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: In which electorate was Simon English elected to the New Zealand Parliament?

Read the following text and answer briefly.

Context 1: 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) 

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 2: consumption influences mercury: Topics by WorldWideScience org
Sample records for consumption influences mercury
Epidemiologic confirmation that fruit consumption influences mercury exposure in riparian communities in the Brazilian Amazon
Sousa Passos, Carlos Jose; Mergler, Donna; Fillion, Myriam; Lemire, Melanie; Mertens, Frederic; Guimaraes, Jean Remy Davee; Philibert, Aline
Since deforestation has recently been associated with increased mercury load in the Amazon, the problem of mercury exposure is now much more widespread than initially thought  A previous exploratory study suggested that fruit consumption may reduce mercury exposure  The objectives of the study were to determine the effects of fruit consumption on the relation between fish consumption and bioindicators of mercury (Hg) exposure in Amazonian fish-eating communities  A cross-sectional dietary survey based on a 7-day recall of fish and fruit consumption frequency was conducted within 13 riparian communities from the Tapajos River, Brazilian Amazon  Hair samples were collected from 449 persons, and blood samples were collected from a subset of 225, for total and inorganic mercury determination by atomic absorption spectrometry  On average, participants consumed 6 6 fish meals/week and ate 11 fruits/week  The average blood Hg (BHg) was 57 1Â±36 3 Î¼g/L (median: 55 1 Î¼g/L), and the average hair-Hg (HHg) was 16 8Â±10 3 Î¼g/g (median: 15 7 Î¼g/g)  There was a positive relation between fish consumption and BHg (r=0 48; P 2 =36 0%) and HHg levels (fish: Î²=1 2, P 2 =21 0%)  ANCOVA models showed that for the same number of fish meals, persons consuming fruits more frequently had significantly lower blood and HHg concentrations  For low fruit consumers, each fish meal contributed 9 8 Î¼g/L Hg increase in blood compared to only 3 3 Î¼g/L Hg increase for the high fruit consumers  In conclusion, fruit consumption may provide a protective effect for Hg exposure in Amazonian riparians  Prevention strategies that seek to maintain fish consumption while reducing Hg exposure in fish-eating communities should be pursued
Influence of mercury bioaccessibility on exposure assessment associated with consumption of cooked predatory fish in Spain 
Torres-Escribano, Silvia; Ruiz, Antonio; Barrios, Laura; VÃ©lez, Dinoraz; Montoro, Rosa
Predatory fish tend to accumulate high levels of mercury (Hg)  Food safety assessment of these fish has been carried out on the raw product  However, the evaluation of the risk from Hg concentrations in raw fish might be modified if cooking and bioaccessibility (the contaminant fraction that solubilises from its matrix during gastrointestinal digestion and becomes available for intestinal absorption) were taken into account  Data on Hg bioaccessibility in raw predatory fish sold in Spain are scarce and no research on Hg bioaccessibility in cooked fish is available  The aim of the present study was to evaluate Hg bioaccessibility in various kinds of cooked predatory fish sold in Spain to estimate their health risk  Both Hg and bioaccessible Hg concentrations were analysed in raw and cooked fish (swordfish, tope shark, bonito and tuna)  There were no changes in Hg concentrations during cooking  However, Hg bioaccessibility decreased significantly after cooking (42 Â± 26% in raw fish and 26 Â± 16% in cooked fish), thus reducing in swordfish and tope shark the Hg concentration to which the human organism would be exposed  In future, cooking and bioaccessibility should be considered in risk assessment of Hg concentrations in predatory fish  Copyright Â© 2011 Society of Chemical Industry 
Intake of mercury through fish consumption
Sarmani, S B ; Kiprawi, A Z ; Ismail, R B ; Hassan, R B ; Wood, A K ; Rahman, S A 
Fish has been known as a source of non-occupational mercury exposure to fish consuming population groups, and this is shown by the high hair mercury levels  In this study, hair samples collected from fishermen and their families, and commercial marine fishes were analyzed for mercury and methylmercury by neutron activation and gas chromatography  The results showed a correlation between hair mercury levels and fish consumption patterns  The levels of mercury found in this study were similar to those reported by other workers for fish consuming population groups worldwide  (author)
Fish consumption limit for mercury compounds
Abbas Esmaili-Sari
Full Text Available Background and objectives: Methyl mercury can carry out harmful effects on the reproductive, respiratory, and nervous system of human  Moreover, mercury is known as the most toxic heavy metal in nature  Fish and seafood consumption is the major MeHg exposure route for human  The present study tries to cover researches which have been conducted on mercury levels in 21 species of fish from Persian Gulf, Caspian Sea and Anzali Wetland during the past 6 years, and in addition to stating mercury level, it provides recommendations about the restriction of monthly fish consumption for each species separately  Material and methods: Fish samples were transferred to the laboratory and stored in refrigerator under -20oC until they were dissected  Afterwards, the muscle tissues were separated and dried  The dried samples were ground and changed into a homogenous powder and then the mercury concentration rate has been determined by advanced mercury analyzer, model 254  Results: In general, mercury contamination in fishes caught from Anzali Wetland was much more than fishes from Caspian Sea  Also, from among all studied fishes, oriental sole (Euryglossa orientalis, caught from Persian Gulf, allocated the most mercury level to itself with the rate of 5 61ml per kg , therefore, it exercises a severe consumption restriction for pregnant women and vulnerable groups  Conclusion: Based on the calculations, about 50% of fishes, mostly with short food chain, can be easily consumed during the year  However, with regard to Oriental sole (Euryglossa orientalis and shark (Carcharhinus dussumieri, caught from Persian Gulf, special consideration should be taken in their consumption  On the other hand, careful planning should be made for the high rate of fish consumption among fishing community 
Hair Mercury Concentrations and Fish Consumption Patterns in Florida Residents
Adam M  Schaefer
Full Text Available Mercury exposure through the consumption of fish and shellfish represents a significant public health concern in the United States  Recent research has demonstrated higher seafood consumption and subsequent increased risk of methylmercury exposure among subpopulations living in coastal areas  The identification of high concentrations of total mercury in blood and skin among resident Atlantic bottlenose dolphins (Tursiops truncatus in the Indian River Lagoon (IRL, a coastal estuary in Florida, alerted us to a potential public health hazard in the contiguous human population  Therefore, we analyzed hair mercury concentrations of residents living along the IRL and ascertained their sources and patterns of seafood consumption  The total mean mercury concentration for 135 residents was 1 53 Â± 1 89 Âµg/g  The concentration of hair mercury among males (2 02 Â± 2 38 Âµg/g was significantly higher than that for females (0 96 Â± 0 74 Âµg/g (p < 0 01  Log transformed hair mercury concentration was significantly associated with the frequency of total seafood consumption (p < 0 01  Individuals who reported consuming seafood once a day or more were 3 71 (95% CI 0 84â€“16 38 times more likely to have a total hair mercury concentration over 1 0 Âµg/g, which corresponds approximately to the U S  EPA reference dose, compared to those who consumed seafood once a week or less  Hair mercury concentration was also significantly higher among individuals who obtained all or most of their seafood from local recreational sources (p < 0 01  The elevated human mercury concentrations mirror the elevated concentrations observed in resident dolphins in the same geographical region  The current study is one of the first to apply the concept of a sentinel animal to a contiguous human population 
Fish consumption and bioindicators of inorganic mercury exposure
Sousa Passos, Carlos Jose; Mergler, Donna; Lemire, Melanie; Fillion, Myriam; Guimaraes, Jean Remy Davee
Background: The direct and close relationship between fish consumption and blood and hair mercury (Hg) levels is well known, but the influence of fish consumption on inorganic mercury in blood (B-IHg) and in urine (U-Hg) is unclear  Objective: Examine the relationship between fish consumption, total, inorganic and organic blood Hg levels and urinary Hg concentration  Methods: A cross-sectional study was carried out on 171 persons from 7 riparian communities on the Tapajos River (Brazilian Amazon), with no history of inorganic Hg exposure from occupation or dental amalgams  During the rising water season in 2004, participants responded to a dietary survey, based on a seven-day recall of fish and fruit consumption frequency, and socio-demographic information was recorded  Blood and urine samples were collected  Total, organic and inorganic Hg in blood as well as U-Hg were determined by Atomic Absorption Spectrometry  Results: On average, participants consumed 7 4 fish meals/week and 8 8 fruits/week  Blood total Hg averaged 38 6 Â± 21 7 Î¼g/L, and the average percentage of B-IHg was 13 8%  Average organic Hg (MeHg) was 33 6 Â± 19 4 Î¼g/L, B-IHg was 5 0 Â± 2 6 Î¼g/L, while average U-Hg was 7 5 Â± 6 9 Î¼g/L, with 19 9% of participants presenting U-Hg levels above 10 Î¼g/L  B-IHg was highly significantly related to the number of meals of carnivorous fish, but no relation was observed with non-carnivorous fish; it was negatively related to fruit consumption, increased with age, was higher among those who were born in the Tapajos region, and varied with community  U-Hg was also significantly related to carnivorous but not non-carnivorous fish consumption, showed a tendency towards a negative relation with fruit consumption, was higher among men compared to women and higher among those born in the region  U-Hg was strongly related to I-Hg, blood methyl Hg (B-MeHg) and blood total Hg (B-THg)  The Odds Ratio (OR) for U-Hg above 10 Î¼g/L for those who ate > 4 carnivorous fish
Methyl mercury exposure in Swedish women with high fish consumption
Bjoernberg, Karolin Ask [Division of Metals and Health, Institute of Environmental Medicine, Karolinska Institutet, Box 210, SE-171 77, Stockholm (Sweden); Vahter, Marie [Division of Metals and Health, Institute of Environmental Medicine, Karolinska Institutet, Box 210, SE-171 77, Stockholm (Sweden); Grawe, Kierstin Petersson [Toxicology Division, National Food Administration, Box 622, SE-751 26 Uppsala (Sweden); Berglund, Marika [Division of Metals and Health, Institute of Environmental Medicine, Karolinska Institutet, Box 210, SE-171 77, Stockholm (Sweden)]  E-mail: Marika Berglund@imm ki se
We studied the exposure to methyl mercury (MeHg) in 127 Swedish women of childbearing age with high consumption of various types of fish, using total mercury (T-Hg) in hair and MeHg in blood as biomarkers  Fish consumption was assessed using a food frequency questionnaire (FFQ), including detailed information about consumption of different fish species, reflecting average intake during 1 year  We also determined inorganic mercury (I-Hg) in blood, and selenium (Se) in serum  The average total fish consumption, as reported in the food frequency questionnaire, was approximately 4 times/week (range 1 6-19 times/week)  Fish species potentially high in MeHg, included in the Swedish dietary advisories, was consumed by 79% of the women  About 10% consumed such species more than once a week, i e , more than what is recommended  Other fish species potentially high in MeHg, not included in the Swedish dietary advisories, was consumed by 54% of the women  Eleven percent never consumed fish species potentially high in MeHg  T-Hg in hair (median 0 70 mg/kg; range 0 08-6 6 mg/kg) was associated with MeHg in blood (median 1 7 {mu}g/L; range 0 30-14 {mu}g/L; r {sub s}=0 78; p<0 001)  Hair T-Hg, blood MeHg and serum Se (median 70 {mu}g/L; range 46-154 {mu}g/L) increased with increasing total fish consumption (r {sub s}=0 32; p<0 001, r {sub s}=0 37; p<0
Context 3: Paper Info

Title: Incorporating Human Path Preferences in Robot Navigation with Minimal Interventions
Publish Date: 16 Mar 2023
Author List: Oriana Peltzer, Dylan Asmar, Mac Schwager, Mykel Kochenderfer

Figure

Hyperplane arrangement of a twodimensional space containing two obstacles (colored in gray) The robot is located inside the pink polytope, surrounded by three adjacent obstacle-free polytopes Each hyperplane on the boundary of the robot's polytope corresponds to one of the nonredundant constraints in eq (4) (b)Graph derived from the hyperplane arrangement The nodes on the graph designate polytopes, and edges designate transitions to adjacent polytopes To estimate the human's preference, the robot updates a posterior over the goal and over which of the graph transitions φ 1 , φ 2 and φ 3 is preferred by the human (c)Example preference defined over the graph The location of the goal is indicated in yellow in the lower right polytope For each node, the outgoing pink arrow designates the edge on the graph corresponding to the preferred transition between polytopes 
Simple, 10 × 10, 8 polytopes (b) Map 2: Office, 10 × 10, 56 polytopes (c) Map 3: Classroom, 20 × 20, 73 polytopes (d) Sampled observations and robot's executed trajectories 
Fig 5: Maps used for simulating the robot navigation problem with path preferences In (d), the heading angles observed are indicated with arrows The goal is indicated with a pink circle, and the orange robot corresponds to the starting location The blue robot follows a policy that accounts for path preference, while the green robot does not The opacity of the robots increases with time 
Map 1 problem setup and example realizations for goal-only (green) and path preference (blue) solution methods The robot starts at the lower left corner of the environment, and the goal of the task (pink circle) is in the upper left area The robot does not know which goal, among 10 options (shown in light blue squares), is the correct goal The human provides noisy observations, indicated by arrows, at each iteration The green robot selects actions according to the goal-only baseline, and the blue robot uses our proposed method to infer path preferences The polytopes composing G are drawn in blue Probability of correct goal WLPHVWHS +J (c) Entropy of goal distribution g 
Fig  6: Probability of the correct goal, fig 6b, and entropy of the goal belief distribution P (g), fig 6c, for the same problem setup, fig 6a In this problem instance, the human's preference is to go to the goal by passing on the right side of the obstacle Results are averaged over 50 runs and the area filled represents one standard deviation above and below the mean value The goal-only baseline shows an over-confident prediction (shown by the strong reduction in belief entropy) that the correct goal is less likely, making it more difficult to reach the correct goal compared to a method that accounts for path preference 
Success rates in the simple environment (Map 1) The results are averaged over 6 randomly sampled problem instances (start location, goal location, and goal possibilities), and over 50 runs per problem instance ∆T is the number of time steps separating two consecutive human inputs The robot's mission time is Tmax = 30 time steps We selected γ h = 1 5, corresponding to relatively noisy human inputs and making the problem more difficult to solve for the robot 
Computation times for Goal Only and Path Preference methods on Map 1 (fig 5a),Map 2 (fig 5b), and Map 3 (fig 5c),averaged over 100 runs with randomly sampled problem instances The 95 % confidence interval is provided with the mean We evaluate computation time at the first iteration of each run (where the search depth takes on its highest value Tmax) 

abstract

Robots that can effectively understand human intentions from actions are crucial for successful human-robot collaboration  In this work, we address the challenge of a robot navigating towards an unknown goal while also accounting for a human's preference for a particular path in the presence of obstacles 
This problem is particularly challenging when both the goal and path preference are unknown a priori  To overcome this challenge, we propose a method for encoding and inferring path preference online using a partitioning of the space into polytopes  Our approach enables joint inference over the goal and path preference using a stochastic observation model for the human 
We evaluate our method on an unknown-goal navigation problem with sparse human interventions, and find that it outperforms baseline approaches as the human's inputs become increasingly sparse  We find that the time required to update the robot's belief does not increase with the complexity of the environment, which makes our method suitable for online applications 

INTRODUCTION

Collaboration between humans and robots has become increasingly important and one key aspect of this collaboration is the ability for robots to adapt to human decisions  In many scenarios, such as a robot navigating through a busy room to deliver an item, it is important for the robot to take into account human preferences 
For instance, humans may prefer a specific path that would allow their colleagues to notice the item being delivered, but this preference may change dynamically based on various factors such as changes in the environment or unforeseen circumstances  While some preferences can be incorporated into the path-planning process, accommodating dynamic user preferences in real-time remains challenging 
In this paper, we propose a way to enable robots to adapt to human preferences dynamically by leveraging real-time feedback to inform decision-making  In this work, we tackle the problem of robot navigation in which the robot cannot observe the goal or the preferred path to the goal, but must make navigation decisions that are influenced by humans through recommended actions 
Prior work has explored how to adapt to a human's preference through feedback, but such approaches often require a high level of intervention, which can be time-consuming and impractical in real-world scenarios  To optimize the use of human input and quickly infer the human's preference, Fig  : An autonomous robot navigates in a simulated classroom towards a goal location (pink circle) 
At the start of its mission, it receives direction indications (arrows) from a human that indicate which path it should take to get to the goal  In this scenario, the human wants the robot to go around the desks on the right side of the classroom  A robot that does not reason over path preferences (green) will take the shortest path to the goal regardless of the human's input 
Our method (blue) infers the human's path preference from these indications and adapts to their recommendations  we propose an approach that leverages probabilistic representations of human preference and incorporates real-time feedback  Previous research by Bajcsy et al  considered an online adaptation problem in a manipulation task, where the person can apply forces to the robot to indicate their preferences 
By allowing the robot to continue its task while taking into account a probabilistic representation of human preference, their approach does not require frequent inputs  Building on this idea, we adopt a similar approach to adapt to a human's preference in the context of a robot autonomously navigating through a known environment, such as a cluttered office space 
Specifically, we focus on allowing the human to influence the robot's trajectory with respect to obstacles, by providing guidance on preferred routes or paths, while the robot continues to execute its task  Paths can be represented using homotopy classes   However, homotopies can pose computational challenges when used to encode and infer human preferences 
When the robot maintains a belief over homotopy classes, the inference problem can become exponentially complex with the number of obstacles in the space  Additionally, when the goal is unknown, the number of variables increases with the number of candidate destinations  This complexity can render the decision-making problem intractable 
Our solution is to encode path preference based on a partitioning of the environment into polytopes   This representation allows path preferences to be expressed as sets of preferred transitions between adjacent polytopes  Paths belonging to different homotopy classes correspond to different sequences of transitions 
By leveraging conditional independence assumptions, we can make the Bayesian inference problem tractable  These assumptions exploit the fact that human actions provide information about the path in a piece-wise manner  For example, indicating a preference for navigating around a particular obstacle only provides information about the local area and not the entire path 
Finally, after updating its belief representation over the human's preference, the robot can adapt to indications by replanning online  Our contributions are as follows  • We formulate the human-robot collaboration problem as a Partially Observable Markov Decision Process (POMDP) where both the goal of the task and the human's path preference are unknown random variables 
• We propose an encoding of a human's path preference using a partitioning of the environment into polytopes, along with conditional independence assumptions that make the Bayesian inference problem tractable to infer the task goal and path preference online  • Through simulations in two environments of different sizes and complexity, we show that our method is effective for solving problems where the robot must reach a goal that is unknown a-priori while simultaneously adapting to a human's indications 
Our method shows higher success rates compared to baseline approaches when the human inputs are sparse  Our approach enables a robot to make effective navigation decisions in collaboration with a human, even when the goal and path preference are not known in advance, and with minimal human input  In recent years, there has been a growing interest in shared autonomy and interactive systems, where humans and robots work together to accomplish tasks 
Several approaches have been proposed to address the challenge of enabling effective collaboration between human and robot agents while still achieving high task performance  Losey et al  and Jeon, Losey, and Sadigh propose a framework where a human operator is given control of a task-relevant latent action space while an autonomous system handles the rest 
Dragan and Srinivasa present a formalism for arbitrating between a user's input and a robot's policy when both human and robot share control of the same action space  Cognetti et al  [7] provide a method for real-time modifications of a path,   



ground_truth: The Wallace electorate.

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 was the conclusion of the study?

Read the following text and answer briefly.

Context 2: 001 and r {sub s}=0 35; p=0 002, respectively)  I-Hg in blood (median 0 24 {mu}g/L; range 0 01-1 6 {mu}g/L) increased with increasing number of dental amalgam fillings  We found no statistical significant associations between the various mercury species measured and the Se concentration in serum  Hair mercury levels exceeded the levels corresponding to the EPA reference dose (RfD) of 0 1 {mu}g MeHg/kg b w  per day in 20% of the women  Thus, there seems to be no margin of safety for neurodevelopmental effects in fetus, for women with high fish consumption unless they decrease their intake of certain fish species 
Bjoernberg, Karolin Ask; Vahter, Marie; Grawe, Kierstin Petersson; Berglund, Marika
We studied the exposure to methyl mercury (MeHg) in 127 Swedish women of childbearing age with high consumption of various types of fish, using total mercury (T-Hg) in hair and MeHg in blood as biomarkers  Fish consumption was assessed using a food frequency questionnaire (FFQ), including detailed information about consumption of different fish species, reflecting average intake during 1 year  We also determined inorganic mercury (I-Hg) in blood, and selenium (Se) in serum  The average total fish consumption, as reported in the food frequency questionnaire, was approximately 4 times/week (range 1 6-19 times/week)  Fish species potentially high in MeHg, included in the Swedish dietary advisories, was consumed by 79% of the women  About 10% consumed such species more than once a week, i e , more than what is recommended  Other fish species potentially high in MeHg, not included in the Swedish dietary advisories, was consumed by 54% of the women  Eleven percent never consumed fish species potentially high in MeHg  T-Hg in hair (median 0 70 mg/kg; range 0 08-6 6 mg/kg) was associated with MeHg in blood (median 1 7 Î¼g/L; range 0 30-14 Î¼g/L; r s =0 78; p s =0 32; p s =0 37; p s =0 35; p=0 002, respectively)  I-Hg in blood (median 0 24 Î¼g/L; range 0 01-1 6 Î¼g/L) increased with increasing number of dental amalgam fillings  We found no statistical significant associations between the various mercury species measured and the Se concentration in serum  Hair mercury levels exceeded the levels corresponding to the EPA reference dose (RfD) of 0 1 Î¼g MeHg/kg b w  per day in 20% of the women  Thus, there seems to be no margin of safety for neurodevelopmental effects in fetus, for women with high fish consumption unless they decrease their intake of certain fish species
Fish Consumption and Mercury Exposure among Louisiana Recreational Anglers
Lincoln, Rebecca A; Shine, James P; Chesney, Edward J
Background: Methylmercury (MeHg) exposure assessments among average fish consumers in the U S  may underestimate exposures among U S  subpopulations with high intakes of regionally specific fish  Objectives: We examined relationships between fish consumption, estimated mercury (Hg) intake      , and measured Hg exposure among one such potentially highly-exposed group, recreational anglers in Louisiana USA  Methods: We surveyed 534 anglers in 2006 using interviews at boat launches and fishing tournaments combined with an internet-based survey method  Hair samples from 402 of these anglers were       collected and analyzed for total Hg  Questionnaires provided information on species-specific fish consumption over 3 months prior to the survey  Results: Anglers' median hair-Hg concentration was 0 81 Âµg/g (n=398; range: 0 02-10 7 Âµg/g), with 40% of participants above 1 Âµg/g, the level that approximately   
Umbilical cord blood and placental mercury, selenium and selenoprotein expression in relation to maternal fish consumption
Gilman, Christy L ; Soon, Reni; Sauvage, Lynnae; Ralston, Nicholas V C ; Berry, Marla J 
Seafood is an important source of nutrients for fetal neurodevelopment  Most individuals are exposed to the toxic element mercury through seafood  Due to the neurotoxic effects of mercury, United States government agencies recommend no more than 340 g (12 oz) per week of seafood consumption during pregnancy  However, recent studies have shown that selenium, also abundant in seafood, can have protective effects against mercury toxicity  In this study, we analyzed mercury and selenium levels an   
Factors that negatively influence consumption of traditionally    
Factors that negatively influence consumption of traditionally fermented milk     in various countries of sub-Saharan Africa and a number of health benefits to human     influence consumption of Mursik, a traditionally fermented milk product fromÂ    
Mercury exposure as a function of fish consumption in two Asian communities in coastal Virginia, USA 
Xu, Xiaoyu; Newman, Michael C
Fish consumption and associated mercury exposure were explored for two Asian-dominated church communities in coastal Virginia and compared with that of two non-Asian church communities  Seafood-consumption rates for the Chinese (36 9Â g/person/day) and Vietnamese (52 7Â g/person/day) church communities were greater than the general United States fish-consumption rate (12 8Â g/person/day)  Correspondingly, hair mercury concentrations for people from the Chinese (0 52Â Âµg/g) and the Vietnamese church (1 46Â Âµg/g) were greater than the overall level for United States women (0 20Â Âµg/g) but lower than the published World Health Organization exposure threshold (14Â Âµg/g)  A conventional regression model indicated a positive relationship between seafood consumption rates and hair mercury concentrations suggesting the importance of mercury exposure through seafood consumption  The annual-average daily methylmercury intake rate for the studied communities calculated by Monte Carlo simulations followed the sequence: Vietnamese communityÂ >Â Chinese communityÂ >Â non-Asian communities  Regardless, their daily methylmercury intake rates were all lower than the United States Environmental Protection Agency reference dose of 0 1Â Âµg/kg body weight-day  In conclusion, fish-consumption patterns differed among communities, which resulted in different levels of mercury exposure  The greater seafood and mercury ingestion rates of studied Asian groups compared with non-Asian groups suggest the need for specific seafood consumption advice for ethnic communities in the United States  Otherwise the health benefits from fish consumption could be perceived as trivial compared with the ill-defined risk of mercury exposure 
Feather growth influences blood mercury level of young songbirds 
Condon, Anne M; Cristol, Daniel A
Dynamics of mercury in feathers and blood of free-living songbirds is poorly understood  Nestling eastern bluebirds (Sialia sialis) living along the mercury-contaminated South River (Virginia, USA) had blood mercury levels an order of magnitude lower than their parents (nestling: 0 09 +/- 0 06 mg/kg [mean +/- standard deviation], n = 156; adult: 1 21 +/- 0 57 mg/kg, n = 86)  To test whether this low blood mercury was the result of mercury sequestration in rapidly growing feathers, we repeatedly sampled free-living juveniles throughout the period of feather growth and molt  Mean blood mercury concentrations increased to 0 52 +/- 0 36 mg/kg (n = 44) after the completion of feather growth  Some individuals had reached adult blood mercury levels within three months of leaving the nest, but levels dropped to 0 20 +/- 0 09 mg/kg (n = 11) once the autumn molt had begun  Most studies of mercury contamination in juvenile birds have focused on recently hatched young with thousands of rapidly growing feathers  However, the highest risk period for mercury intoxication in young birds may be during the vulnerable period after fledging, when feathers no longer serve as a buffer against dietary mercury  We found that nestling blood mercury levels were not indicative of the extent of contamination because a large portion of the ingested mercury ended up in feathers  The present study demonstrates unequivocally that in songbirds blood mercury level is influenced strongly by the growth and molt of feathers 
High mercury seafood consumption associated with fatigue at specialty medical clinics on Long Island, NY
Shivam Kothari
Full Text Available We investigated the association between seafood consumption and symptoms related to potential mercury toxicity in patients presenting to specialty medical clinics at Stony Brook Medical Center on Long Island, New York  We surveyed 118 patients from Aprilâ€“August 2012 about their seafood consumption patterns, specifically how frequently they were eating each type of fish, to assess mercury exposure  We also asked about symptoms associated with mercury toxicity including depression, fatigue, balance difficulties, or tingling around the mouth  Of the 118 adults surveyed, 14 consumed high mercury seafood (tuna steak, marlin, swordfish, or shark at least weekly  This group was more likely to suffer from fatigue than other patients (pÂ =Â 0 02  Logistic regression confirmed this association of fatigue with frequent high mercury fish consumption in both unadjusted analysis (ORÂ =Â 5 53; 95% CI: 1 40â€“21 90 and analysis adjusted for age, race, sex, income, and clinic type (ORÂ =Â 7 89; 95% CI: 1 63â€“38 15  No associations were observed between fish intake and depression, balance difficulties, or tingling around the mouth  Findings suggest that fatigue may be associated with eating high mercury fish but sample size is small  Larg
Context 3:    Fig  : We model the intent inference problem with the above diagram 
At each step in time, the robot receives an observation ot from the human conditioned on its current location st, the intended goal g, and the human's path preference θ  The robot updates its belief over g and θ and transitions to a next location st+1  while Hagenow et al  present a method that allows an outside agent to modify key robot state variables and blends the changes with the original control 
However, a common challenge of these approaches is the high level of intervention required from humans  Best and Fitch propose a method for predicting an agent's intended trajectory from observations  Rather than maintaining a belief over the agent's future path, they infer the agent's intended goal among a set of candidate locations at the boundary of the space 
This approach provides information on where the agent is heading and generates a distribution of candidate future trajectories for the agent  Inferring the goal of the task among a discrete set of candidates is also relevant to the area of shared autonomy  Javdani, Srinivasa, and Bagnell propose a formalism for shared control of a robotic arm, where the robot must assist the human in picking up an object but needs to infer which object the human has chosen from joystick inputs 
Planning with homotopy class constraints is useful in problems where the robot's requirements are given with respect to obstacles, and Yi, Goodrich, and Seppi consider topological constraints provided by human operators  Bhattacharya propose an efficient algorithm for solving pathplanning problems under homotopic constraints 
However, the number of homotopy classes for a given problem can be infinite, and as the robot changes location and updates its representation of the world, carrying out inference over homotopy classes in a dynamic environment requires recomputing the set of homotopies at every iteration, making the belief update challenging 
Prior work has addressed the challenge of shared autonomy by considering how robots can infer a human's intended goal, or how they can infer the preferred path to a goal  However, we argue that inferring the goal and the path as separate problems can lead to over-confidence in incorrect beliefs about the user's preferences 
To illustrate this point, consider the following scenario: a robot and a human are collaborating to move an object from one end of a room to Fig  : Using the hyperplanes composing the H-representation of each obstacle, we construct a hyperplane arrangement of the obstacle-free space (a)  We define the human's preference for the robot's one step action choices as the posterior distribution (given all human input up to that point) over transitions from the current to the neighboring polytopes, i e  edges on the graph 
Each time the robot transitions to a new polytope, the set of neighbor polytopes and the distribution over human preferences are updated  another, but there is an obstacle in the way  The human would like the robot to take a path around the obstacle on the left, even though the goal is on the right  If the robot only infers the goal from the human's inputs, it may incorrectly assume that the goal is on the right, and become over-confident in this belief 
On the other hand, if the robot only infers the preferred path, it may mistakenly assume that the goal is on the left, leading to a failure in completing the task  To overcome these challenges, our work proposes a joint inference approach that considers both the human's intended goal and their preferred path to that goal 
Specifically, we model the human's preference over different homotopy classes and leverage a conditional independence assumption to provide a tractable solution  In our approach, we assume that the human's inputs are noisily rational conditioned on both the goal and the preference  By jointly inferring the goal and path preference, we can avoid over-confidence in incorrect beliefs about the user's preferences, leading to improved system performance 
We consider the problem of robot navigation in a known environment to an unknown destination, where a human can intervene and provide a heading direction to the robot using a joystick or force cues  The human also has a preference on which path the robot should take with respect to obstacles, and our objective is for the robot to understand the human's intentions and execute the task with minimal interventions 
Let g be a discrete random variable denoting the goal of the task, belonging to a set of candidates Ω g , and let θ be a discrete-valued random variable representing the human's path preference, belonging to a set of possible preferences Θ  The physical location of the robot at time index t is denoted by s t ∈ R 2 , and the robot's action at time index t, belonging to some action space A, is denoted by a t  
The transition model T (s t+1 | s t , a t ) is deterministic, meaning the robot has full control over its future location  At any time step, the human may provide an observation to the robot  When the human intervenes, the robot receives a direction (heading angle) that can be mapped to a future location in space 
More specifically, we map the direction to an intended location, which is the resulting robot location after advancing in the indicated direction for one time step  For simplicity, we consider that the robot directly makes an observation o t of the location indicated by the human  We assume that the robot has a stochastic observation model for the human P (o t | s t , g, θ) that is conditioned on both the goal of the task g and the human's preferred path θ 
We further assume that having chosen a goal and path preference, the human takes actions to noisily minimize a cost function C g,θ that measures the cost of moving from the robot's current location to the goal along the preferred path  For example, C g,θ (s t , o t ) can be the length of the shortest path from location s t to the goal g after taking a first step to o t , and constrained by path preference θ 
We use C g,θ to induce a probability distribution over observations, given by: where γ h is a hyperparameter that designates the rationality coefficient  This model assumes the human will pick the lowest cost action with the highest probability and the likelihood of an action decreases exponentially with the increase in cost  
Our inclusion of the path preference θ sets our approach apart from   The model is shown in fig  represented as a Bayesian Network 

Inference

At each time step where the human provides an observation, the posterior P (g, θ) is given through the Bayesian update We note that the number of Bayesian updates required at each iteration to update the belief is equal to the cardinality of Ω g × Θ  In addition, each Bayesian update involves computing C g,θ (  
,   ) in eq  ( ), which involves solving an optimization problem (such as a shortest path problem)  In section IV, we propose a specific encoding of preference θ for resolving eq  ( ), while ensuring the number of computations of the cost C g,θ ( ,  ) per update does not grow exponentially with the number of obstacles 

Decision Making

We consider a navigation problem where the robot receives reward according to the model R(s t , g, θ, a t )  We wish to find the optimal policy π that maximizes the expected discounted sum of future rewards, with discount factor γ  The above problem is a Partially Observable Markov Decision Process (POMDP)  
In this section, we propose an encoding of human's path preference θ for computing the posterior in eq  ( )  Devifrom the concept of homotopy classes, we define the preference according to a partitioning of the environment into polytopes, as shown in fig  , creating a hyperplane arrangement of the space 
Hyperplane arrangements have been used by Vincent and Schwager in the context of Neural Network verification  In our setting, we leverage this representation to define path preferences as preferred transitions between adjacent regions of the space 

Hyperplane Arrangement

We assume a two-dimensional environment composed of m polytopic obstacles, each defined by their half-space representation (H-representation) where A i ∈ R di×2 and b i ∈ R di , and where d i is the number of edges (hyperplanes) composing polytope i  Let n = i d i be the total number of hyperplanes  We leverage each obstacle's H-representation to construct a hyperplane arrangement of the environment as shown in fig 
 e  a partitioning of the space into polytopes  More specifically, each location in space belongs to a polytope j for which we can write an H-representation of the form where α j i ∈ {−1, 1} di is a vector specific to polytope j and obstacle i corresponding to the relative position of any point in the set with respect to each hyperplane in O i  
Fig  : Intent inference model in a hyperplane arrangement of the obstacle free space  We spatially decompose the preference θ into a set of preferred neighboring polytopes per region of the space  Within each polytope j, the human preference pj is a discrete distribution over the preferred neighbor in N (j) 
We assume that for a location st belonging to polytope j, and given goal g and preference pj, the observation ot and any other preference p i,i =j are conditionally independent  Concatenating elements from each obstacle's Hrepresentation, we can write polytope j's H-representation as where Some of the constraints in eq  ( ) (corresponding to rows of A, b and α j ) are redundant, i e  the set P j does not change upon their removal 
We can further reduce the Hrepresentation of a polytope to include only non-redundant constraints  By removing the rows corresponding to redundant constraints, we obtain new matrices A j e , b j e and α j e such that we can write the polytope's reduced H-representation as The non-redundant constraints correspond to edges of the polytope 
In other words, as the robot continually moves in space, the first hyperplane that it will cross upon exiting the polytope will correspond to one of the polytope's nonredundant constraints  Vincent and Schwager outline an iterative method for removing redundant constraints by solving n linear programs 
We use this method in practice for computing α j e for each polytope  We can now characterize each polytope by a vector α j e ∈ {−1, 1} n j e , where n j e ≤ n is the number of essential constraints of the polytope  The polytopes P j partition the environment into a hyperplane arrangement 

Path Preference

In this section, we provide a definition of preference θ according to a graphical representation of the environment based on the hyperplane arrangement  Under this representation, a path preference corresponds to a set of preferred transitions  In other words, for each polytope in the space, the human will have a preference to which neighboring polytope they wish to transition 
Let G := (V, E) be an undirected graph, where vertices are obstacle-free polytopes, and edges connect two adjacent polytopes  Each polytope is described by a unique vector α j as defined in eq  ( )  Two polytopes are adjacent if they share non-redundant constraints (rows in eq  ( )) corresponding to the same hyperplane (i e  they are on opposite sides of the hyperplane)



ground_truth: The conclusion was that fruit consumption may provide a protective effect for mercury exposure in Amazonian riparians.

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

Question: What is the main advantage of the proposed method in terms of computation time?

Read the following text and answer briefly.

Context 3: 
Let N (v) be the set of neighbors of a vertex v  For each vertex, we denote p v the discrete-valued random variable describing which edge in N (v) the human intends to transition to  Using this formalism, we define a path preference as the set of preferred transitions over all nodes in the graph, Let m θ = v∈V |N (v)| be the cardinality of Θ, and m g = |Ω g | the number of possible goals 
A priori, the number of Bayesian updates required to update the belief at every iteration should be m θ × m g   Now, let us assume the conditional independence relationships described by the new problem diagram in fig    More specifically, we introduce the assumption that conditioned on a robot location s t , the goal g, and the preference for the corresponding vertex p v in the graph, the observation o t and the preference for any other vertex are conditionally independent 
In other words, the observations the human provides can be defined conditioned only on the robot location, the goal, and the human's preference for its current vertex p v   By introducing this assumption, each update step only requires updating the joint (p v , g), reducing the number of cost computations to |N (v)| × m g  
We can notice that by introducing this assumption, we removed the direct relationship between the number of polytopes in the environment and the complexity of the Bayesian update in eq  ( )  In practice, components of θ are not mutually independent  For example, if the human preference at a vertex v 1 is
, it is unlikely that the human will also prefer p v2 = (v 2 , v 1 ) (turning back)  We can improve our model by assuming a dependent relationship between preferences for adjacent edges, which does not significantly increase the complexity of the inference problem  An interesting property of our encoding is that any two paths that belong to different homotopy classes will cross different sequences of polytopes, i e  they correspond to a different sequence of edges on G 
This can be proved by contradiction  Let us suppose that two continuous trajectories ξ 1 and ξ 2 , with the same start and end points and that do not intersect any obstacle, traverse the same regions in G in the same order  From the construction of the hyperplane arrangement, each polytope that the paths traverse through is obstacle-free 
Therefore, within each polytope, there is no obstacle in the area located in between the portions of ξ 1 and ξ 2 that belong to the region  A smooth transformation of ξ 1 into ξ 2 can be obtained by transforming each portion of ξ 1 belonging to the polytopes it intersects into the corresponding portion of ξ 2 for the same polytopes, where the extremities of the trajectory portions are connected to one another along the polytope's edges (where the same edge is crossed by both paths) 
Along this transformation, the paths do not intersect any obstacle, and therefore ξ 1 and ξ 2 belong to the same homotopy class 

EXPERIMENTS

We evaluate our model on a simulated navigation task where the robot must reach a goal that is unknown a priori while respecting the path preferences indicated by a human  The robot navigates in a grid world containing obstacles  The transition model is deterministic: the robot selects an adjacent location on the grid to reach at the next time step 
The robot is also allowed to take diagonal actions  Each location s t in the map can be mapped to a vertex v t ∈ G  Therefore, the actions leading to locations mapped to different vertices correspond to edges on the graph  We note f (s t , a t ) the edge crossed by taking action a t from location s t  
The robot is given a mission time limit T max for reaching the goal  In this problem, we assume that the human selects actions to noisily minimize a cost function C g,θ , where θ is defined as per eq  ( ), corresponding to the length of the shortest path to the goal constrained by the preference (where the robot is only allowed to make transitions on G along preferred edges) 
More specifically, where δ(s t , g | o t , p vt ) designates the length of the shortest path from s t to g passing by o t and constrained by preference p vt   This is a slight variant of the cost function proposed by Best and Fitch , where we add in a conditioning on the path preference  We compute costs by running the A path planning algorithm on the environment maps (grid worlds with diagonal actions) and impose preference constraints by pruning invalid transitions from the search tree 
Reward model  At each step in time, the robot receives a reward which is a sum of three components: a goal-specific reward a preference-specific reward or penalty We compute solutions to the POMDP defined in section III-B with the online solver POMCP , and with the particularity that within the rollouts, the robot does not expect to collect human inputs 
Each time a solution is computed, the robot takes an action and may receive an observation  If it does, it updates its belief distribution over the unknown problem variables and resolves the POMDP over a receding horizon 

Baselines

• Goal only  The robot solves the POMDP while ignoring the effects of path preference  Similarly to , we assume the human is taking action to minimize a goaldependent cost C g (s t , o t ) = δ(s t , g | o t ), where the conditioning on the preference is removed  We also omit the path preference's contribution to the reward R pref  
• Compliant  The robot complies with the human input, but does not take an initiative  If the user stops providing information, the robot continues in the last direction indicated for 5 time steps (conserving its momentum), then stops  • Blended  We designed an arbitration function to decide between our proposed policy (accounting for path preferences) and the user's recommendation when the robot receives inputs 
Our metric to evaluate confidence in the robot's prediction for the purpose of arbitration is the entropy of the intention distribution H(g, p i ), where p i denotes the preferred neighbor for the current region  Because our representation of the world is discrete, the arbitration is given by a step function 
Denoted by U , the action corresponding to the human's input, and P , the robot's prediction for the optimal action, we write the policy where we chose h = 1 6 as the confidence threshold 

Results

When evaluating the algorithm, we consider that a run is successful if the robot reached the goal within its allocated mission time T max and only made transitions between graph vertices corresponding to the human's preferences  We vary the time delay between human inputs, from constant guidance (∆ T = 1) to only a single observation (∆ T ≥ T max ) 
Success rates  Table I reports the success rates for experiments conducted over six randomly sampled problem instances and 50 runs per instance in Map 1 (fig  )  When the human provides inputs at every iteration, the compliant policy shows the highest success rates  However, as ∆ T increases, the compliant robot is not able to accomplish the task within the allotted time as it does not receive sufficient inputs to do so, and performance decreases compared to the autonomous baselines 
We find that in these runs, accounting for path preference consistently improves performance compared with the goal-only baseline  Results also show that blending the user's input with the robot's policy (Path Preference + Blend) when the human provides information leads to improved performance  Belief entropy 
Figure shows a challenging problem instance where the directions the human provides do not align directly with the shortest path to the goal  By ignoring the effects of preferences in the problem model (goal only), the robot quickly infers from observations that the upper left goal is less likely than others (P (g) drops) 
The strong decrease in entropy shows that the robot becomes overconfident in this prediction  Overconfidence in an incorrect goal will prevent the agent from finding the correct goal once the human's indications directly align with it, as it needs to correct for the wrong predictions, as shown in the path realization (fig 
)  In this realization, the goal-only method (green robot) fails to search the upper left area within the allotted time  By accounting for path preferences in its model, the blue robot's entropy over the goal distribution decreases more steadily, allowing for it to leverage the human's latest observations and reach the goal successfully 
shows an over-confident prediction (shown by the strong reduction in belief entropy) that the correct goal is less likely, making it more difficult to reach the correct goal compared to a method that accounts for path preference  Computation time  In table II we provide the time required to solve the POMDP, and the time required to update the robot's belief as it receives new observations 
We compute solutions on three maps: a simple 10 × 10 grid world with 8 polytopes (fig  ), a 10 × 10 grid world with 56 polytopes (fig  ), and a 20×20 grid world with 73 polytopes (fig  )  The latter environment being larger, we increase the mission time and the depth of the search tree in POMCP from T max = 30 (Map 1 and Map 2) to T max = 60 (Map 3) 
We do not notice an increase in the time required to update the robot's belief with an increase in problem complexity, which is consistent with our observation that the complexity of the Bayesian update should not increase with the number of obstacles or polytopes  On the contrary, the belief update time on Map 2 and Map 3, containing more obstacles, is reduced compared to the first map 
More obstacles result in fewer iterations when solving the constrained shortest path problem with A   Adding constraints due to the obstacles and polytopes reduces the size of the A search tree  C  Limitations Simulation environments  In our simulations, we hardcoded the preference policy over the maps (e g  in Map 1, go around the table counter-clockwise) 
We randomly sampled problem instances (start and goal locations, and goal options) to reduce the bias introduced by these preference choices  To best evaluate and compare the different approaches, it would be best to sample preferences among a distribution of preferences chosen by a human (for example, from benchmarks resulting from a collection of data) 
Creating such a benchmark is an interesting direction for future work  Hyperplane arrangement construction  The main limitation of our approach is that the size and geometry of each polytope depends strongly on the geometry of the obstacles, as seen in fig    Because of this, the robot can make predictions over preferences that are too refined compared with the topology of the environment 
A direct consequence is that when the size of the polytopes is small, the information provided by the human can be incorrectly interpreted as a preference on the robot's immediate action  Our method can be improved by changing the structure of the hyperplane arrangement so that it relies on the topology of the environment, but does not vary strongly with the geometry of the features in the environment 
For this purpose, topometric maps and region construction algorithms are promising directions  We presented an approach for encoding and inferring a human's path preference in an environment with obstacles  By leveraging a partitioning of the space into polytopes and a stochastic observation model, our method allows for joint inference over the goal and path preference even when both are unknown a-priori 
Our experiments on an unknown-goal navigation problem with sparse human interventions demonstrate the effectiveness of our approach and its suitability for online applications  The time required to update the robot's belief does not increase with the complexity of the environment, which further highlights the practicality of our method 



ground_truth: The time required to update the belief does not increase with the complexity of the environment.