obtained for $T_{g}$ close to 130$^{\circ}$C are discussed in detail in Ref \cite{Jame06} \\
In conclusion, at low growth temperatures ($T_{g}\leq$120$^{\circ}$C), nanocolumns are made of almost 4 independent elongated magnetic nanostructures  For $T_{g}\geq$120$^{\circ}$C, these independent nanostructures percolate into a single nanocolumn sharply leading to higher blocking temperatures  Increasing $T_{g}$ leads to larger columns with a wider size distribution as evidenced by ZFC-FC measurements and given by TEM observations  In parallel, some Ge$_{3}$Mn$_{5}$ clusters start to form and their contribution increases when increasing $T_{g}$  Results on magnetic anisotropy seems counter-intuitive  Indeed Ge$_{3}$Mn$_{5}$ clusters exhibit strong out-of-plane anisotropy whereas nanocolumns which are highly elongated magnetic structures are almost isotropic  This effect is probably due to compensating in-plane magnetoelastic coupling (due to the columns compression) and out-of-plane shape anisotropy  

\section{Conclusion}

In this paper, we have investigated the structural and magnetic properties of thin Ge$_{1-x}$Mn$_{x}$ films grown by low temperature molecular beam epitaxy  A wide range of growth temperatures and Mn concentrations have been explored  All the samples contain Mn-rich nanocolumns as a consequence of 2D-spinodal decomposition  However their size, crystalline structure and magnetic properties depend on growth temperature and Mn concentration  For low growth temperatures, nanocolumns are very small (their diameter ranges between 1 8 nm for 1 3 \% of Mn and 2 8 nm for 11 3 \% of Mn), their Curie temperature is rather low ($<$ 170 K) and they behave as almost four uncorrelated superparamagnetic nanostructures  Increasing Mn concentration leads to higher columns densities while diameters remain nearly unchanged  For higher growth temperatures, the nanocolumns mean diameter increases and their size distribution widens  Moreover the 4 independent magnetic nanostructures percolate into a single magnetic nanocolumn  Some columns are ferromagnetic even if Curie temperatures remain quite low  In this regime, increasing Mn concentration leads to larger columns while their density remains nearly the same  In parallel, Ge$_{3}$Mn$_{5}$ nanoclusters start to form in the film with their $c$-axis perpendicular to the film plane  In both temperature regimes, the Mn incorporation mechanism in the nanocolumns and/or in the matrix changes above 5 \% of Mn and nanocolumns exhibit an isotropic magnetic behaviour due to the competing effects of out-of-plane shape anisotropy and in-plane magnetoelastic coupling  Finally for a narrow range of growth temperatures around 130$^{\circ}$C, nanocolumns exhibit Curie temperatures higher than 400 K  Our goal is now to investigate the crystalline structure inside the nanocolumns, in particular the position of Mn atoms in the distorted diamond structure, which is essential to understand magnetic and future transport properties in Ge$_{1-x}$Mn$_{x}$ films 

\section{Aknowledgements}
The authors would like to thank Dr  F  Rieutord for grazing incidence x-ray diffraction measurements performed on the GMT station of BM32 beamline at the European Synchrotron Radiation Facility 





ground_truth: 1425 $\mu_{B}$.