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: When did Born resign as chairperson of the CFTC?

Read the following text and answer briefly.

Context 1: Brooksley Elizabeth Born (born August 27, 1940) is an American attorney and former public official who, from August 26, 1996, to June 1, 1999, was chair of the Commodity Futures Trading Commission (CFTC), the federal agency which oversees the U S  futures and commodity options markets  During her tenure on the CFTC, Born lobbied Congress and the President to give the CFTC oversight of off-exchange markets for derivatives, in addition to its role with respect to exchange-traded derivatives, but her warnings were ignored or dismissed, and her calls for reform resisted by other regulators <ref name="nytimes">Goodman, Peter S  The Reckoning - Taking Hard New Look at a Greenspan Legacy, The New York Times, October 9, 2008 </ref> Born resigned as chairperson on June 1, 1999, shortly after Congress passed legislation prohibiting her agency from regulating derivatives 

In 2009, Born received the John F  Kennedy Profiles in Courage Award, along with Sheila Bair of the Federal Deposit Insurance Corporation, in recognition of the "political courage she demonstrated in sounding early warnings about conditions that contributed" to the 2007-08 financial crisis 

Early life and education
Born graduated from Abraham Lincoln High School (San Francisco, California) at the age of 16  She then attended Stanford University, where she majored in English and was graduated with the class of 1961   She initially wanted to become a doctor, but a guidance counsellor at Stanford advised her against medicine, so she majored in English literature instead 

She then attended Stanford Law School, one of only seven women in her class   She was the first female student ever to be named president of the Stanford Law Review  She received the "Outstanding Senior" award and graduated as valedictorian of the class of 1964 

Legal career
Immediately after law school Born was selected as a law clerk to judge Henry Edgerton of the U S  Court of Appeals for the District of Columbia Circuit  It was during this time that she met her first husband, Jacob C  Landau, who was a journalist covering the Federal courts at the time  Following her clerkship, she became an associate at the Washington, D C -based international law firm of Arnold & Porter  Born was attracted to Arnold & Porter because it was one of the few major law firms to have a woman partner at that time, Carolyn Agger, who was the head of the tax practice  Born took a two-year leave of absence from Arnold & Porter to accompany her first husband to Boston, where he had received a fellowship  During that time she worked as a research assistant to law professor Alan Dershowitz 

Born's early career at Arnold & Porter focused on international trade law, in which she represented a number of Swiss industries and the government of Switzerland  She developed a practice representing clients in numerous complex litigation and arbitration cases involving financial market transactions  Among her high-profile cases was the matter of the Hunt Brothers attempt to corner the market in silver in the 1970s  She made partner at Arnold & Porter, after moving to a three-day schedule to help raise her second child, and eventually rose to be the head of the firm's derivatives practice 

Born was among the first female attorneys to systematically address inequities regarding how the laws treated women  Born and another female lawyer, Marna Tucker, taught what is considered to have been the first "Women and the Law" course at Catholic University’s Columbus School of Law  The class exclusively concerned prejudicial treatment of women under the laws of the United States, past and present   Born and Tucker were surprised to discover that there was no textbook on the issue at the time   Born is also one of the co-founders of the National Women's Law Center  Born also helped rewrite the American Bar Association rules to make it possible for more women and minorities to sit on federal bench 

During her long legal career, and into her retirement, Born did much pro bono and other types of volunteer work  She was active in the American Bar Association, the largest professional organization of lawyers in the United States   Initially Born was named a member of the governing council of the ABA's Individual Rights Section, eventually becoming chairperson   Born and Tucker founded the ABA Women's Caucus, the first organization of female lawyers in the ABA   She held several other senior positions in the ABA, including being named the first woman member of the ABA's Standing Committee on the Federal Judiciary   As a member of the Judiciary Committee, Born provided testimony and opinion on persons nominated for federal judgeships  In 1980 she was named chair of the committee   As chair of the committee, Born was invited to address the U S  Congress regarding the nomination of Judge Sandra Day O'Connor to the U S  Supreme Court 

In 1993, Born's name was floated as a possible candidate for Attorney General of the United States, but Janet Reno was nominated 

In July 2009, Nancy Pelosi appointed Brooksley Born as a commissioner to the Financial Crisis Inquiry Commission (FCIC) 

Born and the OTC derivatives market
Born was appointed to the CFTC on April 15, 1994, by President Bill Clinton  Due to litigation against Bankers Trust Company by Procter and Gamble and other corporate clients, Born and her team at the CFTC sought comments on the regulation of over-the-counter derivatives, a first step in the process of writing CFTC regulations to supplement the existing regulations of the Federal Reserve System,  the Options Clearing Corporation, and the National Association of Insurance Commissioners  Born was particularly concerned about swaps, financial instruments that are traded over the counter between banks, insurance companies or other funds or companies, and thus have no transparency except to the two counterparties and the counterparties' regulators, if any   CFTC regulation was strenuously opposed by Federal Reserve chairman Alan Greenspan, and by Treasury Secretaries Robert Rubin and Lawrence Summers  On May 7, 1998, former SEC Chairman Arthur Levitt joined Rubin and Greenspan in objecting to the issuance of the CFTC's concept release  Their response dismissed Born's analysis and focused on the hypothetical possibility that CFTC regulation of swaps and other OTC derivative instruments could create a "legal uncertainty" regarding such financial instruments,  hypothetically reducing the value of the instruments  They argued that the imposition of regulatory costs would "stifle financial innovation" and encourage financial capital to transfer its  transactions offshore  The disagreement between Born and the Executive Office's top economic policy advisors has been described not only as a classic Washington turf war, but also a war of ideologies,  insofar as it is possible to argue that Born's actions were consistent with Keynesian and neoclassical economics while Greenspan, Rubin, Levitt, and Summers consistently espoused neoliberal, and neoconservative policies 

In 1998, a trillion-dollar hedge fund called Long Term Capital Management (LTCM) was near collapse   Using mathematical models to calculate debt risk, LTCM used derivatives to leverage $5 billion into more than $1 trillion, doing business with fifteen of Wall Street's largest financial institutions   The derivative transactions were not regulated, nor were investors able to evaluate LTCM's exposures   Born stated, "I thought that LTCM was exactly what I had been worried about"   In the last weekend of September 1998, the President's working group was told that the entire American economy hung in the balance   After intervention by the Federal Reserve, the crisis was averted   In congressional hearings into the crisis, Greenspan acknowledged that language had been introduced into an agriculture bill that would prevent CFTC from regulating the derivatives which were at the center of the crisis that threatened the US economy   U S  Representative Maurice Hinchey (D-NY) asked "How many more failures do you think we'd have to have before some regulation in this area might be appropriate?"  In response, Greenspan brushed aside the substance of Born's warnings with the simple assertion that "the degree of supervision of regulation of the over-the-counter derivatives market is quite adequate to maintain a degree of stability in the system"  Born's warning was that there wasn't any regulation of them   Born's chief of staff, Michael Greenberger summed up Greenspan's position this way: "Greenspan didn't believe that fraud was something that needed to be enforced, and he assumed she probably did  And of course, she did "  Under heavy pressure from the financial lobby, legislation prohibiting regulation of derivatives by Born's agency was passed by the Congress   Born resigned on June 1, 1999 

The derivatives market continued to grow yearly throughout both terms of George W  Bush's administration  On September 15, 2008, the bankruptcy of Lehman Brothers forced a broad recognition of a financial crisis in both the US and world capital markets   As Lehman Brothers' failure temporarily reduced financial capital's confidence, a number of newspaper articles and television programs suggested that the failure's possible causes included the conflict between the CFTC and the other regulators Faiola, Anthony, Nakashima, Ellen and Drew, Jill  The Crash: Risk and Regulation - What Went Wrong, The Washington Post, October 15, 2008 

Born declined to publicly comment on the unfolding 2008 crisis until March 2009, when she said: "The market grew so enormously, with so little oversight and regulation, that it made the financial crisis much deeper and more pervasive than it otherwise would have been " She also lamented the influence of Wall Street lobbyists on the process and the refusal of regulators to discuss even modest reforms 

An October 2009 Frontline documentary titled "The Warning"  described Born's thwarted efforts to regulate and bring transparency to the derivatives market, and the continuing opposition thereto  The program concluded with an excerpted interview with Born sounding another warning: "I think we will have continuing danger from these markets and that we will have repeats of the financial crisis -- may differ in details but there will be significant financial downturns and disasters attributed to this regulatory gap, over and over, until we learn from experience "

In 2009 Born, along with Sheila Bair of the FDIC, was awarded the John F  Kennedy Profiles in Courage Award in recognition of the "political courage she demonstrated in sounding early warnings about conditions that contributed" to the 2007-08 financial crisis   According to Caroline Kennedy, "Brooksley Born recognized that the financial security of all Americans was being put at risk by the greed, negligence and opposition of  powerful and well connected interests     The catastrophic financial events of recent months have  proved them [Born and Sheila Bair] right "  One member of the President's working group had a change of heart about Brooksley Born   SEC Chairman Arthur Levitt stated "I've come to know her as one of the most capable, dedicated, intelligent and committed public servants that I have ever come to know", adding that "I could have done much better  I could have made a difference" in response to her warnings 

In 2010, a documentary film Inside Job further alleged that derivatives regulation was ineffective from the Clinton administration on  Along with fellow whistleblower, former IMF Chief Economist Raghuram Rajan, who was also scorned by the economic establishment, Brooksley Born was cited as one of the authorities arguing that financial derivatives increase economic risk 

 Personal life 
Born is married to Alexander E  Bennett (also retired from Arnold & Porter)   She has five adult children - two from a previous marriage to Jacob Landau and three stepchildren  Notably, Born was named a partner at Arnold & Porter while working part-time so she could raise her two young children   When both of her children were school-age, Born returned to practice full-time 

References

External links
Attorney profile at Arnold & Porter
Brooksley Born (2009 Winner) of the Profiles in Courage Award, with acceptance speech transcript and NECN video

Profile at MarketsWiki
Speeches and statements
"Testimony Of Brooksley Born Chairperson of the CFTC Concerning The Over-The-Counter Derivatives Market", before the House Committee On Banking And Financial Services, July 24, 1998 
"The Lessons of Long Term Capital Management L P ", Remarks of Brooksley Born, Chairperson of the CFTC, Chicago-Kent-IIT Commodities Law Institute, Chicago, Illinois, October 15, 1998 
 Interview: Brooksley Born for "PBS Frontline: The Warning", PBS, (streaming VIDEO 1 hour), October 20, 2009 
Articles
Manuel Roig-Franzia  "Credit Crisis Cassandra:Brooksley Born's Unheeded Warning Is a Rueful Echo 10 Years On", The Washington Post, May 26, 2009
 Taibbi, Matt  "The Great American Bubble Machine", Rolling Stone'', July 9–23, 2009

1940 births
American women lawyers
Arnold & Porter people
Clinton administration personnel
Columbus School of Law faculty
Commodity Futures Trading Commission personnel
Heads of United States federal agencies
Lawyers from San Francisco
Living people
Stanford Law School alumni
21st-century American women
Stanford University alumni
Context 2: Overfishing is a major threat to the survival of shark species, primarily driven by international trade in high-value fins, as well as meat, liver oil, skin and cartilage  The Convention on the International Trade in Endangered Species of Wild Fauna and Flora (CITES) aims to ensure that commercial trade does not threaten wild species, and several shark species have recently been listed on CITES as part of international efforts to ensure that trade does not threaten their survival  However, as international trade regulations alone will be insufficient to reduce overexploitation of sharks, they must be accompanied by practical fisheries management measures to reduce fishing mortality  To examine which management measures might be practical in the context of a targeted shark fishery, we collected data from 52 vessels across 595 fishing trips from January 2014 to December 2015 at Tanjung Luar fishing port in East Lombok, Indonesia  We recorded 11,920 landed individuals across 42 species, a high proportion of which were threatened and regulated species  Catch per unit effort depended primarily on the number of hooks and type of fishing gear used, and to a lesser degree on month, boat engine power, number of sets and fishing ground  The most significant factors influencing the likelihood of catching threatened and regulated species were month, fishing ground, engine power and hook number  We observed significant negative relationships between standardised catch per unit effort and several indicators of fishing effort, suggesting diminishing returns above relatively low levels of fishing effort  Our results suggest that management measures focusing on fishing effort controls, gear restrictions and modifications and spatiotemporal closures could have significant benefits for the conservation of shark species, and may help to improve the overall sustainability of the Tanjung Luar shark fishery  These management measures may also be applicable to shark fisheries in other parts of Indonesia and beyond, as sharks increasingly become the focus of global conservation efforts 
Copyright: © 2018 Yulianto et al  This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 
Funding: Data collection of this study was funded by the Darwin Initiative (grant number 2805)  The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript 
Overfishing is the greatest global threat to marine fish stocks [1–5]  Several shark species (Selachimorpha) are particularly vulnerable to overexploitation due to their conservative life history strategies, large body sizes and the high economic value of their preserved body parts [6–8]  With increasing fishing pressure in recent decades, primarily driven by international demand for a range of consumer goods (including fins, liver oil, skin, cartilage and meat), it is estimated that annual fishing mortality now exceeds the intrinsic rebound potential of most commercially exploited species [5, 9, 10]  This fishing pressure is taking its toll, with an estimated one in four Chondrichthyan species now threatened with extinction, making sharks amongst the most threatened species groups in the world  
It is also increasingly acknowledged that sharks play a critical role in maintaining functional and productive ocean ecosystems , as well as providing an important source of food and income for many coastal communities   Recognising both the plight and importance of shark populations, there is growing professional and public interest to improve shark conservation, and the management of shark fisheries and trade   This is reflected in several recent policy decisions to afford new international regulations for 12 species of sharks across seven genera under the Convention on the International Trade of Endangered Species of Wild Fauna and Flora (CITES)  This is a promising step for shark conservation; however, in order to create tangible outcomes for species conservation CITES must be implemented through domestic measures that are adapted to national and local contexts 
Indonesia is the world’s largest shark fishing nation [9, 14], and a global priority for shark conservation   Until recently Indonesia’s shark fishery has largely functioned as de facto open-access [12, 16]  However, in the past five years the Indonesian government has demonstrated a clear commitment to shark conservation and resource management, with domestic measures put in place to implement international obligations under CITES   Exploitation of all CITES-listed species is now regulated, either through full species protection or export controls (these species are hereafter referred to as ‘regulated’ species)  However, CITES only affords protection to a small number of Indonesia’s 112 known shark species , of which 83 are threatened with extinction according to the IUCN Red List of Threatened Species (i e  Vulnerable (VU), Endangered (EN) or Critically Endangered (CR) , these species are hereafter referred to as ‘threatened’ species), many of which continue to be landed throughout the country   Further, these policy measures predominantly regulate trade at the point of export, but do not necessarily influence fisher behaviour or local demand at the point of catch, such that the ‘trickle-down’ impacts on species mortality are unknown  In addition, effectively implementing species-specific shark mortality controls remains challenging due to the non-selectivity of fishing gears, and practical and cultural barriers to changing fisher preferences for certain gear-types and fishing methods  As such, existing regulations alone (e g  Indonesian Law on Fisheries 31/2004 and its derivative regulations) will likely be insufficient to curb mortality of threatened and regulated species, as fishers must be both willing and able to change their fishing behaviour   Moreover, most of Indonesia’s shark fisheries are small-scale, and in relatively poor coastal communities where there are often no legal, sustainable marine-based alternatives to shark fishing that offer similar financial returns [22, 23]  It is therefore imperative to consider the ethical and socioeconomic impacts of shark trade controls  Most shark species listed under CITES are listed on Appendix II, which is designed for sustainable use  International trade is permitted for CITES Appendix II species provided it is non-detrimental to wild populations of the species, as proven through a scientific non-detriment finding (NDF) report and implemented through a system of export permits  However, in Indonesia there is currently a lack of species-specific trade data for conducting NDFs and setting sustainable export quotas, such that the Indonesian government has to introduce trade bans for these species in order to meet CITES obligations  With new CITES-listings for thresher sharks (Alopias spp ) and silky shark (Carcharhinus falciformis) recently coming into force, this is likely to have huge implications for Indonesia’s economically important shark industry, and the coastal communities depending on it  In order to balance conservation and socioeconomic objectives, robust management systems must be put in place that ensure and allow sustainable fishing and trade  This necessitates the identification of practical management measures that can reduce mortality of threatened and regulated species at the point of catch, and provide realistic options for fishers to effectively and measurably improve the sustainability of their fishing practices 
This study analyses two years of qualitative and quantitative data from one of Indonesia’s targeted shark fisheries in Tanjung Luar, West Nusa Tenggara Province  We outline the key characteristics of the fishery, including fishing behaviour and overall catch volumes and composition  We analyse the impacts of different fishing techniques, and present factors influencing overall catch per unit effort (CPUE) of individual shark fishing trips, as well as factors influencing the likelihood of catching threatened and regulated species  Finally, we discuss the implications of our findings, and provide practical recommendations for fisheries management measures, which can support CITES implementation for sharks and reduce the catch of threatened and regulated species, in Indonesia and beyond 
This work was conducted under a Memorandum of Understanding (MoU) and Technical Cooperation Agreement (TCA) between the Wildlife Conservation Society (WCS) and the Ministry of Environment and Forestry (MoEF), Ministry Marine Affairs and Fisheries (MMAF) and the Marine and Fisheries Agency (MFA) of West Nusa Tenggara Province  These documents were approved and signed by Sonny Partono (Director General of Conservation of Natural Resources and Ecosystem MoEF), Sjarief Widjaja (Secretary General MMAF), and Djoko Suprianto (Acting Head of MFA of West Nusa Tenggara Province)  Due to this MoU and TCA no specific research permit was required  We collected data by measuring sharks that were already caught, dead, and landed by fishers in Tanjung Luar, with no incentives, compensation or specific requests for killing sharks for this study  WCS participates in the Conservation Initiative on Human Rights and the rules and guidelines of our Internal Review Board ensures that any research protects the rights of human subjects  We did not apply for an IRB permit for this study because our study design focused on collecting fish and fisheries data as opposed to personal socio-economic data  The FDGs and interviews were conducted to obtain early scoping information about fishing practices, and to establish protocols for more detailed fisheries data collection (as used in this study), and socio-economic data collection (as used in a later study (Lestari et al ), which underwent further ethical review due to the specific focus on human subjects) 
Tanjung Luar, located in East Lombok, West Nusa Tenggara Province, Indonesia (Fig 1), is a landing site for one of Indonesia’s most well-known targeted shark fisheries  Tanjung Luar serves at least 1,000 vessels, and the majority of these are less than 10 gross tonnes (GT) in size   A group of specialised fishers operating from Tanjung Luar village and a neighbouring island, Gili Maringkik, specifically target sharks  Shark catch is landed in a dedicated auction facility at the Tanjung Luar port  The shark industry is well established in Tanjung Luar, with product processing facilities and trade connections to local, national and international markets  Research by Lestari et al   indicates that the shark industry is significantly more profitable than non-shark fisheries in Tanjung Luar, particularly for boat owners  Strong patron-client relationships exist between boat owners and fishers, with shark fishers exhibiting high dependency on shark fishing, limited occupational diversity and low adaptive capacity for shifting into other fisheries  
Fig 1  Sharks landing monitoring site and fishing grounds of shark fishers that land at Tanjung Luar 
In January 2014 we conducted preliminary scoping research to better understand the operational and socioeconomic characteristics of Tanjung Luar’s shark fishery  During a three-week scoping visit a team of four trained Indonesian enumerators conducted semi-structured interviews and focus group discussions (FDGs) with fishers, boat owners and traders, alongside naturalistic observation in the field  Respondents were selected through purposive sampling, since the research was exploratory in nature and a priori sampling decisions were not possible   We conducted a total of 34 semi-structured interviews (S1 File) and four FDGs, which were attended by a total of 30 individuals  All interviews and discussions took place in Indonesian, with the help of a local enumerator who was fluent in the Tanjung Luar local dialect  Interviews took approximately 30 minutes, with no remuneration for participating  All respondents gave their full prior and informed consent before contributing to the research  During the interviews and FDGs we gathered information on number of boats, fishing gears used, fishing grounds, fishery operational characteristics, and shark supply chain, including estimated volumes and value of shark catch relative to other fisheries  We improved the accuracy of information on shark fishery characteristics and fishing behaviour through informal daily interactions and discussions with 131 shark fishers during our daily landings data collection and community engagement activities  More detailed socioeconomic data were collected in a full household survey in 2016, as outlined in Lestari et al   
Shark landings data were collected by three experienced enumerators, who were trained in species identification and data collection methods during a two-day workshop and three weeks of field mentoring to ensure the accuracy of the data collected  Landings were recorded every morning at the Tanjung Luar shark auction facility where shark fishers usually landed dead sharks, from 5am to 10am from January 2014 to December 2015  The enumerators recorded data on catch composition and fishing behaviour (Table 1) from 52 different vessels across a total of 595 fishing trips  The enumerators also measured the weight of selected sharks to calculate biomass and length-weight relationship 
Table 1  Types of data collected on fishing behaviour and catch composition during daily landings data collection at Tanjung Luar 
From fishing behaviour and catch data we calculated the overall species composition of catch  We calculated catch per unit effort (CPUE) by number of individuals using both catch per set (hereafter CPUE per set) and catch per 100 hooks per set (hereafter standardised CPUE) [25,26]  This was deemed necessary since different vessels and gear-types systematically deploy different numbers of hooks, and standardised CPUE allows for a more meaningful comparison 
To understand factors influencing overall CPUE we log transformed CPUE per trip to fit a normal distribution, and fitted linear models (LMs) of CPUE per trip to fishing behaviour variables (Table 1)  We considered all variables and used minimum AIC values with stepwise analysis of variance to identify the best fit and most significant influencing variables 
To inform the development of practical fisheries management measures (e g  gear restrictions), we also specifically analysed differences in CPUE for surface and bottom longline gears employed in the fishery, using two-way ANOVAs 
Factors affecting catch of threatened and regulated species 
To identify variables influencing the catch of threatened and regulated species we conducted a two-step process  In the first step, we identified factors influencing the likelihood of catching any threatened/regulated species during a given fishing trip, by creating binary response variables for whether a threatened species had been caught during a trip (yes = 1, no = 0), and separately for whether a regulated species had been caught during a trip (yes = 1, no = 0)  We then fitted generalised linear models (GLMs) with binomial errors to the binary response variables, separately for catch of threatened species and catch of regulated species  In the second step we identified variables that significantly influenced the CPUE of threatened species and the CPUE of regulated species, given that any were caught  We removed all records in which no threatened or regulated species were caught, log transformed standardised CPUE of threatened and regulated species, and fitted linear models (LMs) of standardised CPUE of threatened species and standardised CPUE to regulated species to fishing behaviour variables  Again, we considered all meaningful models and used minimum AIC values with stepwise analysis of variance to identify the best fit  and most significant influencing variables  This approach was necessary since catch of threatened and regulated species is zero-inflated, and creating binary response variables with a binomial error structure allowed for a simpler and more powerful statistical analysis  Note that we conducted two separate analyses, one for threatened species only and one for regulated species only, but used the same methods and process, as outlined above, for each analysis  We did not group threatened and protected species together, since although some species are both threatened and protected, this is not the case for all shark species landed in Tanjung Luar 
A total of 52 shark fishing vessels operate from Tanjung Luar, all of which are classified as small-scale according to the Indonesian Ministry of Marine Affairs and Fisheries (MMAF) vessel categorisation system, with <7GT capacity  These vessels are operated by approximately 150 highly-specialised shark fishers, from Tanjung Luar village and Gili Maringkik, who make up roughly 5% of the local fisher population  The shark industry is more profitable than non-shark fisheries, and shark fishers report high household dependency on shark resources, low occupational diversity, and limited capacity and aspirations to move into other fisheries or industries 
Surface and bottom longlines are used as the primary fishing gears to target sharks, with pelagic fish (e g  Euthynnus spp , Rastrellinger spp ) used as bait  Surface and bottom longlines systematically vary in length, depth deployed, number of sets, number of hooks used, and soak times (Table 2)  Gear types are typically associated with certain vessel types, and fishers–captain and crew—tend to exhibit preferences for specific gear types  Shark fishers also use gillnets and troll lines as secondary gears, to catch bait and opportunistically target other species, such as grouper, snapper, skipjack and mackerel tuna 
Table 2  Characteristics of surface and bottom longlines 
The shark fishing vessels can be divided into two broad categories according to fishing behaviour: larger vessels (≥14 m) with higher horsepower (HP) engines spend more time at sea than smaller vessels (≤12m) (p<0 001), and reach fishing grounds outside of West Nusa Tenggara  These vessels primarily fish in southern Sumbawa and Sumba Islands, however, they also reach as far as eastern Flores, Timor Island, and the Java Sea (Fig 1)  Larger, higher HP vessels also tend to employ surface longlines (p<0 001), and since they spend more time at sea, have a higher number of sets per trip than smaller vessels (p<0 001)  Smaller vessels (≤12 m) with smaller engines tend to remain in waters around West Nusa Tenggara only, carrying out shorter fishing trips using bottom longlines (Table 3) 
Table 3  Characterisation of the different fishing vessels used to target sharks in Tanjung Luar 
During the study period we recorded shark catch from a total of 595 fishing trips  We recorded 11,678 individual sharks, with an average total catch of 963 individuals per month (SD ± 434) and 19 7 individuals per trip (SD ± 15 6)  Standardised CPUE (per 100 hooks per set) ranged from 0 05 to 22 13 individuals, with an average of 0 96 and a mode of 0 20  Catch consisted of 42 different species from 18 families (Table 4)  22% of all landings were classified as threatened species (i e  VU, EN, CR) according to the IUCN Red List of Threatened Species, and 73% were near threatened  Almost half (46 3%) of landings were regulated (i e  CITES-listed) species  The most commonly caught species were silky shark (Carcharhinus falciformis), black tip shark (Carcharhinus limbatus) and scalloped hammerhead (Sphyrna lewini) 
Table 4  Sharks species landed in Tanjung Luar from January 2014 –December 2015 (VU = Vulnerable, EN = Endangered, NT = Near Threatened, LC = Least Concern, NE = Not Evaluated (VU and EN classified as ‘threatened’ in this study); II = CITES Appendix II, N = Not CITES-listed (II species classified as ‘regulated’ in this study)) 
Measures of CPUE for the Tanjung Luar shark fishery vary spatially and temporally, and with several aspects of fishing effort including gear type, hook number, engine power and number of sets  An initial comparison of average catch per trip and catch per set of the two major gear types, surface longline and bottom longline, indicates that CPUE of surface longlines was significantly higher than that of bottom longlines (ANOVA, p<0 001)  CPUE (individuals per set) was also positively associated with number of hooks, engine power, and number of sets (Fig 2)  However, these relationships are for unstandardised CPUE i e  without controlling for number of hooks 
Plots of CPUE: Number of individuals per set (A) and number of individuals per 100 hooks per set (standardised CPUE) (B) by gear type (1), number of hooks (2), number of sets (3) and engine horsepower (4) 
When controlling for hook number using standardised CPUE (individuals per 100 hooks per set) the relationships were reversed, with standardised CPUE of bottom longlines significantly higher than that of surface longlines (ANOVA, p<0 001; Fig 2)  A similar pattern was observed when comparing relationships between CPUE (individuals per set) and standardised CPUE for other measures of fishing effort, including numbers of hooks, engine power and number of sets (Fig 2)  There was a positive relationship between unstandardised CPUE (individuals per set) and number of hooks, number of sets and engine power, but a negative relationship between CPUE and these fishing behaviour variables when CPUE was standardised by hook number (individuals per 100 hooks per set) 
The best fit LM of standardised CPUE indicated that the most significant factors influencing standardised CPUE were fishing gear and number of hooks (p<0 001)  Month, engine power, number of sets and fishing ground were also identified as significant variables (Table 5), although there was considerable covariance between these factors  Standardised CPUE was significantly lower in January, and decreased with higher numbers of hooks, despite a higher total catch per trip and set (Fig 2) 
Table 5  Analysis of variance for linear model of standardised CPUE (individuals per 100 hooks per set) data from Tanjung Luar; significant values (p<0 05) are given in bold 
Best fit GLMs indicated that the most significant factors influencing the likelihood of catching threatened species were month (January and November were significantly lower: p<0 001 and p<0 05, respectively) and fishing ground (Other (i e  fishing grounds outside of WNTP and ENTP) was significantly higher: p<0 01)  Significant factors associated with standardised CPUE of threatened species were number of hooks (p<0 001), fishing ground (other: p<0 001, ENTP p<0 05), engine power (p<0 001) and trip length (p<0 001) (Table 6 and Fig 3) 
Plots of most significant factors affecting standardised CPUE (number of individuals per 100 hooks per set) of threatened species: a) hook number, b) fishing ground, c) engine power and d) trip length 
Analysis of variance for the best fit models of factors affecting: a) the likelihood of catching and the standardised CPUE of threatened species b) the likelihood of catching and the standardised CPUE of regulated species 
The most significant factors influencing the likelihood of catching regulated species were month (January was significantly lower: p<0 001), number of hooks (p<0 001) and engine power (<0 01)  Significant factors associated with standardised CPUE of regulated species were number of hooks (p<0 001), fishing gear (<0 001), number of sets (p<0 001), engine power (p<0 01) and month (November and January: p<0 05) (Table 5 and Fig 4) 
Plots of most significant factors affecting standardised CPUE (number of individuals per 100 hooks per set) of regulated species: a) hook number, b) gear type, c) number of sets 
Although Tanjung Luar’s targeted shark fishery is small in scale, considerable numbers of shark are landed, including a large proportion of threatened and regulated species  A key finding is that measures of CPUE, for all sharks and for threatened and regulated species, vary spatially and temporally, and with several aspects of fishing effort including gear type, hook number, engine power and number of sets  Moreover, the relationships between CPUE and fishing behaviour variables are different for different measures of CPUE (CPUE per trip, CPUE per set, CPUE per 100 hooks per set)  This highlights the importance of using appropriate standardisation for meaningful comparisons of CPUE across different gears and vessel types, and has important implications for fisheries management 
Unstandardised CPUE (individuals per set) was significantly lower in January  This is during the west monsoon season, which is characterised by high rainfall and adverse conditions at sea for fishing  Unstandardised CPUE was also significantly lower in West Nusa Tenggara Province (WNTP) than East Nusa Tenggara Province (ENTP) and other provinces, suggesting a lower abundance of sharks in this area  Engine power had a significant positive influence on unstandardised CPUE, and was also associated with longer trips and more sets, which was likely due to the ability of vessels with larger engines to travel longer distances, over longer time periods, and with higher numbers of sets, to favoured fishing grounds  Unstandardised CPUE was also significantly higher for surface longlines than bottom longlines  However, when standardising CPUE for the number of hooks (i e  individuals per 100 hooks per set) this relationship was reversed  Bottom longlines exhibit a higher standardised CPUE, with negative relationships between catch per 100 hooks per set and number of hooks and frequency of sets  Vessels with moderate engine horsepower (50-59hp) also had the highest standardised CPUE  Since surface longlines systematically employ significantly more hooks than bottom longlines (400–600 vs 25–200 hooks), and tend to be associated with larger boats, longer trips and more sets, these findings suggest that although increasing fishing effort increased total catch for these gears and trips, there were diminishing returns of this increased effort above low to moderate levels 
A large proportion of Tanjung Luar’s shark catch consisted of threatened (22%) and regulated species (46%)  Month is a significant factor in explaining standardised CPUE of both threatened and regulated species, which could indicate seasonal variation in the abundance of these species in the Tanjung Luar fishing grounds, or seasonal impacts on CPUE due to poor weather conditions  Fishing ground was a significant factor in explaining the catch of threatened species but not the catch in regulated species  This may be due to differences in range, distribution and relative abundance of species within these groups  Threatened species make up a relatively small proportion of Tanjung Luar’s catch in comparison to regulated species, which make up almost half of the catch (46%)  As such, regulated species may generally be more abundant and spatially diffuse than threatened species, and therefore caught more uniformly across fishing grounds  For example, regulated species catch is dominated by silky sharks (Carcharhinus falciformis), which are circum-tropical and coastal-pelagic, and exhibit limited site-fidelity or aggregation behaviour, while threatened species catch is dominated by scalloped hammerheads (Sphyrna lewini), which are known to aggregate in schools  These schools of scalloped hammerheads may be more restricted to specific aggregation sites outside of WNTP and ENTP waters, while silky sharks are found in uniform abundance throughout fishing grounds 
As with CPUE of all catch, there was a positive relationship between unstandardised CPUE (catch per set) of threatened and regulated species and number of hooks, but a significant negative relationship between standardised CPUE (catch per 100 hooks per set)  This was likely due to diminishing returns of adding additional hooks, and indicates that the effort for threatened and regulated species was exceeding maximum sustainable yield effort, such that increases in effort (e g  hook number) were leading to decreases in catch [28–30] 
Due to the profitability of the shark industry in Tanjung Luar, and limited adaptive capacity and willingness of shark fishers to move into other industries, it is necessary to identify practical and ethical management interventions that can improve the sustainability of the fishery whilst also mitigating the negative socio-economic consequences for coastal communities  Our findings indicate that spatiotemporal closures and restrictions on fishing effort could improve the overall catch per unit effort and sustainability of the Tanjung Luar shark fishery, and lead to positive conservation outcomes for priority species 
Since the location of shark fishing grounds plays a significant role in determining the likelihood of catching threatened species and their associated CPUE, improved marine spatial planning, with the identification of marine protected areas (MPAs) that protect critical shark habitat and shark populations, could reduce catch of species of conservation concern [31–33] and increase abundance of sharks [34, 35]  Provincial governments in West Papua and West Nusa Tenggara have already established ‘shark sanctuary’ MPAs, which protect critical shark habitat and ban shark fishing within their boundaries [16, 36], and monitoring data indicates positive impacts of shark-specific closures on shark abundance [37, 38]  Strengthening Indonesia’s existing MPA network for shark conservation, such as making all MPAs no-take zones for sharks and expanding spatial protection to critical shark habitat, including aggregation sites or pupping and nursery grounds for species of conservation concern, could have considerable conservation benefits  It should be noted, however, that MPAs may only be effective for certain species, such as those with small ranges or site-fidelity   More research is required to identify critical shark habitat and life history stages  For Tanjung Luar these efforts could focus on better understanding scalloped hammerhead (Sphyrna lewini) aggregation sites  Well-targeted spatial closures for this species could significantly reduce catch of threatened species in this fishery 
The relationships between gear type, several aspects of fishing effort (i e  hook number, engine power, number of sets, trip length), standardised CPUE of all shark species and standardised CPUE of threatened and regulated species suggest that there is an optimal effort that could increase overall CPUE of the fishery and significantly reduce fishing mortality of species of conservation concern  For example, our data suggest that CPUE peaks with low to intermediate trip lengths and gear sets, intermediate engine power and hook numbers of less than 75 per set longline  Although standardised CPUE of threatened and regulated species is also higher when fewer hooks are deployed, the catch per set and overall mortality is significantly lower  Regulations that control the number of hooks in combination with incentives for shark fishers to tightly manage the number of hooks they deploy could significantly reduce mortality of threatened and endangered species, maximise the overall CPUE of the fishery, and reduce operational costs for fishers, making shark fishing in Tanjung Luar more sustainable and more cost effective [39–41] 
Acknowledging that almost half of Tanjung Luar’s shark catch consists of CITES-listed species, developing measures that ensure both the sustainability of the fishery, and full traceability and control of onward trade, will be crucial for implementing CITES   The Indonesian government has demonstrated a strong commitment to regulating shark trade and implementing CITES [17–18], as demonstrated through several policy decisions to confer full and partial protection to CITES-listed shark and ray species (Marine Affairs and Fisheries Ministerial Decree No 4 /KEPMEN-KP/2014, Regulation No  48/PERMEN-KP/2016)  This includes zero quotas/export bans for hammerhead and oceanic whitetip sharks  However, these export bans should be considered intermediate policy measures as monitoring systems and data availability are improved, and sustainable quotas are established  This will be challenging, as shark products are often traded in large volumes of fresh and/or preserved body parts, with high morphological similarity between products from regulated species and non-regulated species  To guarantee that trade is not detrimental to the survival of species, sustainable fisheries management will need to be complemented with species-specific trade quotas  This will require catch documentation systems which trace shark products from point of catch to point of export and rapid, low-cost species identification methods 
As baseline data on shark population health are limited, and there is no standardised, fisheries-independent system for monitoring long-term changes in shark populations, indirect bio-indicators (e g  endo- and ectoparasites, [43–45]) could help to elucidate the impact of management measures on fisheries and populations of wild species  In the future, shark conservation and fisheries management could benefit from long-term monitoring of agreed indices of population abundance and health status 
These lessons may also apply to shark fisheries in other parts of the world  As sharks increasingly become the focus of global conservation efforts it should be acknowledged that species protection alone will not be enough to reduce mortality of priority species  More needs to be done to identify practical fisheries management measures that can reduce pressure on the most vulnerable species and populations, but also support sustainable use of species that are less susceptible to overfishing  Shark fishing forms an integral part of the livelihood strategies of many coastal communities [22, 23], and prohibiting catches will not necessarily lead to positive conservation outcomes [21, 46]  Management interventions must take into account local context and the motivations and well-being of fisher communities in order to be ethical, feasible and impactful 
S1 Dataset  Data of landed sharks at Tanjung Luar auction that had been used for this study 
S1 File  Questionnaires have been used to interview shark fishers, collector, traders, and processors 
We wish to acknowledge the support provided by fishers in Tanjung Luar for their great cooperation during fieldwork  We also thank I Made Dharma Aryawan, Muhsin, Abdul Kohar, and Abdurrafik for their assistance during field research, Benaya M Simeon, Peni Lestari, and Siska Agustina for helping with data processing, Ken Kassem for carefully reading the manuscript and providing useful inputs, and the anonymous reviewers for their constructive comments 
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ground_truth: June 1, 1999.

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 are the relationships between catch per set and fishing behavior variables different for different measures of catch per unit effort (CPUE)?

Read the following text and answer briefly.

Context 4: Paper Info

Title: Compressed quantum error mitigation
Publish Date: 10 May 2023
Author List: Maurits Tepaske (from Physikalisches Institut, Universität Bonn), David Luitz (from Physikalisches Institut, Universität Bonn)

Figure

FIG 3 The out-of-time-ordered correlator C otoc i=L/2,j (t) as a function of the operator position j and time t, for the infinite temperature initial state, for a denoised second-order Trotter supercircuit with Trotter depth Mtrot = 32 and denoiser depth M = 2 We consider evolution times t = 0 5, 1,    , 5, for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarizing noise with p = 0 01 
FIG  4  The complex eigenvalues λ of the noisy second-order Trotter supercircuit with Mtrot = 16 at time t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised Trotter supercircuit (right) The Trotter circuit is for a L = 6 Heisenberg model with PBC, and all twoqubit channels are affected by depolarizing noise with p = 0 0046 The unit circle, on which unitary eigenvalues must lie, is shown in black, and the noiseless eigenvalues are shown as blue bars It is evident that the denoiser recovers all the noiseless eigenvalues from the noisy circuit 
FIG  2  The complex eigenvalues λ of the noisy second-order Trotter supercircuit with Mtrot = 16 at time t = 1 (left), the corresponding optimized denoiser with M = 4 (center), and the denoised Trotter supercircuit (right) The Trotter circuit is for a L = 6 Heisenberg model with PBC, and all twoqubit channels are affected by depolarizing noise with p = 0 036 The unit circle, on which unitary eigenvalues must lie, is shown in black, and the noiseless eigenvalues are shown as blue bars It is clear that the denoiser recovers with high accuracy the noiseless eigenvalues from the noisy circuit 
FIG  3  The half-chain channel entanglement entropy S at different two-qubit depolarizing noise strengths p, for a secondorder Trotter supercircuit with Mtrot = 16 and t = 2, for a M = 4 denoiser The Trotter circuit is for a Heisenberg model with PBC of size L = 6 The different curves correspond to the different supercircuits, i e  the noisy supercircuit, the denoiser, the corresponding denoised supercircuit, and the noiseless variant 
FIG  4  The out-of-time-ordered correlator C otoc i=L/2,j (t) as a function of the operator position j and stacked time t, for the infinite temperature initial state, for a denoised secondorder Trotter supercircuit with Trotter depth Mtrot = 32 and denoiser depth M = 2 It is optimized at t = 2 and stacked up to ten times The calculations are for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarization with p = 0 01 The denoiser is affected by the same noise 
FIG 6 The distribution of the ZZ angle α of M = 2 denoisers (top panels) and M = 8 denoisers (bottom panels), with the lightest color corresponding to the denoiser for the Trotter supercircuit with t = 0 5, and the darkest color with t = 5 As usual, we consider the Heisenberg model on a periodic chain, and second-order Trotter supercircuits with depths Mtrot = 8, 16, 32, 64, which together with the denoiser is affected by a two-qubit depolarizing noise with p = 0 01 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively 
FIG  7  The sampling overhead γ of the optimized denoisers from Fig  2 of the main text, with denoiser depths M = 1, 2, 4, 6, 8 and Trotter depths Mtrot = 8, 16, 32, 64 at times t = 0 5, 1,    , 5, for the Heisenberg model on a chain with PBC affected by two-qubit depolarizing noise with p = 0 01 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively 
FIG 8 The domain wall magnetization Z dw after evolving a periodic density wall |dw |dw * with the denoised second-order Trotter supercircuits D C from Fig 2of the main text These supercircuits have various Trotter depths Mtrot = 8, 16, 32, 64, denoiser depths M = 1, 2, 4, 6, 8, and evolution times t = 0 5, 1,    , 5, for the periodic L = 14 Heisenberg chain that is affected by two-qubit depolarizing noise of strength p = 0 01 The denoiser is affected by the same noise The non-denoised results are labelled with M = 0 and the noiseless results with p = 0 The panels are arranged as Mtrot = 8, 16, 32, 64 for top left, top right, bottom left, bottom right, respectively We see that the denoiser allows us to recover the noiseless behavior 

abstract

We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit  Our approach is based on applying an optimal "denoiser" after the action of a noisy circuit and can be performed with an arbitrary number of extra gates 
The denoiser is given by an ensemble of circuits distributed with a quasiprobability distribution  For a simple noise model, we show that efficient, local denoisers can be found, and we demonstrate their effectiveness for the digital quantum simulation of the time evolution of simple spin chains  Introduction 
-Quantum information processing has been theoretically shown to hold great promises, and quantum algorithms were developed which can in principle achieve an exponential speed-up over their classical counterparts, both for general purpose computing and quantum simulation   However, present day quantum computing prototypes still suffer from significant noise processes which hinder the execution of many potentially groundbreaking quantum algorithms  
Nontrivial quantum algorithms typically require large sequences of quantum gates, each of which introduces dissipation and hence an overall loss of coherence, eventually rendering the results useless  Until quantum error correction becomes practical, quantum error mitigation seems to be more feasible to increase the accuracy of expectation values 
Here the goal is to induce the (partial) cancellation of errors that stem from noisy quantum gates by extending the circuit corresponding to the desired algorithm with an ensemble of gates , sampled from a quasiprobability distribution  The traditional way to accomplish this is with the gatewise method from , where noise is mitigated by inverting the noise channel of each gate separately, i e  the cancellation of errors is performed for each gate on its own 
Here the local noise channel is approximated in a way such that it can be easily inverted analytically, e g  using Pauli twirling   Gates are then sampled from the inverted noise channel by interpreting it as a quasiprobability distribution  Because in this gate-wise approach every noisy gate has to be modified separately, the sign problem is exponentially large in the number of gates, limiting the practicality of the mitigation 
The success of the gate-wise approach resulted in a large body of work concerning these methods , including extensions for simultaneous mitigation of multiple gates by Pauli-twirling entire layers or variationally constructing a mitigating matrix product operator   In principle, errors during the execution of a circuit can propagate and accumulate 
These propagated errors * david luitz@uni-bonn de ≈ C

C

FIG  1  An example of the quantum error mitigation procedure used in this work for the time evolution of the wave function of a spin chain  The ideal second-order Trotter supercircuit C of depth Mtrot = 1 (light blue) is approximated by applying a denoiser D of depth M = 1 (red) to the noisy Trotter supercircuit C (dark blue) 
Because the denoiser is applied after fully executing the noisy Trotter supercircuit, it represents an approximate inverse of the global noise channel with a precision tunable by the depth of the denoiser  can potentially blow up and lead to large errors for the circuit as a whole   Here we introduce a mitigation technique that takes into account the propagation of errors, can be performed with a tunable number of extra gates, and works for non-Clifford local noise channels since the inversion of the accumulated global noise channel is implicit 
We first execute the targeted noisy circuit completely, letting the noise propagate and accumulate, and only afterwards we apply an extra random circuit sampled from a quasiprobability distribution  We call the corresponding ensemble of random circuits a denoiser, and we construct it such that upon averaging the accumulated errors cancel 
Essentially, the denoiser inverts a global noise channel  Since we will construct it as a local brickwall circuit, following the classical preprocessing approach from , we call this compressed quantum error mitigation  Method  -Due to the inevitable coupling of a quantum processor to its environment, every qubit operation is affected by noise 
Therefore, the simplest technique to minimize the impact of the resulting noise is to minimize the number of operations when performing a quantum algorithm  In we showed that many-body time evolution operators can be efficiently compressed into brick-wall circuits with high fidelity per gate  In this Letter, we consider the noise explicitly by treating quantum operations as (generally non-unitary) quantum channels, corresponding to completely positive and trace preserving (CPTP) maps  
For example, instead of a noiseless two-qubit gate G, which acts on a quantum state |ρ in superoperator form as G|ρ = G⊗G * |ρ , we get the noisy channel G = N G, where the noise channel N implements the two-qubit noise   These channels are used to construct a "supercircuit" C = N G i=1 Gi , consisting of N G channels, which is affected by multi-qubit accumulated noise 
This supercircuit encodes an ensemble of circuits   For simplicity, we assume that the noisy channels Gi in each half brickwall layer are lattice inversion and translation invariant, such that we can construct a denoiser with these properties, limiting the number of variational parameters  The purpose of quantum error mitigation is to modify the ensemble of circuits described by C in a way that we can use it to obtain the noiseless expectation values 
In superoperator language, we do this by following the supercircuit C with a denoiser supercircuit D, such that D C is as close to the noiseless supercircuit C = C ⊗ C * as possible  Here C is the target unitary circuit  Because the noise channel N is non-unitary, hence making the supercircuit C non-unitary, we need to use a non-unitary denoiser to retrieve the unitary C 
We illustrate the mitigation procedure in Fig  , where a denoiser with one layer is used to mitigate errors for a second-order Trotter supercircuit with one layer  This circuit architecture is commonly used to simulate the time evolution of a quantum many-body system, until some time t, with controllable precision , and we will use it to benchmark the denoiser 
In practice, we cannot directly implement a supercircuit, and so we have to utilize its interpretation as an ensemble of circuits  Essentially, after executing a shot of the noisy circuit we sample the denoiser and apply it  The goal is to construct the denoiser in a way that averaging over many of its samples cancels the accumulated errors and gives us a good approximation of the noiseless expectation values 
It should be noted that our approach requires more gate applications on the quantum processor than with the gate-wise scheme, since there each sample from the mitigation quasiprobability distribution can be absorbed into the original circuit, whereas our approach increases the circuit depth  We take this into account by imposing the same noise on the denoiser 
Furthermore, within our scheme, the dimensionality of the quasiprobabilistic mitigating ensemble can be controlled, in contrast to the gate-wise approach where it is equal to the gate count  To facilitate the stochastic interpretation we parameterize each two-qubit denoiser channel G i as a sum of CPTP maps, such that we can sample the terms in this sum and execute the sampled gate on the quantum processor 
Concretely, we use a trace preserv-ing sum of a unitary and a non-unitary channel  For the unitary part we take a two-qubit unitary channel U( φ i ) = U ( φ i ) ⊗ U * ( φ i ), with U ( φ i ) a two-qubit unitary gate parameterized by φ i   For this we take the two-qubit ZZ rotation exp(−iα(σ z ⊗ σ z )) with angle α, which can be obtained from native gates on current hardware , and dress it with four general one-qubit unitaries, only two of which are independent if we want a circuit that is space inversion symmetric around every bond 
The resulting gate has 7 real parameters φ i   For the non-unitary part, which is essential because D has to cancel the non-unitary accumulated noise to obtain the noiseless unitary circuit, we use a general onequbit measurement followed by conditional preparation channel M( , with V a general one-qubit unitary and each κ i a 3-dimensional vector, resulting in a real 9-dimensional ζ i  
This yields the two-qubit correlated measurement M( With these parts we construct the parameterization with coefficients η i ∈ R that satisfy η 0 + η 1 = 1 because G i is trace preserving  Note that here the tensor product symbol corresponds to combining two one-qubit channels to make a two-qubit channel, whereas in most of the paper it is used to link the column and row indices of a density matrix 
We construct the denoiser from the noisy channels Gi = N G i   With this parameterization one denoiser channel has 17 independent real parameters, such that a denoiser of depth M , i e  consisting of M brickwall layers, has 34M real parameters (we use one unique channel per half brickwall layer)  For reference, a general channel has 544M parameters 
To determine the mitigated expectation values we use the full expression where |ρ 0 is the initial state and |1 is the vectorized identity operator on the full Hilbert space  To evaluate this on a quantum processor, we use the stochastic interpretation of (1) to resample   In particular, from each channel (1) we get a unitary with probability p 0 = |η 0 |/γ and a measurement followed by conditional preparation with probability p 1 = |η 1 |/γ 
Here γ = |η 0 | + |η 1 | is the sampling overhead, which characterizes the magnitude of the sign problem from negative η i   For quasiprobability distributions, i e  with γ > 1, every denoiser sample has an extra sign sgn(η) = N G g=1 sgn(η g ), 2  The normalized distance between the denoised Trotter supercircuit D C and the noiseless Trotter supercircuit C (top panels), at evolution times t = 0 5, 1,    , 5, and the twopoint z-spin correlator C zz i=L/2,j=L/2 (t) of a spin on the middle site at times 0 and t (bottom panels), for the infinite temperature initial state 
We consider denoisers with depths M = 1, 2, 4, 6, 8 and second-order Trotter circuits with depths Mtrot = 16, 32, 64  In the top panels we use a Heisenberg chain with L = 8, and in the bottom panels with L = 14, both with periodic boundary conditions  All gates are affected by two-qubit depolarizing noise with p = 0 01



ground_truth: The relationships between catch per set and fishing behavior variables differ when comparing unstandardized CPUE and standardized CPUE.

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: When did the Tevatron Collider Run II start and when is it expected to end?

Read the following text and answer briefly.

Context 3: \section{INTRODUCTION}
The Tevatron Collider Run II started in March 2002 and is expected
to continue until the end of this decade  The Tevatron and the 
two detectors, CDF and D\O, have been performing  well in 2004,
each experiment is collecting data at the rate 
of $\approx$10 pb$^{-1}$ per week 
The total  luminosity accumulated by August 2004 is $\approx$500 pb$^{-1}$
per detector 
The rich physics program includes the
production and precision measurement of properties of  standard model (SM)
objects, as well as searches for phenomena beyond standard model 
In this brief review we focus on areas of most interest 
to the lattice community  We present
new results on the top quark mass
and their implication for the mass of the SM Higgs boson, 
on searches for the SM Higgs boson, on evidence for the $X(3872)$ state, 
on searches for pentaquarks, and on $b$ hadron properties 
All Run II results presented here are preliminary  

\section{TOP QUARK MASS}

The experiments CDF and D\O\ published several direct  measurements of
the top quark pole mass, $\ensuremath{M_{\mathrm{top}}}$, 
based on Run I data (1992-1996) 
The ``lepton $+$ jets'' channel yields the most precise determination of
$\ensuremath{M_{\mathrm{top}}}$  Recently, the
D\O\ collaboration published a new measurement~\cite{Mtop1-D0-l+j-new},
based on a powerful analysis technique yielding  greatly improved precision 
The differential probability 
that the measured variables in any event correspond to the signal
is calculated as a function of $\ensuremath{M_{\mathrm{top}}}$  
The maximum in the product of the individual event probabilities 
provides the best estimate of $\ensuremath{M_{\mathrm{top}}}$ 
The critical differences from previous analyses 
in the lepton $+$ jets decay channel lie in 
the assignment of more 
weight to events that are well measured or more likely to correspond to  
$t \bar t$ signal, 
and  the handling of the combinations of final-state objects
(lepton, jets, and imbalance in transverse momentum) 
and their identification with
top-quark decay products in an event  
The new combined value for the top-quark mass from Run I is 
$\ensuremath{M_{\mathrm{top}}}  =  178 0\pm4 3~\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ 

In Run II, both collaborations  have been exploring several different techniques 
for $\ensuremath{M_{\mathrm{top}}}$
measurements  The best single CDF result comes from a dynamic likelihood method
(DLM)  The method is similar to
the technique used in Ref ~\cite{Mtop1-D0-l+j-new} 
The result is $\ensuremath{M_{\mathrm{top}}} = 177 8^{+4 5}_{-5 0} (stat) \pm  6 2 (syst) ~\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ 
The joint likelihood of the selected events is shown in Fig  ~\ref{fig:cdf_tml}  
The Run II goal is a 1\% uncertainty on $\ensuremath{M_{\mathrm{top}}}$  




\begin{figure}[htb]
\vspace*{-5mm}
\includegraphics[height=5 8cm,width=8 1cm]  {data_22ev_likelihood eps}
\vspace*{-1 2cm}
\caption{The joint likelihood of top candidates(CDF) }
\label{fig:cdf_tml}
\end{figure}




\section{SEARCH FOR SM HIGGS BOSON}


The constraints on the SM Higgs ($H$)  boson  mass from
published  measurements, updated to include the new D\O\ top mass
measurement~\cite{Mtop1-D0-l+j-new}, are
$M_H = 117 ^{+67}_{-45}~\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$, $M_H < 251~\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ at 95\% C L 
The  new most likely  value of $M_H$
is above the experimentally excluded range,
and sufficiently low for $H$ to be observed at the Tevatron 


\begin{figure}[htb]
\vspace*{-5mm}
\includegraphics[height=7 5cm,width=7 8cm]  {d0_wbb_fig_3_err eps}
\vspace*{-1 1cm}
\caption{Distribution of the dijet
invariant mass for $W+2 b$-tagged jets  events,
compared to the expectation (D\O)  
}
\label{fig:d0_wbb_2tag}
\end{figure}



D\O\  has conducted a search for $H$ at $M_H < 140~\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ 
in the production channel  
$p \bar{p} \rightarrow WH \rightarrow  e \nu b \bar{b}$  
The experimental signature of  $WH \rightarrow e \nu b \bar{b}$
is a final state with 
one high $p_T$ electron, two  $b$ jets, and
large missing transverse energy  resulting from
the undetected neutrino 
The dominant backgrounds to $WH$ production
are  $W b \bar{b}$, $t \bar{t}$ and single-top production 
The distribution 
of the dijet mass for events with two $b$-tagged jets is shown in
Fig ~\ref{fig:d0_wbb_2tag}  
Also shown is the  expected contribution ($0 06$ events)  
from the $b \bar{b}$ decay of a
SM Higgs boson with $M_H =$ 115 $\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ 
No events are observed in the  dijet mass window of 85--135  $\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ 
D\O\ sets a limit on the cross section
for $\sigma( p\bar{p} \rightarrow WH) \times B(H \rightarrow b \bar{b}) $
of 9 0 pb at the 95\% C L ,  for a 115  $\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$ Higgs boson 
The results for mass points 105, 125, and 135 $\ensuremath{\mathrm{ Ge\kern -0 1em V }\kern -0 2em /c^2 }$
 are 11 0, 9 1 and 12 2 pb,  respectively 



\begin{figure}[htb]
\vspace*{-1 2cm}
\includegraphics[height=0 33\textheight,width=8 0cm]{whww_aps04_bw eps}

\vspace*{-1 2cm}
\caption{95\% limits on the $H$ production (CDF) }
\label{fig:cdf_whww}
\end{figure}


CDF  has done  a similar search, allowing either an  electron or a muon  
in the final state   Both groups have also searched for $H$ produced in
gluon-gluon fusion, with subsequent decay to a pair of $W$ bosons 
The CDF results for both channels  are shown in Fig ~\ref{fig:cdf_whww}  



\section{THE STATE X(3872)}


\begin{figure}[htb]

\includegraphics[height=8 0cm,width=7 5cm]  {X3872cdfPRL1FullM eps}
\vspace*{-1cm}
\caption{The $X(3872)$ signal (CDF) }
\label{fig:cdf_x}
\end{figure}




 The existence of the $X(3872)$ state discovered by 
the Belle Collaboration~\cite{Belle-X}
 has been confirmed 
 in $p \bar{p}$ collisions by  CDF~\cite{cdf-X} (see Fig ~\ref{fig:cdf_x})
and D\O~\cite{d0-X} 
 It is still unclear whether this particle is a $c\bar{c}$ state,
 or a more complex object   When the data are separated according to
production and decay variables, D\O\  finds no significant
differences between the $X(3872)$ and
the $c \bar{c}$ state $\psi(2S)$ 
CDF has analysed the ``lifetime'' distribution of the $X(3872)$ events in order to
quantify what fraction of this state arises from decay of $B$ hadrons, as opposed to
those produced promptly  The authors find that for the selected samples
28 3$\pm$1 0$(stat)\pm$0 7$(syst)$\% of $\psi(2S)$ candidates are from $b$ decays,
whereas 16 1$\pm$4 9$(stat)\pm$2 0$(syst)$\% of $X$ mesons arise from such decays 





\section{SEARCH FOR PENTAQUARKS}



\begin{figure}[htb]

\includegraphics[height=0 27\textheight,width=7 6cm]  {mpks_1stminbias eps}
\vspace*{-1 2cm}

\caption{Invariant mass distribution of an identified proton and a $K^0_s$ candidate  (CDF)
}
\label{fig:pqtheta}
\end{figure}



\begin{figure}[htb]

\vspace*{-0 9cm}
\includegraphics[height=0 25\textheight,width=8 0cm]  {CM_xicst_cc_1 eps}
\vspace*{-1 2cm}
\caption{Invariant mass distribution of the $(\Xi^-,\pi^+)$ system  (CDF) 
}
\label{fig:pqxi}
\end{figure}


\begin{figure}[htb]
\vspace*{-0 9cm}

\includegraphics[height=0 25\textheight,width=7 6cm]  {theta_note_dstp_dedx_pt eps}
\vspace*{-1 2cm}
\caption{Mass of the ($D^{*+}\bar p$) system  The arrow indicates the position of 
the $\Theta_c$ state (CDF) }
\label{fig:pqthetac}
\end{figure}



Following reports of evidence for exotic
baryons containing five quarks (pentaquarks), CDF has analysed 
its data for evidence of the following pentaquarks:
$\Theta^+$ ($uud\bar d \bar s$), doubly strange states 
$\Xi_{3/2}$, charmed states $\Theta_c$, and, most recently, 
a state $(udus\bar b)$, dubbed $R^+_s$, through its weak decay to $(J/\psi, p)$  
With its excellent particle indentification and mass resolution,
CDF has a unique capability to search for  pentaquark states 
The signals of known states: $\phi$, $\Lambda$,
$\Lambda(1520)$, $K^*$, $\Xi$, 
compare favorably with those provided
by the authors of  the pentaquark evidence 
The group finds no evidence for pentaquark states, see Figs 
~\ref{fig:pqtheta},{\ref{fig:pqxi},\ref{fig:pqthetac} 
This can be interpreted as an indication that the pentaquark production 
in $p \bar p$ collisions is heavily suppressed compared to the conventional
hadron production, or as an evidence against the existence of pentaquarks 

\clearpage

\section{RECENT B PHYSICS RESULTS}


\subsection{Spectroscopy}

CDF has measured the mass of $b$ hadrons in exclusive $J/\psi$ channels 
The measurements of the $B_s$ and $\Lambda_b$ (Fig  \ref{fig:masslb})
masses are the current world's best \\

$m(B^+)$ = 5279 10$\pm$0 41$(stat)\pm$0 36$(syst)$,

$m(B^0)$ = 5279 63$\pm$0 53$(stat)\pm$0 33$(syst)$,

$m(B_s)$ = 5366 01$\pm$0 73$(stat)\pm$0 33$(syst)$,

$m(\Lambda_b)$ = 5619 7$\pm$1 2$(stat)\pm$1 2$(syst)$ MeV/$c^2$ \\


\begin{figure}[htb]
\vspace*{-1mm}
\includegraphics[height=0 30\textheight,width=7 5cm]  {lambdav1c eps}
\vspace*{-1cm}

\caption{The mass spectrum of $\Lambda_b$ candidates (CDF) }
\label{fig:masslb}
\end{figure}


D\O\ reports the first observation of the excited $B$ mesons 
$B_1$ and $B^*_2$ as two separate states in fully reconstructed
decays to $B^{(*)}\pi$  The mass of $B_1$ is measured to be
5724$\pm$4$\pm$7 MeV/c$^2$, and the mass difference $\Delta M$ between
$B^*_2$ and $B_1$ is 23 6$\pm$7 7$\pm$3 9 MeV/c$^2$
(Fig   \ref{fig:d0_bexc}) 

D\O\ observes semileptonic $B$ decays to narrow $D^{**}$ states,
the orbitally excited states  of the $D$ meson
seen as resonances in the $D^{*+}\pi^-$ invariant mass spectrum 
The $D^*$ mesons are reconstructed through the decay sequence 
$D^{*+} \rightarrow D^0\pi^+$, $D^0\rightarrow K^-\pi^+$ 
The invariant mass  of oppositely charged $(D^*,\pi)$ pairs
is shown in Fig   \ref{fig:d0_dstst} 
The mass peak between 2 4 and 2 5 GeV/$c^2$ can be interpreted as two merged 
narrow $D^{**}$ states, $D^0_1(2420)$ and $D^0_2(2460)$ 
The combined branching fraction is 
$ {\cal B}(B\rightarrow D^0_1,D^0_2)\cdot {\cal B}(D^0_1,D^0_2\rightarrow D^{*+}\pi^-)=(0 280\pm0 021(stat)\pm0 088(syst)$\%  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: The Tevatron Collider Run II started in March 2002 and is expected to continue until the end of this decade.