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: Can someone sell or modify the Agency Spotter Content?

Read the following text and answer briefly.

Context 1: By purchasing now, you agree to the following terms  You authorize Agency Spotter to store and charge your payment method on file  Your paid account will renew automatically, unless you terminate it, or you notify Customer Service by email ([email protected]) of your decision to terminate your paid account  You must cancel your subscription before it renews in order to avoid billing of subscription fees for the renewal form to your credit card 
Should You object to any of the Terms or any subsequent modifications thereto, or become dissatisfied with the Site in any way, Your only recourse is to immediately discontinue use of the Site  Agency Spotter has the right, but is not obligated, to strictly enforce the Terms through self-help, community moderation, active investigation, litigation and prosecution 
(b) Agency Spotter will use commercially reasonable efforts to make the Services available on a 24 hours a day, 7 days a week, and 365 days a year basis, subject to Section 23 below and to downtime for maintenance purposes 
(c) Agency Spotter may from time to time modify the Services and add, change, or delete features of the Services in its sole discretion, without notice to you  Your continued use of the Service after any such changes to the Service constitutes your acceptance of these changes  Agency Spotter will use commercially reasonable efforts to post information on the Site regarding material changes to the Services 
(d) The contents of the Site, such as text, graphics, images, logos, user interfaces, visual interfaces, photographs, button icons, software, trademarks, sounds, music, artwork and computer code, and other Agency Spotter content (collectively, “Agency Spotter Content”), are protected under both United States and foreign copyright, trademark and other laws  All Agency Spotter Content is the property of Agency Spotter or its content suppliers or clients  The compilation (meaning the collection, arrangement and assembly) of all content on the Site is the exclusive property of Agency Spotter and is protected by United States and foreign copyright, trademark, and other laws  Unauthorized use of the Agency Spotter Content may violate these laws, and is strictly prohibited  You must retain all copyright, trademark, service mark and other proprietary notices contained in the original Agency Spotter Content on any authorized copy You make of the Agency Spotter Content 
(e) You agree not to sell or modify the Agency Spotter Content or reproduce, display, publicly perform, distribute, or otherwise use the Agency Spotter Content in any way for any public or commercial purpose, in connection with products or services that are not those of the Site, in any other manner that is likely to cause confusion among consumers, that disparages or discredits Agency Spotter or its licensors, that dilutes the strength of Agency Spotter’s or its licensor’s property, or that otherwise infringes Agency Spotter’s or its licensor’s intellectual property rights  You further agree to in no other way misuse Agency Spotter Content that appears on this Site  Any code that Agency Spotter creates to generate or display any Agency Spotter Content or the pages making up the Website is also protected by Agency Spotter’s copyright and You may not copy or adapt such code 
2  Site Restrictions  You may not use the Site in order to transmit, post, distribute, store or destroy material, including without limitation, the Agency Spotter Content, (a) in violation of any applicable law or regulation, (b) in a manner that will infringe the copyright, trademark, trade secret or other intellectual property rights of others or violate the privacy, publicity or other personal rights of others, (c) that is defamatory, obscene, threatening, abusive or hateful, or (d) that is in furtherance of criminal, fraudulent, or other unlawful activity  You are also prohibited from violating or attempting to violate the security of the Site and Services, including without limitation, the following activities: (a) accessing or attempting to access data not intended for You or logging into a server or account which You are not authorized to access; (b) attempting to probe, scan or test the vulnerability of a system or network or to breach security or authentication measures without proper authorization; (c) attempting to interfere with service to any other user of the Site or Services, host or network, including, without limitation, via means of submitting a virus to the Website, overloading, “flooding”, “spamming”, “mailbombing” or “crashing”; or (d) forging any TCP/IP packet header or any part of the header information in any e-mail or newsgroup posting  Violations of system or network security may result in civil and/or criminal liability 
3  Specific Prohibited Uses  The Agency Spotter Content and other features of the Site may be used only for lawful purposes  Agency Spotter specifically prohibits any other use of the Site, and You agree not to do any of the following: (a) use the Site for any purpose other than as a platform for connecting businesses and agencies, including but not limited to using the information in the Website to sell or promote any products or services; (b) post or submit to the Website any incomplete, false or inaccurate biographical information or information which is not Your own; (c) post on the Website any franchise, pyramid scheme or “club membership”; (d) send unsolicited mail or e-mail, make unsolicited phone calls or send unsolicited faxes regarding promotions and/or advertising of products or services to any other user(s) of the Website; (e) delete or revise any material posted by any other person or entity; (f) take any action that imposes an unreasonable or disproportionately large load on the Website’s infrastructure; (g) notwithstanding anything to the contrary contained herein, use or attempt to use any engine, software, tool, agent or other automatic device, program, algorithm, methodology or mechanism (including without limitation browsers, spiders, robots, avatars or intelligent agents) to navigate or search the Website other than the search engine and search agents available from Agency Spotter on the Website and other than through generally available third party web browsers (e g , Internet Explorer, Firefox, Safari); (h) decipher, decompile, disassemble or reverse engineer any of the software comprising or in any way making up a part of the Website; or (i) aggregate, copy or duplicate in any manner any of the Agency Spotter Content or information available from the Website, without express written consent from Agency Spotter 
(a) Certain features or services offered on or through the Site to users or agencies may require you to open a user or agency account (“Agency Account”) (including setting up a user ID and password)  You are entirely responsible for maintaining the confidentiality of the information you hold for your account, including your password, and for any and all activity that occurs under your account until you close down your account or prove that your account security was compromised due to no fault of your own  To close your account, please email us at [email protected] You agree to notify Agency Spotter immediately of any unauthorized use of your account or password, or any other breach of security  You may be held liable for losses incurred by Agency Spotter or any other user of or visitor to the Site due to someone else using your Agency Spotter ID, password or account as a result of your failing to keep your account information secure and confidential  You may not use anyone else’s Agency Spotter ID, password or account at any time without the express permission and consent of the holder of that Agency Spotter ID, password or account  Agency Spotter cannot and will not be liable for any loss or damage arising from your failure to comply with these obligations  Agency Spotter may verify Agency Accounts to confirm that such accounts meet Agency Spotter’s minimum requirements to be an agency, as the same may be modified or amended from time to time, and may assign an administrator to such verified Agency Account 
(b) To eligible to use the Site and the Services, you must meet the following criteria and represent and warrant that you: (i) are at least 18 years of age; (ii) are not currently restricted from the Site or Services, and are not otherwise prohibited from having an Agency Spotter account, (iii) are not a competitor of Agency Spotter or are not using the Site or Services for reasons that are in competition with Agency Spotter, (iv) will only maintain one Agency Spotter account at any given time, (v) have full power and authority to enter into this Agreement and doing so will not violate any other agreement to which you are bound, (vi) will not violate any rights of Agency Spotter, including intellectual property rights such as copyright and trademark rights, and (vii) agree to provide at your cost all equipment, software and internet access necessary to use the Site or Services 
6  User Content and Submissions  You understand that all information, data, text, software, music, sound, photographs, graphics, video, advertisements, messages or other materials submitted, posted or displayed by You on or through the Website (“User Content”) is the sole responsibility of the person from which such User Content originated  Agency Spotter claims no ownership or control over any User Content  You or a third party licensor, as appropriate, retain all patent, trademark and copyright to any User Content You submit, post or display on or through Agency Spotter and You are responsible for protecting those rights, as appropriate  By submitting, posting or displaying User Content on or through Agency Spotter, You grant Agency Spotter a worldwide, non-exclusive, royalty-free license to reproduce, adapt, distribute and publish such User Content through Agency Spotter  In addition, by submitting, posting or displaying User Content which is intended to be available to the general public, You grant Agency Spotter a worldwide, non-exclusive, royalty-free license to reproduce, adapt, distribute and publish such User Content for the purpose of promoting Agency Spotter Services  Agency Spotter will discontinue this licensed use within a commercially reasonable period after such User Content is removed from the Site  Agency Spotter reserves the right to refuse to accept, post, display or transmit any User Content in its sole discretion 
You also represent and warrant that You have the right to grant, or that the holder of any rights has completely and effectively waived all such rights and validly and irrevocably granted to You the right to grant, the license stated above  If You post User Content in any public area of the Website, You also permit any user of the Website to access, display, view, store and reproduce such User Content for personal use  Subject to the foregoing, the owner of such User Content placed on the Website retains any and all rights that may exist in such User Content 
Agency Spotter does not represent or guarantee the truthfulness, accuracy, or reliability of User Content or endorse any opinions expressed by users of the Website  You acknowledge that any reliance on material posted by other users will be at Your own risk 
The following is a partial list of User Content that is prohibited on the Website  Prohibited Content includes, but is not limited to, Content that: is implicitly or explicitly offensive, such as User Content that engages in, endorses or promotes racism, bigotry, discrimination, hatred or physical harm of any kind against any group or individual; harasses, incites harassment or advocates harassment of any group or individual; involves the transmission of “junk mail”, “chain letters,” or unsolicited mass mailing or “spamming”; promotes or endorses false or misleading information or illegal activities or conduct that is abusive, threatening, obscene, defamatory or libelous; promotes or endorses an illegal or unauthorized copy of another person’s copyrighted work, such as providing or making available pirated computer programs or links to them, providing or making available information to circumvent manufacture-installed copy-protect devices, or providing or making available pirated music or other media or links to pirated music or other media files; contains restricted or password only access pages, or hidden pages or images; displays or links to pornographic, indecent or sexually explicit material of any kind; provides or links to material that exploits people under the age of 18 in a sexual, violent or other manner, or solicits personal information from anyone under 18; or provides instructional information about illegal activities or other activities prohibited by these Terms and Conditions, including without limitation, making or buying illegal weapons, violating someone’s privacy, providing or creating computer viruses or pirating any media; and/or solicits passwords or personal identifying information from other users 
It is your responsibility to keep your Agency Spotter profile information accurate and updated 
7  User-to-User Communications and Sharing (Agency Spotter Groups, Ratings, Reviews, Updates, Agency Pages, etc )  Agency Spotter offers various forums such as Agency Spotter Groups, Ratings, Reviews, and Updates, where you can post your observations and comments on designated topics  Agency Spotter also enables sharing of information by allowing users to post updates, including links to news articles and other information such as product recommendations, job opportunities, and other content to their profile and other parts of the Site, such as Agency Spotter Groups and Agency Pages  Agency Spotter members can create Agency Spotter Groups and Agency Pages for free; however, Agency Spotter may close or transfer Agency Spotter Groups or Agency Pages, or remove content from them if the content violates these Terms or others’ intellectual property rights  To create an Agency Spotter Agency Page, the Agency must be a company or legal entity that meets Agency Spotter’s minimum requirements for an Agency, and you must have the authority to create the Agency Page on behalf of the third party Agency 
For clarity, only DMCA Notices should go to the Copyright Agent; any other feedback, comments, requests for technical support, and other communications should be directed to: [email protected] You acknowledge that if you fail to comply with all of the requirements of this Section, your DMCA Notice may not be valid 
Upon receipt of a Notice, Agency Spotter will take whatever action, in its sole discretion, it deems appropriate, including removal of the challenged material from the Site and/or termination of the User’s account in appropriate circumstances  Please note that a Complainant may be liable for damages (including costs and attorneys’ fees) if he or she knowingly makes a material misrepresentation that content is infringing 
(i) If you have posted material subject to a DMCA Notice that allegedly infringes a copyright (the “Counterclaimant”), you may send Agency Spotter a written Counter Notice pursuant to Section 512(g), (ii) and 512(g), (iii) of the DMCA  When Agency Spotter receives a Counter Notice, it may, in its discretion, reinstate the material in question not less than ten (10) nor more than fourteen (14) days after receiving the Counter Notice unless Agency Spotter first receives notice from the Claimant that he or she has filed a legal action to restrain the allegedly infringing activity  Please note that Agency Spotter will send a copy of the Counter Notice to the address provided by the Claimant  A Counterclaimant may be liable for damages (including costs and attorneys’ fees) if he or she knowingly makes a material misrepresentation that that material or activity was removed or disabled by mistake or misidentification 
1  Identification of the material that has been removed or to which access has been disabled and the location at which the material appeared before it was removed or access to it was disabled 
2  A statement under penalty of perjury that you have a good faith belief that the material was removed or disabled as a result of mistake or misidentification of the material to be removed or disabled 
3  Your name, address, and telephone number, and a statement that you consent to the jurisdiction of Federal District Court for the judicial district in which the address is located, or if your address is outside of the United States, for any judicial district in which Agency Spotter may be found, and that you will accept service of process from the person who provided notification under subsection (c)(1)(C) of the DMCA or an agent of such person 
(c) AGENCY SPOTTER HAS NO OBLIGATION TO ADJUDICATE CLAIMS OF INFRINGEMENT – EACH USER’S AGREEMENT TO HOLD AGENCY SPOTTER HARMLESS FROM CLAIMS  Claimants, Counterclaimants, and users understand that Agency Spotter is not an intellectual property tribunal  While Agency Spotter may, in its discretion, use the information provided in a DMCA Notice and Counter Notice in order to decide how to respond to infringement claims, Agency Spotter is not responsible for determining the merits of such claims  If a Counterclaimant responds to a claim of infringement by providing a Counter Notice, the Counterclaimant agrees that if Agency Spotter restores or maintains the content, the Counterclaimant will defend and hold Agency Spotter harmless from any resulting claims of infringement against Agency Spotter 
10  Advertisements and Other Potential Sources Of Revenue  Some of the Services may now or in the future be supported by advertising revenue, pay-per-click mechanisms, or other funding, and the Site may display advertisements and promotions  These advertisements may be targeted to the content of information stored via the Site, queries made through the Services, or other criteria  The manner, mode and extent of advertising on the Site are subject to change without specific notice to you  In consideration for Agency Spotter granting you access to and use of the Site and the Services, you agree that the Agency Spotter may place such advertising on the Site and/or incorporate such advertisements into the Services 
11  DISCLAIMERS  THE SITE AND ITS CONTENT AND THE SERVICES ARE PROVIDED “AS IS” AND AGENCY SPOTTER MAKES NO REPRESENTATIONS OR WARRANTIES OF ANY KIND, EITHER EXPRESS OR IMPLIED, ABOUT THE IMAGES OR SITE INCLUDING, WITHOUT LIMITATION, WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR NON-INFRINGEMENT, TO THE FULLEST EXTENT PERMISSIBLE UNDER APPLICABLE LAW  AGENCY SPOTTER DOES NOT WARRANT THAT ACCESS TO THE SITE OR ITS CONTENTS OR THE SERVICES WILL BE UNINTERRUPTED OR ERROR-FREE, THAT DEFECTS WILL BE CORRECTED, OR THAT THIS SITE OR THE SERVERS THAT MAKE IT AVAILABLE ARE FREE OF VIRUSES OR OTHER HARMFUL COMPONENTS  AGENCY SPOTTER DOES NOT WARRANT OR MAKE ANY REPRESENTATIONS REGARDING THE USE OR THE RESULTS OF THE USE OF ANY CONTENT ON THE SITE IN TERMS OF ITS CORRECTNESS, ACCURACY, RELIABILITY, OR OTHERWISE  ACCORDINGLY, YOU ACKNOWLEDGE THAT YOUR USE OF THE SITE IS AT YOUR OWN RISK  YOU (AND NOT AGENCY SPOTTER) ASSUME THE ENTIRE COST OF ALL NECESSARY SERVICING, REPAIR, OR CORRECTION RESULTING FROM COMPUTER MALFUNCTION, VIRUSES OR THE LIKE  APPLICABLE LAW MAY NOT ALLOW THE EXCLUSION OF IMPLIED WARRANTIES, SO THE ABOVE EXCLUSION MAY NOT APPLY TO YOU 
12  Limitation on Liability  Neither Agency Spotter, nor its licensors, representatives, affiliates, employees, shareholders or directors (collectively, “Agency Spotter Affiliates”), shall be cumulatively responsible or liable for (a) any damages in excess of three (3) times the most recent monthly fee that you paid for a Premium Service, if any, or US $100, whichever amount is greater, or (b) any damages of any kind including, without limitation, lost business, profits or data (or the cost to recreate such data), direct, indirect, incidental, consequential, compensatory, exemplary, special or punitive damages that may result from Your access to or use of Website, the Agency Spotter Content, or the Services, or any content or other materials on, accessed through or downloaded from the Site  The allocations of liability in this Section represent the agreed and bargained-for understanding of the parties and the fees herein reflects such allocation  These limitations of liability will apply notwithstanding any failure of essential purpose of any limited remedy, whether your claim is based in contract, tort, statute or any other legal theory, and whether we knew or should have known about the possibility of such damages; provided, however, that this limitation of liability shall not apply if you have entered into a separate written agreement to purchase Premium Services with a separate Limitation of Liability provision that expressly supersedes this Section in relation to those Premium Services 
13  Indemnification  In the event that You use the Website, the Agency Spotter Content, or any portion thereof, in any manner not authorized by Agency Spotter, or if You otherwise infringe any intellectual property rights or any other rights relating to other users, You agree to indemnify and hold Agency Spotter, its subsidiaries, affiliates, licensors and representatives, harmless against any losses, expenses, costs or damages, including reasonable attorneys’ fees, incurred by them as a result of unauthorized use of the Website or the Agency Spotter Content and/or Your breach or alleged breach of these Terms and Conditions 
(a) You agree that Agency Spotter and its licensors own all intellectual property rights in and to the Services, the Site and related Software, including but not limited to the look and feel, structure, organization, design, algorithms, templates, data models, logic flow, text, graphics, logos, and screen displays associated therewith 
(b) You will not reverse engineer, decompile or disassemble the Software, or otherwise attempt to reconstruct or discover the source code for the Software  You further agree not to resell, lease, assign, distribute, time share or otherwise commercially exploit or make the Services available to any third party for such third party’s benefit 
(c) You may make a single copy of the Downloaded Software for backup purposes only; provided that any such copies contain the same proprietary rights notices that appear on the Downloaded Software  Agency Spotter reserves all rights in the Services and Software not expressly granted to you hereunder  As used herein, “Software” means Agency Spotter’s proprietary software used to deliver the Services, made available to you as part of the Site and/or Services, and all updates and associated documentation thereto made available as a part of the Site or Services pursuant to these Terms, including Downloadable Software  The term “Downloadable Software” means client software downloaded by you from the Site that augments your use of the Site and/or Services, including add-ins, sample code, APIs and ancillary programs 
(d) Agency Spotter shall have a perpetual, royalty-free, worldwide, and transferable license to use or incorporate into the Site and Services any suggestions, ideas, enhancements, feedback, or other information provided by you related to the Site or Services 
(e) Agency Spotter may derive and compile aggregated and/or analytical information from your usage of the Site and Services  Such aggregated data and metadata may be used for Agency Spotter’s own purposes without restriction, including, but not limited to, using such data in conjunction with data from other sources to improve Agency Spotter’s products and services and to create new products 
15  Third Party Software and Features; Agency Spotter Applications  (a) Agency Spotter may make software from third-party companies available to You  To download such software, You may be required to agree to the respective software licenses and/or warranties of such third-party software  Each software product is subject to the individual company’s terms and conditions, and the agreement will be between You and the respective company  This means that Agency Spotter does not guarantee that any software You download will be free of any contaminating or destructive code, such as viruses, worms or Trojan horses  Agency Spotter does not offer any warranty on any third-party software You download using the Site  Further, the Site and/or Service may contain features, functionality and information that are provided through or by third-party content, software, websites, and/or system (“Third Party Materials”)  Your use and access of these features and functionality are subject to the terms published or otherwise made available by the third-party providers of Third Party Materials  Agency Spotter has no responsibility for any Third-Party Materials, and you irrevocably waive any claim against Agency Spotter with respect to such Third-Party Materials 
(b) Agency Spotter may also offer the Services through applications built using Agency Spotter’s platform (“Agency Spotter Applications”), including smart phone applications, “Share” and other similar buttons and other interactive plugins distributed on websites across the Internet  Agency Spotter Applications are distinct from Third-Party Materials and applications address in Section 14(a), above  If you use an Agency Spotter application or interact with a website that has deployed a plugin, you agree that information about you and your use of the Services, including, but not limited to, your device, your mobile carrier, your internet access provider, your physical location, and/or web pages containing Agency Spotter plugins that load in your browser may be communicated to us  You acknowledge that you are responsible for all charges and necessary permissions related to accessing Agency Spotter through your mobile access provider  You should therefore check with your provider to find out if the Services are available and the terms for these services for your specific mobile devices  Finally, by using any downloadable application to enable your use of the Services, you are explicitly confirming your acceptance of the terms of the End User License Agreement associated with the application provided at download or installation, or as may be updated from time to time 
16  International Use  Agency Spotter makes no representation that materials on this site are appropriate or available for use in locations outside the United States, and accessing them from territories where their contents are illegal is prohibited  Those who choose to access this site from other locations do so on their own initiative and are responsible for compliance with local laws 
17  Dispute Resolution  These Terms and any claim, cause of action or dispute (“claim”) arising out of or related to these Terms shall be governed by the laws of the State of Georgia, regardless of your country of origin or where you access Agency Spotter, and notwithstanding any conflicts of law principles and the United Nations Convention for the International Sale of Goods  You and Agency Spotter agree that all claims arising out of or related to these Terms must be resolved exclusively by a state or federal court located in Fulton County, Georgia, except as otherwise mutually agreed in writing by the parties or as described in the Arbitration option in Section 16(b), below  You and Agency Spotter agree to submit to the personal jurisdiction of the courts located within Fulton County, Georgia, for the purpose of litigating all such claims  Notwithstanding the foregoing, you agree that Agency Spotter shall still be allowed to seek injunctive remedies (or an equivalent type of urgent legal relief) in any jurisdiction 
18  Arbitration  You agree that any dispute, claim or controversy arising hereunder or relating in any way to the Terms, shall be settled by binding arbitration in Fulton County, Georgia, in accordance with the commercial arbitration rules of Judicial Arbitration and Mediation Services (“JAMS”)  The arbitrator shall issue a written decision specifying the basis for the award made  The party filing a claim or counterclaim in the arbitration proceeding shall pay the deposit(s) determined by JAMS with respect to such claim or counterclaim  All other costs associated with the arbitration and imposed by JAMS shall be paid as determined by the arbitrator(s) and, in absence of such determination, equally by each party to the arbitration  In addition, unless the arbitrator awards payment of reasonable attorney and other fees to a party, each party to the arbitration shall be responsible for its own attorneys’ fees and other professional fees incurred in connection with the arbitration  Determinations of the arbitrator will be final and binding upon the parties to the arbitration, and judgment upon the award rendered by the arbitrator may be entered in any court having jurisdiction, or application may be made to such court for a judicial acceptance of the award and an order of enforcement, as the case may be  The arbitrator shall apply the substantive law of the State of Georgia, without giving effect to its conflict of laws rules 
19  Export Control  You agree to comply with all relevant export laws and regulations, including, but not limited to, the U S  Export Administration Regulations and Executive Orders (“Export Controls”)  You warrant that you are not a person, company or destination restricted or prohibited by Export Controls (“Restricted Person”)  You will not, directly or indirectly, export, re-export, divert, or transfer the Site or Service or any related software, any portion thereof or any materials, items or technology relating to Agency Spotter’s business or related technical data or any direct product thereof to any Restricted Person, or otherwise to any end user and without obtaining the required authorizations from the appropriate governmental entities 
(a) These Terms will continue until terminated in accordance with this Section 
(b) You may cancel your legal agreement with Agency Spotter at any time by (i) notifying Agency Spotter in writing, (ii) ceasing to use the Services, and (iii) closing your accounts for all of the Services which you use, if we have made this option available to you  Your cancellation of the Services will not alter your obligation to pay all charges incurred prior to your effective date of termination 
Agency Spotter may terminate its legal agreement with you if, (i) you have breached any provision of the Terms (or have acted in manner which clearly shows that you do not intend to, or are unable to comply with the provisions of the Terms), or (ii) Agency Spotter is required to do so by law (for example, where the provision of the Services to you is, or becomes, unlawful), or (iii) Agency Spotter is transitioning to no longer providing the Services to users in the country in which you are resident or from which you use the service, or (iv) the provision of the Services to you by Agency Spotter is, in Agency Spotters’ opinion, no longer commercially viable 
(c) The terms provided in Sections 2, 3, 6, 11, 12, 13, 14, 17, 19, 20, 21 and 22 of these Terms shall survive any termination of these Terms 
21  Independent Contractors  The parties are and intend to be independent contractors with respect to the Services contemplated hereunder  You agree that neither you nor any of your employees or contractors shall be considered as having an employee status with Agency Spotter  No form of joint employer, joint venture, partnership, or similar relationship between the parties is intended or hereby created 
22  Assignment and Delegation  You may not assign or delegate any rights or obligations under these Terms  Any purported assignment or delegation shall be ineffective  We may freely assign or delegate all rights and obligations under these Terms, fully or partially, without notice to you  We may also substitute, by way of unilateral novation, effective upon notice to you, Agency Spotter Inc  for any third party that assumes our rights and obligations under these Terms 
The personally identifiable information we collect from you allows us to provide you with the Services and to enable users to navigate and enjoy using the Site  We will also use your personally identifiable information to develop, improve and advertise the Site and Services  We may also use your personally identifiable information for internal purposes such as auditing, data analysis and research to improve our Services and customer communications  We do not rent, sell or otherwise provide your personally identifiable information to third parties without your consent, except as described in this policy or as required by law 
When you register with us through the Site or Services and become a Registered User, or when you wish to contact another Registered User, we will ask you for personally identifiable information  This refers to information about you that can be used to contact or identify you (“Personally Identifiable Information“)  Personally Identifiable Information includes, but is not limited to, your name, phone numbers, email address, home postal address, business address, social media user names, employer/affiliated organization, reasons for accessing the Site, and intended usage of requested information, but does not include your credit card number or billing information  We may also use your email address or phone number (if provided by you) to contact you regarding changes to the Services; system maintenance and outage issues; account issues; or otherwise to troubleshoot problems  In order to process some of your transactions through the Site and Services, we may also ask for your credit card number and other billing information (“Billing Information“; and, together with Personally Identifiable Information, “Personal Information“) 
Information you provide to us also includes your account profile and your contributions to discussion groups and community features Agency Spotter may offer  Do not upload or insert any information to or into the Site or Services that you do not want to be shared or used in the manner described in this section 
In addition, when you use the Site, our servers automatically record certain information that your web browser sends whenever you visit any website  These server logs may include information such as your web request, Internet Protocol address, browser type, browser language, referring/exit pages and URLs, platform type, number of clicks, domain names, landing pages, pages viewed and the order of those pages, the amount of time spent on particular pages, the date and time of your request, and one or more cookies that may uniquely identify your browser 
Information from third party services and other websites 
Do not upload or insert any information to or into the Site or Services that you do not want to be shared or used in the manner described in this section 
Advertisements  Advertisers who present ads on the Site may use technological methods to measure the effectiveness of their ads and to personalize advertising content  You may use your browser cookie settings to limit or prevent the placement of cookies by advertising networks  Agency Spotter does not share personally identifiable information with advertisers unless we get your permission 
Links  When you click on links on Agency Spotter you may leave our site  We are not responsible for the privacy practices of other sites, and we encourage you to read their privacy statements 
If we are requested to disclose your information to a government agency or official, we will do so if we believe in good faith, after considering your privacy interests and other relevant factors, that such disclosure is necessary to: (i) conform to legal requirements or comply with a legal process with which we are involved; (ii) protect our rights or property or the rights or property of our affiliated companies; (iii) prevent a crime or protect national security; or (iv) protect the personal safety of Site users or the public  Because Agency Spotter is a United States limited liability company and information collected on our Site is stored in whole or in part in the United States, your information may be subject to U S  law 
We also reserve the right to disclose Personally Identifiable Information and/or other information about users that Agency Spotter believes, in good faith, is appropriate or necessary to enforce our agreements, take precautions against liability, investigate and defend itself against ay third-party claims or allegations, assist government enforcement agencies, protect the security or integrity of our Site or Services, and protect the rights, property or personal safety of Agency Spotter, our users and others 
Cookies allow us to (i) manage, present and keep track of temporary information, such as data you upload onto the Site for use with the Services; (ii) register you as a Registered User on the Site or in other various programs associated with the Site; (iii) remember you when you log in to the places on the Site that require you to be a Registered User of the Site; (iv) help us understand the size of our audience and traffic patterns; (v) collect and record information about what you viewed on the Site; and (vi) deliver specific information to you based on your interests 
When you access the Site, the Site automatically collects certain non-personally identifiable information through the use of electronic images known as web beacons (sometimes called single-pixel gifs) and log files  Such information may include your IP address, browser type, the date, time and duration of your access and usage of the Site and whether you opened emails You received from us 
This information is collected for all visits to the Site and then analyzed in the aggregate  This information is useful for, among other things, tracking the performance of our online advertising, such as online banner ads, and determining where to place future advertising on other websites 
Editing your profile  You may review and change or remove your personal information or the settings for your Agency Spotter account at any time by going to your account profile  You can edit your name, email address, password and other account information here  Please be aware that even after your request for a change is processed, Agency Spotter may, for a time, retain residual information about you in its backup and/or archival copies of its database 
Deactivating or deleting your account  If you want to stop using your account you may deactivate it or delete it  When you deactivate an account, no user will be able to see it, but it will not be deleted  We save your profile information in case you later decide to reactivate your account  Many users deactivate their accounts for temporary reasons and in doing so are asking us to maintain their information until they return to Agency Spotter  You will still have the ability to reactivate your account and restore your profile in its entirety  When you delete an account, it is permanently deleted from Agency Spotter  You should only delete your account if you are certain you never want to reactivate it  You may deactivate your account or delete your account within your account profile 
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Context 2: Sir Simon William English  (born 30 December 1961) is a New Zealand former National Party politician who served as the 39th prime minister of New Zealand from 2016 to 2017  He had previously served as the 17th deputy prime minister of New Zealand and minister of finance from 2008 to 2016 under John Key and the Fifth National Government 

A farmer and public servant before entering politics, English was elected to the New Zealand Parliament in  as the National Party's candidate in the Wallace electorate  He was elevated to Cabinet in 1996 and in 1999 was made minister of finance, although he served for less than a year due to his party's loss at the 1999 general election  In October 2001, English replaced Jenny Shipley as the leader of the National Party (and consequently as Leader of the Opposition)  He led the party to its worst defeat at the 2002 general election, and as a consequence, in October 2003 he was replaced as leader by Don Brash 

In November 2006, after Brash's resignation, English became deputy leader under John Key  After National's victory at the 2008 general election, he became deputy prime minister and was also made minister of finance for the second time  Under English's direction New Zealand's economy maintained steady growth during National's three terms of government  He became a list-only MP after stepping down as an electorate MP at the 2014 general election 

John Key resigned as leader of the National Party and prime minister in December 2016  English won the resulting leadership election unopposed and was sworn in as prime minister on 12 December 2016  His tenure was only ten months, and included a three-month election campaign  In the 2017 general election, National won the largest number of seats but fell short of a majority  The parties holding the balance of power declined to support the existing government, and English was subsequently replaced as prime minister by Jacinda Ardern, leader of the Labour Party  English initially continued on as Leader of the Opposition, but resigned as leader of the National Party on 27 February 2018 and left parliament two weeks later 

Early life
English was born on 30 December 1961 at Lumsden Maternity Centre in Lumsden  He is the eleventh of twelve children of Mervyn English and Norah (née O'Brien) English  His parents purchased Rosedale, a mixed sheep and cropping farm in Dipton, Southland from Mervyn's uncle, Vincent English, a bachelor, in 1944  English was born in the maternity unit at Lumsden 

English attended St Thomas's School in Winton, then boarded at St  Patrick's College in Upper Hutt, where he became head boy  He played in the first XV of the school's rugby team  English went on to study commerce at the University of Otago, where he was a resident at Selwyn College, and then completed an honours degree in English literature at Victoria University of Wellington 

After finishing his studies, English returned to Dipton and farmed for a few years  From 1987 to 1989, he worked in Wellington as a policy analyst for the New Zealand Treasury, at a time when the free market policies favoured by Labour's finance minister Roger Douglas (known collectively as "Rogernomics") were being implemented 

English joined the National Party in 1980, while at Victoria University  He served for a period as chairman of the Southland branch of the Young Nationals, and became a member of the Wallace electorate committee  After moving to Wellington, he served for periods on the Island Bay and Miramar electorate committees, respectively 

Fourth National Government (1990–1999)

At the 1990 general election, English stood as the National candidate in Wallace, replacing the retiring Derek Angus, and was elected with a large majority  He would hold this seat, renamed Clutha-Southland in 1996, until 2014  He and three other newly elected National MPs (Tony Ryall, Nick Smith, and Roger Sowry) were soon identified as rising stars in New Zealand politics, and at various points were dubbed the "brat pack", the "gang of four", and the "young Turks"  In his first term in parliament, English chaired a select committee into social services  He was made a parliamentary under-secretary in 1993, serving under the Minister of Health 

First period in cabinet (1996–1999)
In early 1996, English was elevated to cabinet by Prime Minister Jim Bolger, becoming the Minister for Crown Health Enterprises and Associate Minister of Education (to Wyatt Creech)  He was 34 at the time, becoming the cabinet's youngest member  After the 1996 general election, the National Party was forced into a coalition with New Zealand First to retain government  In the resulting cabinet reshuffle, English emerged as Minister of Health  However, as a condition of the coalition agreement, NZ First's Neil Kirton (a first-term MP) was made Associate Minister of Health, effectively becoming English's deputy  This arrangement was described in the press as a "shotgun marriage", and there were frequent differences of opinion between the two ministers  After their relationship became unworkable, Kirton was sacked from the role in August 1997, with the agreement of NZ First leader Winston Peters 

As Minister of Health, English was responsible for continuing the reforms to the public health system that National had begun after the 1990 general election  The reforms were unpopular, and health was perceived as one of the government's weaknesses, with the health portfolio consequently being viewed as a challenge  English believed that the unpopularity of the reforms was in part due to a failure in messaging, and encouraged his National colleagues to avoid bureaucratic and money-focused language (such as references to "balance sheets" and "user charges") and instead talk about the improvements to services the government's reforms would bring  He also rejected the idea that public hospitals could be run as commercial enterprises, a view which some of his colleagues had previously promoted 

By early 1997, as dissatisfaction with Bolger's leadership began to grow, English was being touted as a potential successor, along with Jenny Shipley and Doug Graham  His age (35) was viewed as the main impediment to a successful leadership run  National's leadership troubles were resolved in December 1997, when Bolger resigned and Shipley was elected to the leadership unopposed  English had been a supporter of Bolger as leader, but Shipley reappointed him Minister of Health in her new cabinet 

English was promoted to Minister of Finance in a reshuffle in January 1999, a position which was at the time subordinate to the Treasurer, Bill Birch  After a few months, the pair switched positions as part of Birch's transition to retirement, with English assuming the senior portfolio  In early interviews, he emphasised his wish to be seen as a pragmatist rather than an ideologue, and said that the initiatives of some of his predecessors (Roger Douglas's "Rogernomics" and Ruth Richardson's "Ruthanasia") had focused on "fruitless, theoretical debates" when "people just want to see problems solved" 

Opposition (1999–2008)

After the National Party lost the 1999 election to Helen Clark's Labour Party, English continued on in the shadow cabinet as National's spokesperson for finance  He was elected deputy leader of the party in February 2001, following the resignation of Wyatt Creech, with Gerry Brownlee being his unsuccessful opponent 

Leader of the Opposition
In October 2001, after months of speculation, Jenny Shipley resigned as leader of the National Party after being told she no longer had the support of the party caucus  English was elected as her replacement unopposed (with Roger Sowry as his deputy), and consequently became Leader of the Opposition  However, he did not openly organise against Shipley, and according to The Southland Times "there was almost an element of 'aw, shucks, I'll do it then' about Mr English's ascension" 

Aged 39 when he was elected, English became the second-youngest leader in the National Party's history, after Jim McLay (who was 38 when elected in 1984)  He also became only the third Southlander to lead a major New Zealand political party, after Joseph Ward and Adam Hamilton  However, English failed to improve the party's performance  In the 2002 election, National suffered its worst electoral defeat ever, gaining barely more than twenty percent of the vote  English described it as "the worst day of my political life"  Both party insiders and the general public were split as to how much to blame him for the loss, but most of the party believed that English would be able to rebuild National's support 

By late 2003, however, National's performance in opinion polls remained poor  The party had briefly increased its popularity in the year following the election, but by October its support had fallen to levels only slightly better than what it achieved in the last ballot  English also appeared in a boxing match for a charity against entertainer Ted Clarke  This did not boost his polling or that of the National party either, with suggestions that it devalued his image as a serious politician  Don Brash, former governor of the Reserve Bank and a relative newcomer to politics, began to build up support to replace English  On 28 October, Brash gained sufficient backing in Caucus to defeat English in a leadership contest 

Shadow cabinet roles and deputy leader
On 2 November 2003, when Brash changed responsibilities for certain MPs, English became National's spokesman for education, ranked at fifth place in the party's parliamentary hierarchy  He remained in parliament after the 2005 election  In his new shadow education portfolio, English performed strongly, and remained a party favourite despite his election defeat as leader in 2002, eventually being returned to the finance portfolio in August 2004 as deputy spokesman (while still retaining responsibility for education) 

In November 2006, Brash resigned as leader  English was considered as a potential replacement leader (running against John Key) or deputy leader (against incumbent Gerry Brownlee) in the ensuing leadership election  However, a contest was avoided when the MPs agreed a Key/English ticket would run unopposed in a display of party unity  English took over the deputy leadership and the finance portfolio in the Key shadow cabinet 

Fifth National Government (2008–2017)

Deputy Prime Minister and Minister of Finance (2008–2016)

At the 2008 election, English was re-elected by his electorate, winning by a margin of about 15,500 votes  He became Deputy Prime Minister of New Zealand and Minister of Finance in the fifth National Government, being sworn into office on 19 November 2008 and continued to serve in those roles until becoming Prime Minister on 12 December 2014  He was also made Minister of Infrastructure in National's first term of government and Minister responsible for Housing New Zealand Corporation and minister responsible for the New Zealand flag consideration process in its third 

He was comfortably re-elected in Clutha-Southland in the 2011 election but opted to run as a party-list candidate in 2014  

The pairing of John Key as leader of the National Party and English as his deputy has been compared to that of Bob Hawke and Paul Keating (in Australia) and Tony Blair and Gordon Brown (in the UK)



ground_truth: No.

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 position did Simon English hold in the 2008 general election?

Read the following text and answer briefly.

Context 2: 

English acceded to the role of Finance Minister in the continuing wake of the financial crisis  In response to New Zealand's rising debt, English made budget deficit-reduction his main priority  His first budget outlined three focuses in New Zealand's financial recovery: "improving the business environment and removing roadblocks to growth; investment in productive infrastructure; and improving the way government works"  One of his first acts was creating the National Infrastructure Unit, charged with formulating a plan for infrastructure projects and investments  He commissioned a government-wide spending review, with an aim to reducing government expenditure—with the exceptions of a two-year stimulus package and long-term increases on infrastructure spending 

In April 2011, the Opposition criticised English for suggesting that New Zealand businesses could use New Zealand's low wages to help it compete with Australia  The National Government campaigned for re-election in 2011 on its economic record  The Government boasted growth for five consecutive quarters up to mid-2010, totalling 1 6% of real GDP 

Strong growth resulted in a surplus of $473 million for the 2015/16 financial year, projected to rise to $8 5 billion by 2020/21  In his 2016 Economic and Fiscal Update address, English stated that reducing debt and tackling the costs of the 2016 Kaikōura earthquake were higher priorities than reducing rates of tax 

Allowances issue
In 2009, the media, including TVNZ and TV3 revealed that English was receiving about NZ$900 a week as part of a living allowance for ministers, to live in his own NZ$1 2 million Wellington home  At the time, English also received $276,200 in his annual salary as Deputy Prime Minister  It was also revealed other ministers with homes in the capital city were also claiming accommodation allowances  On 3 August 2009, Prime Minister John Key started a review of the housing allowances claimed by cabinet ministers  English subsequently paid back $12,000 and only claimed about $24,000 a year in living allowances  The Auditor-General's office said in September 2009 that they were making "preliminary enquiries" into parliamentary housing expenses in response to a letter of complaint from Progressive party leader Jim Anderton  Two days later English stated that he would no longer take up any housing allowance and had paid back all the allowance he had received since the November 2008 election 

Prime Minister (2016–2017)

John Key resigned on 12 December, and endorsed English as his successor in the resulting leadership election  Following the drop-out of both Judith Collins and Jonathan Coleman from the leadership election, English was sworn in as the 39th Prime Minister of New Zealand on 12 December 2016 

English appointed his first cabinet on 18 December  In a reshuffle, he appointed Steven Joyce to succeed him as Finance Minister, while most ministerial portfolios remained the same 

In February 2017, English did not attend Waitangi Day commemorations at the historic treaty grounds, reportedly in response to the Ngāpuhi iwi's decision to stop the Prime Minister from speaking at the marae  Ngāpuhi have protested the Government's negotiation of the Trans Pacific Partnership Agreement (TPPA), which the iwi believe infringes upon Māori sovereignty, and thus does not adhere to the Treaty of Waitangi  English had been invited to attend in an official capacity; his non-attendance was criticised by a Ngāpuhi elder and Opposition leader Andrew Little 

In his first overseas trip as Prime Minister, English travelled to Europe to discuss trade ties, including a prospective New Zealand–European Union free trade agreement  He first travelled to London on 13 January 2017 to meet British Prime Minister Theresa May  Discussing trade relations, English said the two nations were "natural partners" and would "continue to forge ties" after the UK's withdrawal from the EU  He also arranged to meet with London Mayor Sadiq Khan, Belgian Prime Minister Charles Michel and German Chancellor Angela Merkel   In a meeting with Merkel, English received crucial backing from Germany for a trade deal with the EU  On 16 January, English stated that his government would continue to promote TPPA, despite the United States' decision to withdraw from the agreement  He explained that Southeast Asian countries would now be treated as a priority in negotiations—he also asserted that the United States was ceding influence to China by its rejection of the trade pact 

At a press conference at the Beehive on 1 February 2017, English announced that the 2017 general election would be held on 23 September  The Prime Minister later confirmed that his party would approach ACT, United Future and the Māori Party if confidence and supply agreements were required to form a government following the election  In his second cabinet reshuffle on 24 April, English appointed Gerry Brownlee as his new Foreign Affairs Minister; he also promoted Nikki Kaye to the portfolio of Education Minister, and moved Mark Mitchell into the cabinet to become Defence Minister  The reshuffle was perceived as an election preparation 

On 13 February 2017, English welcomed Australian Prime Minister Malcolm Turnbull to Wellington  The two leaders reaffirmed their shared trade agenda, and discussed changes to the Australian citizenship pathway which will affect permanent residents originating from New Zealand 

On 19 June, it was reported that Todd Barclay, who succeeded English as MP for Clutha-Southland, had clandestinely recorded one of his employee's conversations the previous year, and that John Key's leaders' budget was used to pay a confidential settlement after the employee resigned  English admitted that he had been aware of the illegal recording and the settlement, and thus implicated in the scandal 

During the 2017 National campaign launch, English introduced a $379 million social investment package including digital learning academies for high school students, more resources for mathematics, and boosting support for teaching second languages in schools, and maintaining National Standards in the school curriculum  Prime Minister English also sought to defend National's financial management and economic track record and claimed that the opposition Labour Party would raise taxes  Early opinion polling had forecast a poor showing in the election for the Labour Party, but in early August 37-year-old Jacinda Ardern took over as Labour leader and seemingly energised younger voters 

At the 2017 general election, National won the largest share of the party vote (44 4%) and the largest number of seats (56) in the House Representatives  However, National lacked enough seats to govern alone due to two of the party's support partners, the Māori Party and United Future, losing their parliamentary seats  In response, English stated that the party would be entering into talks to form a coalition with New Zealand First  Following talks with the two largest parties, New Zealand First entered a coalition arrangement with the Labour Party  English was succeeded as prime minister by Jacinda Ardern on 26 October 

Opposition (2017–2018)

Leader of the Opposition
English was re-elected as National Party leader on 24 October 2017  At the time of his re-election, English announced his intention to stay on as leader until the next general election  On 13 February 2018, however, he stood down as National Party leader due to personal reasons, and instructed the party to put into motion the processes to elect a new leader  He also retired from Parliament  English's resignation followed weeks of speculation that he would step aside for a new leader  On 27 February, he was succeeded as party leader by Simon Bridges as the result of the leadership election held that day 

Post-premiership 
In 2018, English joined the board of Australian conglomerate, Wesfarmers  English serves in Chairmanships of Mount Cook Alpine Salmon, Impact Lab Ltd and Manawanui Support Ltd  He is also a director of The Instillery, Centre for Independent Studies and The Todd Corporation Limited, and is a member of the Impact Advisory Group of Macquarie Infrastructure and Real Assets 

Political and social views

English is regarded as more socially conservative than his predecessor, John Key  He has stated his opposition to voluntary euthanasia and physician-assisted suicide, same-sex civil unions, and the decriminalisation of prostitution  As Prime Minister he opposed any "liberalisation" of abortion law 

In 2004, English voted against a bill to establish civil unions for both same-sex and opposite-sex couples  In 2005, he voted for the Marriage (Gender Clarification) Amendment Bill, which would have amended the Marriage Act to define marriage as only between a man and a woman  English voted against the Marriage (Definition of Marriage) Amendment Bill, a bill that legalised same-sex marriage in New Zealand  However, in December 2016 he stated, "I'd probably vote differently now on the gay marriage issue  I don't think that gay marriage is a threat to anyone else's marriage" 

In 2009, English voted against the Misuse of Drugs (Medicinal Cannabis) Amendment Bill, a bill aimed at amending the Misuse of Drugs Act so that cannabis could be used for medical purposes 

Personal life 
English met his future wife, Mary Scanlon, at university  She was studying medicine at the time, and became a general practitioner  Both her parents were immigrants, her father being Samoan and her mother Italian, born on the island of Stromboli  They have six children: a daughter and five sons 

English is a practising Roman Catholic, but has stated that he considers his religious beliefs personal and thus separate from politics 

In June 2002, English took part in TV3's Fight For Life, a celebrity boxing fundraiser to raise money for the Yellow Ribbon anti-youth-suicide campaign, influenced by the death of a teenage nephew in 1997  He lost a split decision to former university colleague Ted Clarke 

Honours
In the 2018 Queen's Birthday Honours, English was appointed a Knight Companion of the New Zealand Order of Merit, for services of over 27 years to the State 

See also

List of New Zealand governments
Politics of New Zealand

References

External links

Profile at National Party 
Profile on Parliament nz
Releases and speeches at Beehive govt nz

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1961 births
21st-century New Zealand politicians
Candidates in the 2017 New Zealand general election
Deputy Prime Ministers of New Zealand
Leaders of the Opposition (New Zealand)
Living people
Members of the Cabinet of New Zealand
Members of the New Zealand House of Representatives
New Zealand farmers
New Zealand finance ministers
New Zealand list MPs
New Zealand MPs for South Island electorates
New Zealand National Party MPs
New Zealand National Party leaders
New Zealand Roman Catholics
New Zealand people of Irish descent
People educated at St  Patrick's College, Silverstream
People from Dipton, New Zealand
People from Lumsden, New Zealand
Prime Ministers of New Zealand
University of Otago alumni
Victoria University of Wellington alumni
Knights Companion of the New Zealand Order of Merit
New Zealand politicians awarded knighthoods
Context 3: Paper Info

Title: Interpretable reduced-order modeling with time-scale separation Interpretable reduced-order modeling with time-scale separation
Publish Date: 7 March 2023
Author List: Sebastian Kaltenbach (from CSE-Lab, ETH Zurich, Harvard SEAS), Phaedon-Stelios Koutsourelakis (from CSE-Lab, ETH Zurich, Harvard SEAS), Petros Koumoutsakos (from CSE-Lab, ETH Zurich, Harvard SEAS), Harvard Seas (from CSE-Lab, ETH Zurich, Harvard SEAS)

Figure

FIG  5  Comparison between the phase-space of the reference solution (left) and the phase-space of the predictions
FIG  7  Comparison between predictions and reference solutions for a new initial condition fort = 1 25, 3 75, 7 5, 12 5, 20, 30  (from left to right and top to down) We note that with longer prediction time the uncertainty bounds increases Despite the chaotic nature of the KS equation, the predictive posterior mean is close to the reference solution for t ≤ 12 5

abstract

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering  However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial  We propose such a data-driven scheme that automates the identification of the time-scales involved and, can produce stable predictions forward in time as well as under different initial conditions not included in the training data 
To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space  It readily allows for the inclusion of sparse and irregularly sampled training data  The learned, latent dynamics are interpretable and reveal the different temporal scales involved 
We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix  Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation 
Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework 

INTRODUCTION

High-fidelity simulations of critical phenomena such as ocean dynamics and epidemics have become essential for decision-making  They are based on physically-motivated PDEs expressing system dynamics that span multiple spatiotemporal scales and which necessitate cumbersome computations   In recent years there is increased attention to the development of data-driven models that can accelerate the solution of these PDEs as well as reveal salient, lower-dimensional features that control the long-term evolution 
In most cases, data-driven reduced-order models are not interpretable  In particular, models based on neural networks despite good predictive capabilities , they offer a black-box description of the system dynamics  A possible remedy is applying a symbolic regression to the learned neural network representation , but this adds additional computational cost due to the two-step procedure 
A number of frameworks such as SINDy allows to learn interpretable dynamics but it relies on the a-priori availability of lower-dimensional descriptors and of time-derivatives which can be very noisy for both simulation and experimental data  Other frameworks are tailored to specific problems such as molecular dynamics  
Here, we present a framework that only needs the value of the observables, and not their derivatives, as training data and is capable of identifying interpretable latent dynamics  The deployment of interpretable latent dynamics ensures that conservation of important properties of that are reflected in the reduced-order model  
The present method is related to approaches based on the Koopman-operator extended Dynamic Mode Decomposition (eDMD) but uses continuous complex-valued latent space dynamics and only requires one scalar variable per latent dimension to describe the latent space dynamics  Therefore we do not have to enforce any parametrizations on the Koopman matrix  
The time-continuous formulation moreover allows to incorporate sparse and irregularly sampled training data and fast generation of predictions after the training phase  By using a complex-valued latent space we can also incorporate harmonic effects and reduce the number of latent variables needed  Linear and non-linear autoencoders are used to map the observed, high-dimensional time-series to the lower-dimensional, latent representation and we identify simultaneously the autoencoder as well as the latent dynamics by optimizing a combined loss function 
Hence the to tasks of dimensionality reduction and discovery of the reduced dynamics are unified while other frameworks treat the two parts separately   Apart from using an architecture based on autoencoders to identify the latent space, projection-based methods could also be employed   We are also proposing a probabilistic version of our algorithm ) that makes use of probabilistic Slow Feature Analysis  
This allows for a latent representation that arart from being time-continuous, can quantify the predictive uncertainty and hierarchically decompose the dynamics into their pertinent scales while promoting the discovery of slow processes that control the system's evolution over long time horizons  The rest of the paper is structured as follows: We introduce the methodological framework as well as algorithmic details in section II 
Particular focus is paid on the interpretability of the inferred lower-dimensional dynamics  In section III we present three numerical illustrations, i e  a system of linear ODEs, a hidden Markov Model and the discretized KS-equation  We then present in section IV the probabilistic extension of the framework and apply it to the KS-equation 
We conclude with a summary and a short discussion about possible next steps  We introduce the autoencoders deployed in this work, followed by the interpretable latent space dynamic and discuss the training process  We consider data from high-dimensional time series x n ∈ R f with n = 1,    , T   We remark that the intervals between the different states do not need to be uniformly spaced 

Autoencoder

A core assumption of the method is that each high-dimensional state x n can be compressed to a lower-dimensional representation z n ∈ C c with c << f   We identify this lower-dimensional representation by an autoencoder consisiting of a parameterized encoder and decoder  The encoder maps the high-dimensional representation to the latent space as:
The latent space is complex-valued  The decoder reconstructs the high-dimensional representation based on the latent variables as: We denote the parameters of the encoder as well as the decoder by θ  As discussed later in Section II C, both set of parameters are optimized simultaneously during training and therefore there is no need for differentiating them 

Interpretable Latent Space Dynamics

We employ a propagator in the latent space to capture the reduced-order dynamics of the system  In contrast to other time-extended variational autoencoder frameworks, our representation uses complex valued latent variables  In addition the latent variables are treated independently  The latter feature enables us to have an interpretable latent dynamics as well as a model that is especially suitable for being trained in the Small Data regime due to the small number of required parameters 
This is in contrast to temporal propagators such as LSTMs   For each dimension i of the latent variable z we are using the following continuous ODE in the complex plane: By solving this ODE, we can define the operator: Interpretable reduced-order modeling with time-scale separation Here, λ is a vector containing all the individual λ's and ∆t n indicates the time-step between the latent states 
The symbol is used to indicate a component-wise multiplication  We remark that the latent variables and the parameter governing the temporal evolution are complex numbers and their role in describing the system dynamics is similar to that of an eigenvalue  The real part is associated with growth and decay whereas the imaginary part is representing the periodic component 
This approach has similarities with the Koopman-operator based methods and the extended dynamic mode decomposition   In contrast to the methods mentioned before we are using a continuous formulation in the latent space that allows us to incorporate scarce and irregularly sampled training data and directly rely on complex numbers in the latent space 

Training and Predictions

We optimize a loss function that combines both a reconstruction loss as well as a loss associated with the error of our learned propagator in the latent space: (5) We note that we could directly incorporate mini-batch training by only taking the summation over a subset of the N available training data 
For new predictions of unseen states, we use the encoder to generate a latent representations which is then advanced in time by the learned propagator  At a designated time step we are using the decoder to reconstruct the high-dimensional solution  We applied our algorithm to three systems  First, we show that the algorithm is capable of exactly reproducing the solution of a linear ODE and to identify its eigenvalues 
Afterwards we are applying the framework to a high-dimensional process generated by a complex latent dynamics, which is correctly identified  As a final test case, we are applying the algorithm to a Kuramoto Shivashinski (KS) equation  Interpretable reduced-order modeling with time-scale separation

Linear ODE

We are considering a two-dimensional ODE system for x = y 1 y 2 : Based on the obtained training data we run our algorithm using a linear encoder and decoder structure as well as two latent variables z  The loss function was optimized using the Adam algorithm   As we consider a linear ODE we can analytically compute the eigenvalues involved and compare it with the parameters λ identified by our algorithm 
We observe in Figure that the algorithm was able to recover the correct values, i e  the eigenvalues 7 and 3 of the given linear ODE  The system does not have a periodic component and the two imaginary parts correctly go to zero, whereas the real parts converge to the reference value  Moreover we are also able to identify for the linear mapping between our latent variables z and the training data a matrix consisting of a multiple of the eigenvectors (1,1) and (1,-1) and thus the correct solution 
This example was chosen to show that the algorithm is able to quickly identify the exact solution of a linear ODE in terms of its linearly independent components 

Hidden multiscale dynamics

We consider eight-dimensional synthetic time series data produced by an underlying twodimensional complex valued process  In particular, the data points x are generated by first solving for the temporal evolution for the two complex-valued processes p 1 and p 2 and than mapping to the eight-dimensional space by using a randomly sampled linear mapping W  
One of the two processes used to generate the data is chosen to be much slower than the other one and both processes have a periodic component  dp 2 dt = (−0 9 + 1 5i)p 2 (8) As training data we consider 40 time series with 150 data points each, obtained by simulating the described processes for a maximum of t = 15 s and then sampling from the obtained data points 
Hence the training data consists of: • 40 time-series • with each consisting 150 observations of the x at a uniform time-step ∆t = 0 0025 The autoencoder obtained consists of one linear layer for both the decoder as well as the encoder  The model is trained for 5000 iterations using the Adam optimizer and a learning rate of 10 −3  
The results for the convergence of the parameters λ 1 and λ 2 can be found in Figure   We note that the process which is slower decaying and thus more responsible for the long-term evolution of the system has a higher convergence rate than the faster process  With the obtained parameters λ as well as the trained autoencoder, we compute predictions based on the last time step used for training, i e  we apply the encoder to obtain our latent representation and than use the latent dynamics to advance the latent representation in time 
Afterwards, we employ the decoder to reconstruct the full high-dimensional system  The results can be found in Figure and show very good agreement between predictions and reference data  This example shows that our model is successfully able to carry out dimensionality reduction and moreover indicates that the convergence rate between latent processes can be different 
The latter is relevant when training models as for accurate predictions all latent processes and their dynamics should be converged 

Kuramoto-Sivashinsky

Finally, we applied our algorithm to the KS equation and aim to identify a reduced-order model for the solution u(y, t): We employed periodic boundary conditions, µ = 1 and a domain size y ∈ [0, 22]  For this domain-size, the KS-equation exhibits a structurally stable chaotic attractor as discussed in The black lines divides the area for which training data was given from the area without raining data 
;   The equation is discretized in space using a discretization step of 22 64 resulting in a state vector x of dimension 64 and a nonlinear system of coupled ODEs  This is solved using a stiff fourth-order solver  We employed a non-linear encoder and decoder with four fully-connected layers each and ReLU-activation functions as well as Dropout Layers between the fully-connected layers 
We trained the model for 200000 iterations using Adam and a learning rate of 5 • 10 4 and assuming a five-dimensional latent space  We obtained the λ's in Figure   Four latent variables have λ's close to zero and thus a slow temporal dynamic that is responsible for the long-term evolution whereas one latent variable is quickly decaying 
Based on the obtained parameters, we do predictions based on an unseen initial condition not contained in the training data  We are able to reconstruct the correct phase space based on our predictions despite only using a very limited amount of training data  The results for the phase space can be seen in Figure  
Although the small-scale fluctuations in the temporal dynamics are not well captured, the model identifies the correct manifold which has a good accuracy compared to the reference solution  All phase-spaces were obtained by using a finite-difference operator on the data or predictions  These results are in accordance Interpretable reduced-order modeling with time-scale separation with whose LSTM-based temporal dynamic model was also able to find the correct phase space but not to track the actual dynamics for long-term predictions 
Our model is not able to account for noise in the temporal evolution and thus dealing with chaotic, small-scale fluctuations is challenging  We believe that a probabilistic version of our algorithm could be advantageous here  This section contains a fully probabilistic formulation for the deterministic model discussed before 
We replace the Autoencoder with a Variational Autoencoder and the ODE in the latent space with a SDE  The loss function which we optimize is the Evidence-Lower Bound (ELBO) 

Model Structure

We postulate the following relations for our probabilistic model using an Ornstein-Uhlenbeck (OU) for each dimension i of the latent space and a Wiener process W t in the latent space: We again assume that the latent variables z t are complex-valued and a priori independent  Complex variables were chosen as their evolution includes a harmonic components which are observed in many physical systems 
We assume an initial conditions z 0,i ∼ CN (0, σ 2 0,i )  The total parameters associated with the latent space dynamics of our model are thus {σ 2 0,i , σ 2 i , λ i } c i=1 and will be denoted by θ together with all parameters responsible for the decoder mapping G (see next section)  These parameters along with the state variables z t have to be inferred from the data x t  
Based on probabilistic Slow Feature Analysis (SFA) , we set σ 2 i = 2; (λ j ) and σ 2 0,i = 1  As a consequence, a priori, the latent dynamics are stationary  A derivation and reasoning for this choice can be found in Appendix A  Hence the only independent parameters are the λ i , the imaginary part of which can account for periodic effects in the latent dynamics 

Variational Autoencoder

We employ a variational autoencoder to account for a probabilistic mappings from the lower-dimensional representation z n to the high-dimensional system x n   In particular we are employing a probabilistic decoder The encoder is used to infer the state variables z based on the given data and thus defined in the inference and learning section 

Inference and Learning

Given the probabilistic relations , our goal is to infer the latent variables z 0:T as well as all model parameters θ  We follow a hybrid Bayesian approach in which the posterior of the state variables is approximated using amortized Variational Inference and Maximum-A-Posteriori (MAP) point-estimates for θ are computed 
The application of Bayes' rule for each data sequence x 0:T leads to the following posterior: where p(θ) denotes the prior on the model parameters  In the context of variational inference, we use the following factorization of the approximate posterior i e  we infer only the mean µ and variance σ for each state variable based on the given data points 
This conditional density used for inference is the encoder-counterpart to the probabilistic decoder defined in the section before  It can be readily shown that the optimal parameter values are found by maximizing the Evidence Lower Bound (ELBO) F(q φ (z 0:T ), θ) which is derived in Appendix B  We compute Monte Carlo estimates of the gradient of the ELBO with respect to φ and θ with the help of the reparametrization trick and carry out stochastic optimization with the ADAM algorithm  

Results for the probabilistic extension

We applied our probabilistic version to the KS-equation  We used the same settings as for the deterministic approach but considered up to 10 complex latent variables  The obtained λ's are in Figure   The probabilistic model allows us to quantify the uncertainty in predictions  In Figure predictions for various time-steps and the respective uncertainty bounds are shown for an unseen initial condition 
Due to the chaotic nature of the KS-equation and the small amount of training data, the underlying linear dynamic of our model is only able to capture the full dynamics for a limited time horizon  Fortunately, due to the probabilistic approach the model is capable of capturing chaotic fluctuations with increasingly wide uncertainty bounds 
We also computed the phase space representation for the KS-equation based on the predictions obtained by our model and compare it with the reference solution  The probabilistic model identifies the correct manifold with a better accuracy than the deterministic model  As some of the small-scale fluctuations are accounted as noise, the resulting manifold is more concentrated at the origin and the obtained values are slightly smaller than the reference manifold although their shape is very similar 



ground_truth: He became deputy prime minister and minister of finance.

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 does the framework capture the reduced-order dynamics?

Read the following text and answer briefly.

Context 4:  The systematic error includes the unknown phase between the
two resonances  Work is in progress on extracting the two Breit-Wigner
amplitudes 


\begin{figure}[htb]
\vspace*{-2mm}
\hspace*{-3mm}
\includegraphics[height=0 28\textheight,width=8 3cm]  {B08F02 eps}

\vspace*{-1cm}
\caption{Mass difference $\Delta M = M(B\pi)-M(B)$ for exclusive $B$ decays 
The background-subtracted signal is a sum of 
$B^*_1 \rightarrow B^* \pi$, $B^* \rightarrow B \gamma $ (open area)
and $B^*_2 \rightarrow B^*\pi$ $B^*\rightarrow B \gamma$ (lower peak in the shaded area)
and $B^*_2 \rightarrow B \pi$ (upper peak in the shaded area)  
(D\O) }
\label{fig:d0_bexc}
\end{figure}


\begin{figure}[htb]
\includegraphics[height=0 25\textheight,width=7 5cm]  {B05F03 eps}

\vspace*{-1cm}
\caption{The invariant mass distribution of
$(D^*,\pi)$ pairs, opposite sign (points) and same-sign (solid histogram) }
\label{fig:d0_dstst}
\end{figure}






\subsection{Lifetimes}


CDF and D\O\ have measured  lifetimes of $b$ hadrons through the exclusively
reconstructed decays $B^+ \rightarrow J/\psi K^+$, $B^0 \rightarrow J/\psi K^{*0}$,
$B_s \rightarrow J/\psi \phi$, 
and $\Lambda_b \rightarrow J/\psi \Lambda$
(Fig  \ref{fig:d0_lbctau}) 
The latest results are:  \\



 $\tau(B^+)$=1 65 $\pm$ 0 08 $^{+0 096}_{-0 123}$  ps ~(D\O\ 2003),

 $\tau(B^+)$=1 662 $\pm$ 0 033  $\pm$ 0 008  ps ~(CDF),

 $\tau(B^0_d)$=1 473  $^{+0 052}_{-0 050}$ $\pm$ 0 023    ps ~(D\O) 

 $\tau(B^0_d)$=1 539 $\pm$ 0 051  $\pm$ 0 008  ps ~(CDF),

 $\tau(B^0_s)$=1 444   $^{+0 098}_{-0 090}$ $\pm$ 0 020   ps ~(D\O),

 $\tau(B^0_s)$=1 369 $\pm$ 0 100 $\pm$ $^{+0 008}_{0 010}$  ps ~(CDF),


 $\tau(\Lambda_b)$=1 221 $^{+0 217}_{-0 179}$ $\pm$ 0 043  ps ~(D\O),


 $\tau(\Lambda_b)$=1 25 $\pm$ 0 26 $\pm$ 0 10  ps ~(CDF 2003) \\



The measured lifetimes correspond to the following lifetime ratios:\\

$\tau(B^+)/\tau(B^0_d)$   =  1 080$\pm$0 042     ~(CDF),
 
$\tau(B^0_s)/\tau(B^0_d)$ =  0 890$\pm$0 072    ~(CDF),

$\tau(B^0_s)/\tau(B^0_d)$ = 0 980$ ^{+0 075}_{-0 070}   \pm$0 003    ~(D\O),

$\tau(\Lambda_b)/\tau(B^0_d)$ =  0 874$ ^{+0 169}_{-0 142}   \pm$0 028    ~(D\O) \\



\begin{figure}[htb]
\includegraphics[height=0 3\textheight,width=8 2cm]  {d0_lbctau_B11F02 eps}
\vspace*{-1cm}

\caption{ Fit projection on  $c\tau$ for the $\Lambda_b$ candidates   (D\O)}
\label{fig:d0_lbctau}
\end{figure}


The $B_s$ lifetime measurements listed above are results of
a single-lifetime fit to data, integrated over the decay angles 
Because  of the presence of  final
states  common to ${B_s^0}$\ and its charge conjugate ${\overline{B}_s^0}$,
the two meson states   are expected
to mix in such a way that the two CP  eigenstates may have a relatively
large lifetime difference 
It is possible to
separate the two CP components of ${B_s^0 \rightarrow J/\psi \phi}$\ and thus to measure the
lifetime difference by studying the time evolution of the
polarization states of the vector mesons in the final state 
CDF has carried out a combined analysis of $B_s$ lifetimes 
and polarization amplitudes  The results for the lifetimes of the
low mass (CP even) and high mass (CP odd) eigenstates, and the relative 
width difference are:\\

 $\tau_L = 1 05 ^{+0 16}_{-0 13} \pm 0 02$ ~ps,
 
 $\tau_H = 2 07 ^{+0 58}_{-0 46} \pm 0 03$ ~ps,

 $\Delta \Gamma /\overline \Gamma   = 0 65 ^{+0 25}_{-0 33} \pm 0 01$ \\

Figure \ref{fig:cdf_dg} shows  the scan of the likelihood function 
for $\Delta \Gamma /\overline \Gamma$ 
Pseudoexperiments tossed with $\Delta \Gamma /\overline \Gamma =0$
yield the betting odds for observing the above results at
1/315  For $\Delta \Gamma /\overline \Gamma = 0 12$ (SM prediction,
which has recently been updated to 0 14$\pm$0 05~\cite{dg_un}) the betting odds are
1/84 

\begin{figure}[htb]
\vspace*{-1mm}
\includegraphics[height=0 3\textheight,width=8 2cm]  {cdf_scan-dg-un eps}

\vspace*{-1cm}
\caption{Scan of the likelihood function 
for $\Delta \Gamma /\overline \Gamma$ (CDF) 
}
\label{fig:cdf_dg}
\end{figure}




D\O\ has used a novel technique to  measure the lifetime ratio
of the charged and neutral $B$ mesons, exploiting the large
semileptonic sample  $B$ hadrons were reconstructed in the channels
$B\rightarrow \mu^+ \nu D^*(2010)^-X$, which are dominated by $B^0$ decays, 
and  $B\rightarrow \mu^+ \nu D^0X$, which are dominated by $B^+$ decays 
The lifetime ratio was
obtained from the variation of the ratio of the number of events in these two
processes at different decay lengths 
The result is \\


$\tau(B^+)/\tau(B^0_d)$   =  1 093$\pm$0 021$\pm$0 022       ~(D\O)




\subsection{Towards $B_s$ mixing}

Measurement of the $B_s$ oscillation frequency via ${B_s^0}$ -${\overline{B}_s^0}$ ~mixing
will provide an important constraint on the CKM matrix  The oscillation
frequency is proportional to the mass difference between the mass eigenstates,
$\Delta m_s$, and is related to the CKM matrix through 
$\Delta m_s \propto |V_{tb}V_{ts}|$  When combined with the
$B_d$ mass difference, $\Delta m_d$ it helps in extraction of $|V_{td}|$,
and thereby the CP violating phase  

As a benchmark for future $B_s$ oscillation measurement, both groups
study  $B_d$ mixing, gaining an understanding of the different components
of a $B$ mixing analysis (sample composition, flavor tagging, vertexing,
asymmetry fitting)  For a sample of partially reconstructed decays
$B\rightarrow D^*(2010)^+\mu^-X$, D\O\ obtains 
$\Delta m_d = 0 506 \pm 0 055 (stat) \pm  0 049 (syst))$ ps$^{-1}$ and
$\Delta m_d = 0 488 \pm 0 066 (stat) \pm  0 044 (syst))$ ps$^{-1}$
when employing  opposite side muon tagging and the same side tagging,
respectively 

The CDF result for semileptonic channels is
$\Delta m_d = 0 536 \pm 0 037 (stat) \pm  0 009 (s c ) \pm 0 015 (syst)$ ps$^{-1}$ 
CDF also reports a result on $B$ oscillations using fully reconstructed
decays:
$\Delta m_d = 0 526 \pm 0 056 (stat) \pm  0 005 (syst))$ ps$^{-1}$ 

Reconstructing $B_s$ decays into different final states is another
important
 step in the ${B_s^0}$ -${\overline{B}_s^0}$ ~mixing analysis 
Thanks to the  large muon and tracking coverage,   D\O\ is accumulating
a  high statistics sample of semileptonic $B_s$ decays 
D\O\ reconstructs the $B_s \rightarrow D^+_s \mu^- X$ decays, with
$D^+_s \rightarrow \phi \pi^+ $ and
$D^+_s \rightarrow K^* K^+ $,
at a rate of $\approx$ 40(25) events per pb$^{-1}$,  respectively 
Figure \ref{fig:d0_bsdsphipi} shows the mass distribution of the
$D^+_s \rightarrow \phi \pi$ candidates 


\begin{figure}[htb]
\vspace*{-5mm}
\includegraphics[height=0 3\textheight,width=8 0cm]  {blds-250 eps}
\vspace*{-1 2cm}
\caption{  $D^+_s \rightarrow \phi \pi^+$  signal  (D\O)}
\label{fig:d0_bsdsphipi}
\end{figure}


\begin{figure}[htb]
\vspace*{-10mm}
\hspace*{-4mm}
\includegraphics[height=0 35\textheight,width=7 9cm]  {cdf_Bs-DsPi-PhiPi eps}

\vspace*{-1 0cm}
\caption{ $B_s \rightarrow D_s \pi$, $D_s \rightarrow \phi \pi$  signal   (CDF)}
\label{fig:cdf_bsdsphipi}
\end{figure}


CDF has clean signals for fully hadronic, flavor-specific  $B_s$ decays,
providing the best sensitivity to $B_s$ oscillations at high
$\Delta m_s$  Figure \ref{fig:cdf_bsdsphipi} shows the signal for
the best channel, $B_s \rightarrow D_s \pi$, $D_s \rightarrow \phi \pi$ 

\clearpage


\subsection{Rare decays}

The purely leptonic decays $B_{d,s}^0 \rightarrow \mu^+
\mu^-$ are flavor-changing neutral current (FCNC) processes 
In the standard model, these decays are forbidden at the tree level and
proceed at a very low rate through higher-order diagrams 
The latest SM prediction~\cite{sm_ref3}
is ${\cal B}(B^0_s \rightarrow \mu^+ \mu^-)=(3 42\pm 0 54)\times
10^{-9}$, where the error is dominated by non-perturbative uncertainties  The
leptonic branching fraction of the $B_d^0$ decay is suppressed by CKM matrix elements $|V_{td}/V_{ts}|^2$
leading to a predicted SM branching fraction of $(1 00\pm0 14)\times 10^{-10}$ 
The best published experimental bound (Fig ~\ref{fig:cdf_bsmumu})
 for the branching fraction
of $B^0_s$ $(B^0_d)$ is presently
${\cal B}(B^0_s \, (B^0_d) \rightarrow \mu^+\mu^-)<7 5\times 10^{-7}\, 
(1 9\times 10^{-7})$ at the 95\% C L ~\cite{cdfII} 
The decay amplitude of $B^0_{d,s} \rightarrow \mu^+ \mu^-$ can be
significantly enhanced in some extensions of the SM  

\begin{figure}[htb]
\includegraphics[height=8 3cm,width=7 9cm]  {cdfbsmumu_results_prl eps}

\vspace*{-1cm}
\caption{Invariant mass for the events passing all requirements  (CDF)}
\label{fig:cdf_bsmumu}
\end{figure}


Assuming no contributions 
from the decay $B^0_d\rightarrow \mu^+\mu^-$ in the signal region,
D\O\  finds the conservative upper limit on the branching fraction 
to be ${\cal B}(B^0_s \rightarrow \mu^+ \mu^-) \leq 4 6\times 10^{-7}$ 
at the 95\% C L  (Fig ~\ref{fig:d0_bsmumu}) 






\begin{figure}[htb]
\includegraphics[height=5 0cm,width=8 0cm]  {B06F03 eps}
\vspace*{-1cm}
\caption{Invariant mass for the events  passing all requirements  (D\O)}
\label{fig:d0_bsmumu}
\end{figure}





ground_truth: By using a propagator in the latent space.