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Despite the lifting of the warning, the public should always be cautious for signs of algal blooms if using lakes. "Algal blooms can develop rapidly and unpredictably and can sometimes produce toxins that are harmful for people as well as animals. If the water looks discoloured, has an unusual smell, or has green or brown particles suspended in it then it is best to avoid contact with it," says Dr Phil Shoemack, Medical Officer of Health for Toi Te Ora Public Health.
"Experience shows that Lake Okaro is prone to algal blooms at any time of the year. Lake users must exercise caution and make their own judgement about water quality by looking at the colour and clarity of the water, and whether it smells at all," says Dr Shoemack.
"Laboratory testing of lake water by Bay of Plenty Regional Council only occurs on a weekly basis during summer months so it is important to look before you leap. If in doubt, it is best to avoid contact with the water and swim or play somewhere else," says Dr Shoemack.


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Supreme Court Hearing on Duweik Family Eviction Case Adjourns Without a Verdict
On October 25, the Supreme Court convened a hearing on the leave to appeal request filed by the Duweik family (five households) who is facing eviction from their home in Batan al-Hawa, Silwan. The hearing adjourned with no verdict. A court decision will be issued at a later unspecified time.
After the lower courts ruled in 2020 to evict the Duweik family in favor of the Ateret Cohanim settler organization, the family filed a request to appeal to the Supreme Court. If the Supreme Court rejects the leave to appeal, the lower courts' decisions will remain in force, ultimately leading to the family's eviction.
The Duweik family is among 85 Palestinian families, numbering over 700 individuals, who stand to be displaced from Batan al-Hawa due to eviction lawsuits filed by Ateret Cohanim via its co-optation of the Benvenisti Trust – a Jewish trust which once owned property in the area from over a century ago. As a result of the state's appointment of two Ateret Cohanim members as trustees to the trust, the organization has initiated dozens of eviction demands based on the exploitation of the discriminatory 1970 law, which affords Jews the exclusive right to reclaim pre-1948 assets in East Jerusalem. Palestinians, however, are denied the same right to retrieve lost properties in West Jerusalem and other areas on the Israeli side of the Green Line.
Among the 85 families, the Duweik family case was the first to reach the Supreme Court level, and its outcome will inevitably set a precedent, significantly impacting the rest of the cases in the neighborhood.
The nearly two-hour hearing was comprised of mainly deliberations on the parties' contested claims concerning the respective plot of land and specific questions posed by the three-justice panel. While many topics were discussed, the proceedings revolved primarily around two central questions pertaining to the issue of statute of limitations and the existence of potential property rights (beyond that of ownership) which the Duweik family may possess.
According to the Duweik family claims, the statute of limitations should preclude Ateret Cohanim from the right to demand the family's eviction since decades had passed between the family's land purchase in 1965 and the filing of the eviction lawsuit in 2014. Ateret Cohanim contests such argument and asserts that the statute of limitations should only apply from the time the General Custodian transferred the property into their hands in 2002, which would still grant them the right to file an eviction demand. Israeli law treats officially registered land and non-registered land differently. Hence, one of the central questions which emerged was how to treat the respective plot of land and from which date and if the statute of limitations can be applied in this circumstance.
The other main question revolved around the potential existence of other property rights the Duweik family may be entitled to beyond the right of ownership. It appeared that the court accepted the claim that the family purchased the land in good faith from an individual who held rights to the land during the Jordanian period. Based on this claim, they would not be viewed as squatters. Under Israeli law, there are certain conditions and/or circumstances in which an individual who builds in good faith on land owned by another party cannot be evicted and therefore enjoys certain property rights to the asset. While the Duweik family claims such an argument, the settler organization asserted that the law does not apply to the land in question as it was considered public land when under the management of the General Custodian.
It should be noted that despite repeated requests, the court declined to allow for the presentation of an amicus curiae brief submitted by four leading Israeli legal experts on international human rights law, which could have further reinforced the family's claims of certain property rights to the land. Initiated by Peace Now and represented by human rights attorney, Michael Sfard, the brief is based on a legal approach in international jurisprudence on human rights law, which focuses on group vulnerability of occupants facing eviction while subject to institutional discrimination. It holds that in certain circumstances, occupants' rights to continue residing in their homes trump ownership rights and/or the right to land reclamation (if in the event the court ultimately recognizes Ateret Cohanim's ownership of the land in question).
While the court did not allow for the brief's presentation, it does not imply that it has outright rejected the request to file the amicus brief in the Duweik family case. However, it does indicate that during the hearing the justices chose not to adjudicate from a broader legal perspective, which would include consideration of the human right to housing and shelter and the right to family and community life.
In addition, the justices referred to the fact that the Attorney General decided not to provide an explicit position on the legal questions posed by the Supreme Court earlier this year. The court likewise expressed bewilderment that the Attorney General requested repeated extensions to the deadline despite only submitting a two-sentence response last week. When the justices further pressed the issue during the hearing, the Attorney General's representative provided a vaporous and abstruse response, again giving the impression that the state has intentionally evaded expressing a concrete position on the case and its overarching implications.
As noted previously, the Attorney General and by extension, the state, was given a rare opportunity to take a moral stand by providing a legal opinion and/or policy position to help prevent the mass displacement of these families. Yet, as in the eviction cases in Sheikh Jarrah, the Attorney General has again declined to intervene and left a decision with far-reaching geopolitical and humanitarian ramifications in the hands of court.
The Duweik family home is marked in orange with the number 1.
Attorney General Benvenisti Trust Supreme Court Ateret Cohanim Evictions Settler Organizations Silwan
More on Supreme Court
Demolition Freeze In Al-Walaja Case Remains In Place To Allow For Further Urban Planning Progress
Decisive Supreme Court Hearing Concerning 38 Homes In Al-Walajeh To Take Place On March 30
Postponed: December 26th Supreme Court Hearing on al-Walajeh Residents' Appeal

redpajama_set_name: RedPajamaCommonCrawl


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This Is Not A Computer
When you think of a computer, what do you envision? I see a clunky 90's desktop with a big, CRT monitor.
Photo by Lorenzo Herrera on Unsplash
One of the most interesting things I learned watching Hidden Figures and reading Code Girls, was that the first computers were people. Many were women. A "computer" was someone who did mathematical calculations with pencil and paper, " often taking more than a week to complete and filling up six to eight notebooks with data and formulas."
Can you imagine having the job title "computer"?
I think it's amazing how far we've come from a time not that long ago when performing computational work that affected "wing sections, propellers, and even whole airplanes" was considered women's work. The beauty of science and math is that it doesn't matter what the person who's doing it looks like but how good they are at understanding the problem and figuring out the result.
Unfortunately, this wasn't always the case at engineering labs like National Advisory Committee for Aeronautics (NACA) which later became NASA. NACA was segregated like we saw in the the movie Hidden Figures. Working as a "Computer" paid better than a school teacher (the majority of women previous professions) but it was not classified the same as an engineer.
The qualifications required of women who applied to be computers varied, but everyone had to take the Civil Service Examination. In the 1940s, computers were classed as "subprofessionals," SP-3 (Junior Computer, $1440/year) through SP-8 (Chief Computer, $3200/year).
via NASA Cultural Resources
In the late 1930's at California's Jet Propulsion Laboratory (JPL), Barbara Canright was hired as the first woman computer. Macie Roberts was another computer at JPL. "When tasked with building out her team, she made the decision to hire only women, believing men would undermine the cohesion of the group and not take direction well from a woman." This set a precedent "for future female supervisors who made it their job to hire women."
When electric computers were invented and brought to JPL, the male engineers gave the IBMs to the women computers, "dismissing computer programming as "women's work,". This gave the women the opportunity to work with the computers and learn to code.
Women "Computers" in History
via fanart.tv
If you watched or read Hidden Figures, you're probably familiar with Katherine Johnson, Dorothy Vaughan, and Mary Jackson. Here's a brief list of other women who held the title "computer".
Edith Clarke worked as a computer and "became the first professionally employed female electrical engineer in the United States in 1922." She was inducted into the National Inventors Hall of Fame in 2015.
Barbara Paulson worked at California's Jet Propulsion Laboratory. She calculated rocket paths. Paulson plotted data from the satellite, JPL-built Explorer 1, that launched on January 31, 1958.
Virginia Tucker was "a former high school teacher with a college degree in mathematics." Tucker was hired at the Langley Memorial Aeronautical
Laboratory in 1935 along with four other women. By 1946 Tucker was promoted to Overall Supervisor for Computing and "trained about 400 women and placed them in computing sections across the facility."
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The Inlands Farm Site
Wasdell and Swindon Science Park
Water Environment
Heritage and Ecology
About Wasdell Properties
Wasdell Packaging is the largest independent high-tech pharmaceutical & healthcare packaging and research company in Europe. Its current HQ is at Blagrove, near Junction 16 of the M4.
Wasdell makes a significant contribution to the local and regional economy. It:
employs more than 800 people in the UK, with around 650 in Swindon, including highly skilled and lower skilled staff – such as scientists, doctors, operators, and packers
has seen turnover rise from £2m to £36m in six years – and is on track to turn over more than £40m in 2018/19
exports 85 per cent of its turnover
uses 230 suppliers within ten miles of Swindon.
Future Need for Development
Pharmaceuticals and life-sciences drive inward investment and exports, and are a focus for government funding.
New contracts already secured by Wasdell, as well as new worldwide markets for pharmaceuticals, means the number of production lines available needs to increase substantially. Wasdell will need to employ 1200 people in Swindon by 2021, and create further jobs year-on-year. The company currently works across several Swindon sites, none of which has space to accommodate the expansion needed to support this growth. The company needs to relocate and consolidate operations on to one site.
Swindon Science Park
Wasdell Group, in joint venture with a partner developer, has formed Wasdell Properties to lead investment in a new Science Park for Swindon.
Science Parks provide a space and community for entrepreneurs, start-ups and academics to create a working environment based on innovation, collaboration and sharing of knowledge.


02/07/2012 Referred to the Subcommittee on Readiness.
01/17/2012 Referred to the Subcommittee on Nutrition and Horticulture .
12/23/2011 Referred to the Subcommittee on Economic Opportunity.
12/09/2011 Referred to the Subcommittee on Environment and the Economy.
12/09/2011 Referred to the Subcommittee on Water Resources and Environment.
12/08/2011 Referred to the Committee on Education and the Workforce, and in addition to the Committees on Armed Services, Veterans' Affairs, Agriculture, Natural Resources, the Judiciary, Energy and Commerce, and Transportation and Infrastructure, for a period to be subsequently determined by the Speaker, in each case for consideration of such provisions as fall within the jurisdiction of the committee concerned.
H.R.4297 Workforce Investment Improvement Act of 2012 Related bill CRS 12/14/2012 Placed on the Union Calendar, Calendar No. 513.
Streamlining Workforce Development Programs Act of 2011 - Amends the Workforce Investment Act of 1998 to: (1) eliminate members of the state legislature and representatives of labor organizations from state workforce investment boards, and (2) specify that representatives of business on a board represent large and small businesses with immediate and long-term employment opportunities in in-demand industries and other occupations important to the state economy.
Requires a state board to assist the state governor by developing: (1) policies and programs that support a comprehensive statewide workforce development system, and (2) a statewide employment statistics system.
Revises requirements for: (1) a state workforce development plan; (2) local workforce investment areas, boards, and plans; (3) one-stop delivery systems; and (4) the allotment of federal funds among states for employment and training activities.
Eliminates specific funding for adult and dislocated worker employment and training. Specifies state use of federal funds to set up a Workforce Investment Fund, a Youth Workforce Investment Fund, a Veterans Workforce Investment Fund, and a Targeted Populations Workforce Investment Fund.
Requires state governors to use funds to award competitive grants for programs and activities to assist eligible youth in acquiring the education and skills, credentials, and employment experience necessary to succeed in the labor market.
Revises requirements for the state unified plan for adult education and literacy programs.
Repeals the Youth Conservation Corps Act of 1970, the Public Lands Corps Act of 1993, the Snyder Act of 1921, the Indian Adult Vocational Training Act of 1956, and the Indian Self-Determination and Education Assistance Act, as well as the Job Corps, the YouthBuild program, and other job programs under the Workforce Investment Act of 1998 and other specified Acts, including the National Guard Youth Challenge Program of opportunities for civilian youth.
Amends the Rehabilitation Act of 1973 (RA73) to require an eligible state to use a certain percentage of the federal share of the cost of vocational rehabilitation services to award grants to create practical job and career readiness and training programs and provide job placements and career advancement.
Repeals the authority of the Commissioner of the Rehabilitation Services Administration in the Department of Education to make grants and contracts for: (1) vocational rehabilitation services to individuals with disabilities who are migrant or seasonal farmworkers; (2) recreational programs for such individuals; and (3) in-service training of vocational rehabilitation personnel.
Repeals title VI (Employment Opportunities for Individuals with Disabilities) of the RA73.


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British homeowner arrested for assaulting knife-wielding burglar – In his home!
Aug 10, 2016 |
Date:9 August 2016 Location: Basildon, Essex, England. Cops have arrested Brian Sharp (pictured), a heroic homeowner for ASSAULT after he fought off a knife-wielding burglar who burst into his home. Pictured: Mr Sharp pictured outside his home. (from Sun.co.uk)
His neighbors say that 40 year old homeowner Brian Sharp is a hero after he confronted a knife-wielding burglar in his home.
From Sun.co.uk:
"Whoever did this is a hero in my eyes, they have done everyone down here a favour. "I hope they gave him such a good hiding he won't think about going into someone's house."
Her Majesty's Constabulary sees things differently. They arrested Sharp, who claims to have not laid a finger on the perpetrator, for assault.
Brian denies touching the burglar, but was arrested the following morning as the man suffered head injuries after leaving the 40-year-old's home.
He claims the burglar may have been mugged, attacked by an accomplice who betrayed him or assaulted by a vigilante who witnessed the confrontation after leaving the dad's home – but denies causing the thief's injuries.
Despite his protestations, Brian spent seven hours locked up in a cell and had DNA swabs and urine samples taken.
Police even seized all his clothes – except for his underwear – and sent the stunned dad home in a red "suicide suit".
Furious Brian explained the terrifying ordeal, saying: "I asked the burglar to leave and said, 'Get out of my house'.
"He replied by saying, 'If you don't get back in the front room, I'm going to stab you'.
"Then he lunged at me and the knife came just millimetres from my neck – if I hadn't moved back he would have stabbed me."
Brian says the man then fled his home and claims he followed him out of the house for about 30 metres before returning to his property and waiting for police.
Much to Brian's amazement police turned up at 8.30am the following morning to arrest him for allegedly attacking the raider.
He said: "It's worrying but I don't know why I was arrested. The police didn't give me any reason at all.
"It was all just questioning on 'how he hurt himself' and whether I was 'defending myself'.
"I said to the cops, 'You can do whatever you want to me'. They took swabs off my hands, they took urine, they basically checked me over."
As the Brits would say, "I'm gobsmacked!". It is bad enough that the British Government denies the citizenry the right to keep and bear tools with which to defend themselves, it doesn't even recognize the God-given right of defending one's self from assault.
And the citizenry is fed up. While this travesty of justice cannot be blamed on Brussels, the Brexit vote is proof that the British people have had enough. As a certain band of British colonials once said,
"…in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation"
While I don't believe that the unarmed British populace will actually revolt against the Crown and Parliament, when said entities prove unable to protect them they will take measures to protect themselves. After the 2011 riots, baseball bat sales increased 5000%. It is a travesty that they should be penalized for doing so.
In case you missed it: check out this video ride-along with the UK Anti-Knife Task Force. While it may seem like parody, it is unfortunately not the case.
Dan Eastland says:
this makes my brain hurt!
In England, a man's home is the intruder's castle. It has been this way for five years or more, IIRC. I remember reading about home intrusions and the right of the intruder to go about his business "without let or hindrance". Yes, it's insane.
Jay smith says:
Great Britain… They don't know how to defend themselves, or brush their teeth. A nation of pussies !!


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TV Girl
Date: Thursday 09/06/2022
Californian electronic indie-pop group TV Girl will come to Clwb Ifor Bach in June 2022 to woo the crowd as their whirling, nostalgic, and psychedelic musings wash over them like a hypnotic dream.
On the surface, TV Girl is a sunny, throwback splash of '60s French pop and southern California soul. Yet, under that shiny veneer lays a dark heart, beating with sharp wit and cynical alienation, and the music is all the more alluring for it. TV Girl, composed of Brad Petering, Jason Wyman, and Wyatt Harmon, was formed in 2010 by Petering as an outlet to blend the love of Spector-esque girl group pop with an emerging interest in hip-hop.
In 2014, TV Girl unveiled their first full-length, the critically acclaimed French Exit. The album keeps true to the TV Girl charm with a bevy of electronic samplings infused throughout light and airy guitars, whirring organs, and ethereal vocals. However, this record is not all summer nostalgia, and there are plenty of times where French Exit reads like disaffected fiction. The moody characters in these songs are fueled by revenge as often as love, underpinned by desperation and a deep yearning to connect. The band takes self-identity and ponders it alongside themes of sexuality, isolation, and social status.
To date they've released three albums, including French Exit, Who Really Cares, and Death of a Party Girl.
Metronomy @ Tramshed, Cardiff
Sunday 01/05/2022


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July 26, 2021 · by amyyeewrites	· in Asian American, Inequality, Poverty/Inequality, Public health, Race & Ethnicity, science.	·
Funders and peer reviewers are contributing to systemic racism through their biases about members of these populations
For instance, the Midwest Longitudinal Study of Asian American Families, the largest study of its kind, delves into mental health challenges among more than 800 Asian American families in metropolitan Chicago. The National Institutes of Health (NIH) this year rejected a grant proposal to expand the study, which began in 2014. Three reviewers made broad comments that diminished anti-Asian racism or that the struggles of Asian Americans were "not as bad as for Blacks and Latinos," says David Takeuchi, co-investigator of the study and a professor of sociology and social work at the University of Washington.
Unfortunately, these kinds of comments are common. Takeuchi recalls submitting a paper to a prominent sociology journal when he was a graduate student in the late 1980s. A peer reviewer said his analysis of low academic performance among 8,000 AAPI students in Hawaii was "really fascinating." But the reviewer also made a comment to the effect of: "'Too bad this is about Asian Americans. If this had a Black sample, we might think about publishing it,'" says Takeuchi. "I was discouraged, so never submitted the paper again for publication."
Could myopic gatekeepers stymie research on AAPIs? It seems likely, especially considering data shows a stark gap in funding for research on AAPIs. A 2019 study in JAMA Network Open found that clinical research focused on AAPIs and funded by the NIH comprised just 0.17 percent of its total budget, based on 529 projects between 1992 and 2018.
And just 0.01 percent of articles from 1966 to 2000 in MEDLINE, the National Library of Medicine's database, mentioned AAPIs, according to a 2003 paper.
Without funding, there are fewer resources for research, thus creating a vicious cycle of omitting AAPIs from influential scholarly work. There is also a chilling effect on researchers who want to study AAPI issues but implicitly know there might be more barriers to funding and publishing their work.
Even when researchers can analyze data on AAPIs, they face roadblocks from dismissive academic peer reviewers.
"We face discrimination as researchers. We hear that Asian Americans don't count, they don't have health disparities," says Stella Yi, assistant professor at N.Y.U. School of Medicine. "Even when we have data, people still come back with these stereotypical tropes about healthy Asians: tai chi, soy sauce. It's crazy."Advertisement
The lacuna extends beyond health research. Sociologists of Asian descent were 74 percent less likely than white sociologists to receive government funding, including from NIH and National Science Foundation (NSF).
In addition, Asians are not considered an underrepresented minority group by NIH and NSF so Asian investigators are not eligible for supplements aimed at increasing diversity in research, says XinQi Dong, professor at Rutgers University.
Without funding and research, urgent social problems among AAPI related to everything from health disparities and mental illness to poverty and crime are not even acknowledged, much less studied and addressed. "We have all heard about, and personally experienced or witnessed, reviews that have been clouded by the model minority stereotype: 'Asians are doing great, we don't need to study them,'" says Tiffany Yip, professor and chair of the psychology department chair at Fordham University.
They remain invisible although Asians in the U.S. have displaced Blacks as the racial group with the greatest income inequality in the country, according to Pew Research. Social inequities among nearly 20 million AAPIs, the fastest-growing racial or ethnic group in the U.S., are neglected. To be clear, calling for attention and research on AAPIs should not take away from resources for Blacks, Latinos, Indigenous and other marginalized communities in need. Rather, efforts to reduce social inequities must also include AAPIs.
AAPIs who are low-income, limited-English-speakers, immigrants, elderly and undocumented are especially vulnerable to social problems but suffer in silence. Ignoring them in research could contribute to their erasure in press coverage, policy and philanthropy—and vice versa.
Consider that AAPIs were the focus of media stories on racial and economic inequality less than 4 percent of the time in an analysis of some 380 articles from 2019, according to a report from Asian Americans/Pacific Islanders in Philanthropy (AAPIP). Even if research did include data about AAPI inequality, media articles omitted it 37 percent of the time.
It has taken a surge in anti-Asian racism and violence during the pandemic for many to recognize that AAPIs do experience bigotry and social inequity. Otherwise, poor, elderly Asians collecting cans in New York and San Francisco don't make it into headlines—until they are beaten into a coma on a busy street. Low-income Asian salon workers fly under the radar—until they are murdered, as in the Atlanta spa shootings this March.
Part of the problem is that even if data on AAPIs are collected, the information gets lumped together. This aggregation masks deep disparities. The troughs experienced by vulnerable AAPIs are hidden by the peaks of high-income Asians. The diverse, bumpy landscape of AAPI communities becomes flattened.
When AAPI data are disaggregated, the results can be striking. Incidence of liver cancer is seven times and nine times higher for Laotian men and women, respectively, compared with non-Hispanic white adults.
More than 34 percent of Cambodian, Laotian and Hmong students do not complete high school, compared with 13 percent of the general U.S. population. Crime research with disaggregated AAPI data is rare, but one study showed youth arrest rates were highest for people of Samoan ethnicity, followed by Black, Laotian and Vietnamese people, in Alameda County in the San Francisco Bay Area.
In New York City, a study of Chinese immigrants showed high rates of diabetes and pre-diabetes at 38 percent. Filipinos in California had higher prevalence of obesity, high blood pressure, diabetes, or asthma. The same study showed that Japanese had 40 percent higher odds of being obese or overweight that whites. South Asians are four times more likely to have heart disease or diabetes than the general US population. More surprising data about Asian disparities remain largely hidden and unaddressed.
It's a frustrating chicken-and-egg scenario. Myopic gatekeepers convinced that AAPIs don't experience health and social problems reject efforts to study these issues, which renders inequities invisible. The irony is that gatekeepers, who are experts in public health, medicine, social science and other fields, contribute to systemic racism through their preconceptions and biases.
Lack of attention can translate into a big gap in social services for AAPIs in need. In New York City, about 22 percent of Asian Americans live in poverty, according to a government report. Asians comprised nearly 15 percent of New York City's population, yet just 1.4 percent of city-based agency contracts were awarded to Asian American social services providers over 13 years, according to a 2015 report from Asian American Federation.
Across the U.S., only 0.20 percent of foundation funding for work in the U.S. is designated for AAPI communities, according to an AAPIP report. In other words, for every $100 awarded by foundations, only 20 cents go to AAPIs.
In March, NIH announced its UNITE initiative to end structural racism in health research. Including AAPIs must be part of efforts at NIH, as well as at other agenda-setting institutions. More staff and grant reviewers with expertise on AAPIs should be recruited and given anti-bias training. They can also simply be open-minded that social inequities exist among AAPIs. And they can take a trip to food banks and overwhelmed social service agencies that serve thousands of low-income AAPIs every week.Advertisement
The need is obvious—if only gatekeepers choose to look and listen. It's a travesty that it takes a mass shooting and racist attacks to make AAPIs worthy of attention and finally impossible to ignore.
This is an opinion and analysis article; the views expressed by the author or authors are not necessarily those of Scientific American.
https://www.scientificamerican.com/article/research-on-asian-americans-and-pacific-islanders-is-being-stifled/
Tags: Scientific American
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\section{Introduction}\label{intro}
Markov Chain Monte Carlo (MCMC) methods have become the standard computational tool for bayesian inference. But the great flexibility of the method comes with a price. Namely, it is very difficult to determine a priori (before the simulation) or a posteriori whether a given MCMC sampler can mix or has mixed in a given computing time. The challenge becomes that of designing fast converging Monte Carlo algorithms. Contributions in this field can have significant impact in other scientific disciplines where these methods are used.

In this paper, we propose a new and general approach to increase the convergence rate of MCMC algorithms. The method is based on resampling. Suppose that at time $n$, we want to sample $X_n$ in a MCMC algorithm. Instead of sampling $X_n$ from $P(X_{n-1},\cdot)$ for some transition kernel $P$, we propose to obtain $X_n$ by resampling independently from $\{X_B,\ldots,X_{n-1}\}$, where $B\geq 0$ is some burn-in period. This \textit{resampling from the past} step is then repeated during the simulation at some predetermined times  $a_1<a_2<\ldots$. Basically, the idea is to look at $\{X_B,\ldots,X_{n-1}\}$ as a sample from $\pi$. Therefore resampling from the past allows the sampler to move more easily and according to a distribution that is close to $\pi$. The resampling schedule plays an important role. As long as we do not resample too much (typically, we need $(a_n)$ such that $a_n/n\to\infty$ as $n\to\infty$), we show that resampling from the past does not disturb the limit distribution of the sampler.

Resampling from the past can perform poorly if the original sampler has a very poor convergence rate. We extend the framework above by allowing resampling from an auxiliary process $\{X^{(0)}_n\}$ that has a better convergence rate towards its target distribution $\pi^{(0)}$. Resampling from an auxiliary process is not new and is the idea behind the equi-energy sampler  recently proposed by \citep{kzw06}. But the equi-energy sampler has a number of complications that we avoid here by using an \textit{importance-resampling}. The idea is also apparent in the ``Metropolis with an adaptive proposal'' of \citep{chauveauetvand01}. On the theoretical side, we show in the case of \textit{importance-resampling}, that resampling from an auxiliary process does not disturb the limit distribution of the sampler.

We apply our methods to two examples from Bayesian data analysis. First, we consider the Bayesian analysis of stochastic volatility models \citep{kimetal97}. We improve the efficiency of the basic Gibbs sampler for this problem by a factor of fifty (50). In the second example, we look at Bayesian phylogenetic trees reconstruction. Our methods improve the efficiency of the MCMC sampler of \citep{largetetsimon99} by a factor of hundred (100).

The paper is organized as follows. In Section \ref{past}, we present the idea of resampling from the past. Resampling from an auxiliary process is discussed in Section \ref{auxil}. All the theoretical proofs are postponed to Section \ref{proof} and the simulation examples are presented in Section \ref{examples}.

\section{Resampling from the past}\label{past}
Let $\{X_n\}$ be a Markov chain with state space $(\mathcal{X},\mathcal{B})$, transition kernel $P$ and invariant distribution $\pi$ started at $X_0=x$. If the chain is ergodic then $\mathcal{L}_x(X_n)$, the distribution of $X_n$, will converge to $\pi$ as $n\to\infty$. But it is well known that for MCMC algorithms, the convergence of $\mathcal{L}_x(X_n)$ to $\pi$ can be too slow for the sampler to be useful. We propose the following idea to accelerate the convergence of Markov chains. Suppose that after a burn-in period $B$, we have the sample $\{X_B,X_{B+1},\ldots,X_{n-1}\}$ at time $n$. Instead of sampling $X_n\sim P(X_{n-1},\cdot)$ as we normally do, we obtain $X_n$ by resampling independently and with equal weight from $\{X_B,X_{B+1},\ldots,X_{n-1}\}$. The resampling step is then repeated at some predetermined times $a_1<a_2<\ldots$. Intuitively, if $P$ mixes reasonably well, $\{X_B,X_{B+1},\ldots,X_{n-1}\}$ can be seen as a sample points from $\pi$ and resampling will operate as an i.i.d. sampling from $\pi$.

Consider the following toy example. We want to use the Random Walk Metropolis (RWM) algorithm with proposal density $q(x,y)=\mathcal{N}(y-x;0,\sigma^2)$ with $\sigma=0.1$ to sample from the standard normal density $\mathcal{N}(x;0,1)$; where $\mathcal{N}(x;\mu,\sigma^2)$ denotes the density of the normal distribution $N(\mu,\sigma^2)$ with mean $\mu$ and variance $\sigma^2$. We compare the plain RWM with a RWM with resampling. Each sampler is run for $25,000$ iterations. Graph 1 (a) shows the last $5,000$ sample points and Graph (b), the autocorrelation function from the last $20,000$ points in the plain RWM sampler. For the RWM with resampling, we resample at times $B+\lceil k^\alpha\rceil$ (see the justification below), with $B=5,000$ and $\alpha=1.3$. Graph 1 (c) and (d) show the corresponding results for the RWM with resampling. As we can see, there is a significant gain in efficiency.

Intuitively, resampling helps to the extend that $P$ mixes rapidly. Differently put, the slower $P$ converges to $\pi$, the longer we should wait between two resampling. What should be the resampling schedule $(a_k)$? Obviously, we should not resample all the time. We find that the choice $a_k=b_1+b_2k^\alpha$, $\alpha>1$ is a valid choice and works well in practice for $b_2=1$, and $\alpha\approx 1.3$. The choice $a_k=b_1+b_2k$ is also theoretically valid as long as $b_2$, the time between two resampling, is large enough.
\bigskip

\begin{center}
\scalebox{0.5}{\includegraphics{graph1.eps}}\\
\noindent\underline{Graph 1}: Comparing a plain RWM and a RWM with resampling in sampling from the standard norma distribution $N(0,1)$.
\end{center}
\bigskip

\subsection{Theoretical discussion}\label{theorie1}
What can we prove about this algorithm? We can prove that despite the resampling, the limit distribution of the algorithm is $\pi$ under certain conditions on $P$ and on the resampling schedule $(a_k)$. We recall the algorithm. The resampling schedule $0<a_1<a_2<\cdots<a_n<\infty$ is given and is nonrandom. Fix $B$ the burn-in period. We start the sampler at some arbitrary point $X_0=x$. At time $n\geq 1$, given $\{X_0,\ldots,X_{n-1}\}$, if $n>B$ and $n=a_k$ for some $k\geq 1$ then $X_n\sim\frac{1}{n-B}\sum_{j=B}^{n-1}\delta_{X_j}(\cdot)$. Otherwise sample $X_n\sim P(X_{n-1},\cdot)$. We denote $\Pr$ the underlying probablity measure and $\mathbb{E}$ its expectation operator. Here are some standard notations that we use below. If $P_1$ and $P_2$ are two transition
kernels on $\mathcal{X}$, the product $P_1P_2$ denotes the transition kernel
$P_1P_2(x,A):=\int P_1(x,dy)P_2(y,A)$. Recursively, we can
define $P_1^n$ by $P_1^1=P_1$ and $P_1^n=P_1^{n-1}P_1$. A transition kernel $P_1$ defines a linear operator (also denoted $P_1$) on the space of $\mathbb{R}$-valued functions on $(\mathcal{X},\mathcal{B})$ into itself, by $P_1f(x):=\int P_1(x,dy)f(y)$. If $\mu$ is a signed measure on $(\mathcal{X},\mathcal{B})$, we denote $\mu(f):=\int\mu(dx)f(x)$ and we will also write $\mu$ to denote the linear functional on the space of $\mathbb{R}$-valued functions on $(\mathcal{X},\mathcal{B})$ thus induced. Finally, we define $\mu P_1(A):=\int\mu(dx)P_1(x,A)$. Let $V:\;\mathcal{X}\to [1,\infty)$ be given. For $f:\;\mathcal{X}\to\mathbb{R}$, we define its $V$-norm $\abs{f}_V:=\sup_{x\in\mathcal{X}}\frac{\abs{f(x)}}{V(x)}$ and we introduce the space $L_{V}:=\{f:\;\mathcal{X}\to\mathbb{R}:\;\; \abs{f}_V<\infty\}$. For a signed measure $\mu$ on $(\mathcal{X},\mathcal{B})$ we define its $V$-norm $\norm{\mu}_V:=\sup_{f\in L_V,\;\abs{f}_V\leq 1}\abs{\mu(f)}$. Similarly, for a linear operator $T$ from the space of $\mathbb{R}$-valued functions on $\mathcal{X}$ into itself, we define $\nnorm{T}_V:=\sup_{f\in L_V,\;\abs{f}_V\leq 1}{\abs{Tf}_V}$. If $\nnorm{T}_V<\infty$, then $T$ defines a bounded linear operator from the Banach space $(L_V,\abs{\cdot}_V)$ into itself.

We assume that the transition kernel $P$ in the algorithm is geometrically ergodic in the sense that:

\noindent\textbf{Assumption (A):} \textit{$P$ is irreducible, aperiodic and there exists $\rho\in (0,1)$, a measurable function $V:\;\mathcal{X}\longrightarrow
[1,\infty)$ such that
\begin{equation}\nnorm{P^{n}-\pi}_V=O\left(\rho^n\right),\end{equation} }

This assumption implies that $\pi(V)<\infty$ and that $\sup_nP^nV^\alpha(x)<\infty$ for any $x\in\mathcal{X}$, $\alpha\in[0,1]$. We refer the reader to \citep{meynettweedie93} for more on geometrically ergodic Markov chains. This is a convenient assumption that is known to hold for many MCMC sampler.

Define $c:=\frac{1}{1-\rho}$ and $\delta_n:=-a_1\log(\rho)+\sum_{k=2}^n\log(a_{k})-\log(c+a_{k-1})$.
\begin{theorem}\label{thm1}
Assume (A). Then there exists a constant $C\in (0,\infty)$ such that for $a_k\leq n<a_{k+1}$:
\begin{equation}\nnorm{\mathcal{L}^{(n)}-\pi}_V\leq C\rho^{n-k}\exp\left[-\delta_k\right],\end{equation}
where the transition kernel $\mathcal{L}^{(n)}$ is defined by $\mathcal{L}^{(n)}(x,A):=\Pr\left[X_n\in A\vert X_0=x\right]$. In particular if $\delta_n\to\infty$ as $n\to\infty$, the algorithm has limit distribution $\pi$.
\end{theorem}
\begin{proof}See Section (\ref{proof}).\end{proof}

\bigskip

Resampling from the past can sensibly reduce the autocorrelation in the output of a MCMC algorithm. But when the sampler has a very slow mixing time, it might be better to resample from an auxiliary process that has a better mixing time.

\section{Resampling from an auxiliary process}\label{auxil}
As above, $\pi(dx)\propto h(x)\lambda(dx)$ is the probability measure of interest on the measure space $(\mathcal{X},\mathcal{B},\lambda)$. We introduce another probability measure $\pi^{(0)}(dx)\propto h^{(0)}(x)\lambda(dx)$ on $(\mathcal{X},\mathcal{B},\lambda)$. Let $\{X^{(0)}_n\}$ be a Markov chain with invariant distribution $\pi^{(0)}$ and transition kernel $P^{(0)}$. Let $k:\;\mathcal{X}\times\mathcal{X}\to [0,\infty)$ be a measurable function and $T$ a transition kernel on $(\mathcal{X},\mathcal{B})$. Define the transition kernel $Q(x,dy)=\frac{\int\pi^{(0)}(dz)k(x,z)T(z,dy)}{\int \pi^{(0)}(dz)k(x,z)}$. Following \citep{tierney98}, let $S\subseteq\mathcal{X}\times\mathcal{X}$ be such that the probability measures $\pi(dx)Q(x,dy)$ and $\pi(dy)Q(y,dx)$ are mutually absolutely continuous on $S$ and mutually singular on $\mathcal{X}\setminus S$.

We assume that $\{X^{(0)}_n\}$ converges (reasonably quickly) to $\pi^{(0)}$. Let $P$ be a transition kernel with invariant distribution $\pi$ and $\theta\in[0,1]$. The algorithm works as follows. Given $(X_0^{(0)},\ldots,X_n^{(0)},X_0,\ldots,X_n)$:
\begin{itemize}
\item with probability $\theta$, we sample $X_{n+1}$ from $P(X_n,\cdot)$;
\item with probability $1-\theta$, we propose $Y$ from $R_n(X_n,\cdot)$ where $R_n(x,A)=\frac{\sum_{l=0}^nk(x,X_l^{(0)})T(X^{(0)}_l,A)}{\sum_{l=0}^nk(x,X_l^{(0)})}$. In other words, we resample $Y_1$ from $\{X_0^{(0)},\ldots,X_n^{(0)}\}$ with weights $k(X_n,X_l^{(0)})$ and propose $Y\sim T(Y_1,\cdot)$.

Then we either ``accept'' $Y$ and set $X_{n+1}=Y$ with probability $\alpha(X_n,Y)$, or ``reject'' $Y$ and set $X_{n+1}=X_n$ with probability $1-\alpha(X_n,Y)$, where
\begin{equation}\label{acc}
\alpha(x,y)=\left\{\begin{array}{lc}\min\left[1,\frac{\pi(dy)Q(y,dx)}{\pi(dx)Q(x,dy)}\right] & \mbox{ if } (x,y)\in S\\
0 & \mbox{ otherwise}.\end{array}\right.\end{equation}
\end{itemize}

For $n$ large enough, a sample from $R_n(x,\cdot)$ can be seen as a sample from $Q(x,dy)$ which explain the acceptance probability (\ref{acc}). But the algorithm is not feasible as such because the ratio in (\ref{acc}) cannot be computed in general. The natural choice which simplifies $Q$ is to choose a transition kernel $T$ that is invariant under $\pi$ and $k(x,y)=\omega(y)=h(y)/h^{(0)}(y)$. With this choice, we get $\alpha(x,y)\equiv 1$ on $S$. We call this scheme \textit{importance-sampling} resampling. It is not necessary to choose a complicated transition kernel for $T$. Throughout, we choose $T$ to be the identity transition kernel, $T(x,A)=\textbf{1}_A(x)$ in which case $S=\{(x,y):\; 0<h(x)k(x,y)<\infty\}$.

Another choice for which the acceptance ratio $\alpha(x,y)$ simplifies is $T(x,A)=\textbf{1}_A(x)$ and $k(x,y)=\textbf{1}_{\{D(x)\}}(y)$ where $(D_i)$ is a given partition of $\mathcal{X}$ and $D(x)=D_i$ if $x\in D_i$. This corresponds to the set-up of the equi-energy sampler of \citep{kzw06}. With this choice of $k$, the acceptance probability becomes $\alpha(x,y)=\min\left(1,\frac{\omega(y)}{\omega(x)}\right)$ (and $0$ if $\omega(x)=0$ or $\omega(x)=\infty$). The drawback with this choice is that we have to define the partition $(D_i)$ in the first place and an inadequate partition can result in a high rejection rate for the resampling step.

\bigskip
\begin{algo}[MCMC with Importance-Resampling from an auxiliary process]
\bigskip
At some time $n\geq 1$, given $\left(X_0^{(0)},\ldots,X_n^{(0)},X_0,\ldots,X_n\right)$:
\begin{description}
\item [(i)] With probability $\theta$, sample $X_{n+1}$ from $P(X_n,\cdot)$. Otherwise with probability $1-\theta$ sample $X_{n+1}$ from \[\frac{\sum_{i=0}^n\omega(X_i^{(0)})\delta_{X_i^{(0)}}(\cdot)}{\sum_{i=0}^n\omega(X_i^{(0)})}.\]
\item [(ii)] Sample $X_{n+1}^{(0)}$ from $P^{(0)}(X_n^{(0)},\cdot)$.
\end{description}
\end{algo}
\bigskip

\subsection{Theoretical discussion}\label{theorie2}
We look more closely to $\{X_n\}$ when the importance-resampling scheme is used. \citep{atchadeetliu06} have shown that the limit distribution of the equi-energy sampler is indeed $\pi$ under a number of conditions. We can study the process $\{X_n\}$ along the same line. The assumption we impose are less stronger than in \citep{atchadeetliu06}. We continue with the notations in Section \ref{theorie1}. Essentially we will assume that $P^{(0)}$ is geometrically ergodic and that the weight function satisfies $\abs{\omega}_{V^{\alpha}}<\infty$, for some $\alpha\in[0,1/4)$. Typically $\omega$ is bounded.
\bigskip

\noindent\textbf{Assumption (A0):}\textit{ $P^{(0)}$ is irreducible and aperiodic and there exists $\rho_0\in (0,1)$ such that
\begin{equation}\nnorm{P^{(0)^n}-\pi^{(0)}}_V=O\left(\rho_0^n\right),\end{equation} where $V$ is as in (A).
}

\bigskip

\begin{theorem}\label{thm2}
Assume that $P$ satisfies (A), $P^{(0)}$ satisfies (A0) and $\abs{\omega}_{V^{\alpha}}<\infty$ for some $\alpha\in[0,1/4)$. Then for any measurable function $f:\;\mathcal{X}\to\mathbb{R}$ such that $\abs{f}_{V^{\alpha}}<\infty$,
\begin{equation}\mathbb{E}\left[f(X_n)\vert X_0=x\right]\longrightarrow\pi(f), \; \mbox{ as } n\to\infty\end{equation}
and
\begin{equation}\frac{1}{n}\sum_{i=0}^{n-1}\left(f(X_i)-\pi(f)\right)\stackrel{a.s.}{\longrightarrow} 0,\; \mbox{ as } n\to\infty.\end{equation}
\end{theorem}
\begin{proof}See Section \ref{proof}.\end{proof}

\section{simulation examples}\label{examples}
We illustrate the methods developed above with two examples from bayesian modelling. In the first example, we consider the Bayesian analysis of stochastic volatility models (\citep{kimetal97}) and in the second example, we look at Bayesian phylogenetic trees reconstruction (\citep{largetetsimon99}).
\subsection{Bayesian analysis of stochastic volatility models}
We consider the Bayesian analysis of the basic stochastic volatility model:
\begin{eqnarray}\label{svmodel}y_t&=&e^{h_t/2}\varepsilon_t,\;\;t=0,\ldots,T\\
h_{t+1}&=&\mu+\phi(h_t-\mu)+\sigma u_t,\;\; t=0,\ldots,T-1,\end{eqnarray}
where $(\varepsilon_t)$ and $(u_t)$ are two uncorrelated sequences of i.i.d. standard normal random variables. We assume that $h_0\sim N\left(\mu,\frac{\sigma^2}{1-\phi^2}\right)$ and $\abs{\phi}<1$ to assure the stationarity of the process $(h_t)$. We observe $(y_t)$ but not $(h_t)$, the so-called volatility process. The objective is to estimate $\theta=(\sigma,\phi,\beta)$ where $\beta=e^{\mu/2}$. This model and its generalizations  have attracted attention in the financial econometrics literature as a better way to model financial markets series. A bayesian approach to analyze this model has been proposed by a number of authors (see e.g. \citep{kimetal97} and the references therein). The difficulty is that the volatility process $(h_t)$ is not observed making the likelihood of $\theta$ analytically intractable. The natural solution is to see $(h_t)$ as a parameter and to design a Gibbs sampler on the posterior distribution $\pi(\theta,h_0,\ldots,h_T)$, of the parameter $\theta$ and the volatility process $(h_0,\ldots,h_T)$. But, due to the high autocorrelation in the volatility process, this sampler mixes very slowly. This mixing problem has motivated some authors to propose more sophisticated reparametrization of the model for better MCMC convergence. We show here that by resampling from the past in the Gibbs sampler, we can match the performances of the sophisticated solution proposed in \citep{kimetal97}.

We use the same prior distribution for $\theta$ as in \citep{kimetal97} and essentially the same Gibbs sampler to sample from $\pi(\theta,h_0,\ldots,h_T)$ except when sampling from the conditional $\pi(h_t\vert \theta,h_{-t})$. To sample from this conditional, we use an Independent Metropolis sampler instead of the Accept-Reject method adopted in \citep{kimetal97}. The proposal distribution of our Independent Metropolis sampler is the same as the dominating distribution in the Accept-Reject sampler of \citep{kimetal97}. We refer the reader to \citep{kimetal97} for the details.

Following \citep{kimetal97} and \citep{shephardetpitt97}, we use model (\ref{svmodel}) to analyze the Sterling dataset, which gives the daily observations of weekday close exchange rates for the UK Sterling/US Dollar exchange rate from $1/10/81$ to $28/6/85$. The total number of observations is $T=946$. We first center the series with the formula \\$y_t=100\left[(\log(r_t)-\log(r_{t-1}))-\frac{1}{n}\sum_{j=1}^n(\log(r_j)-\log(r_{j-1}))\right]$, where $(r_t)$ is the observed exchange rates. We then model $(y_t)$ with the model (\ref{svmodel}).

We compare the plain Gibbs sampler with the 2 strategies discussed above: a Gibbs sampler with resampling from the past and a Gibbs sampler with resampling from an auxiliary process. To assure that the three sampler have about the same computational cost (storage requirement aside), we set the auxiliary process to be another copy of the plain Gibbs sampler with the same target distribution. The three samplers are run for $N=250,000$ iterations. For each sampler and for each of the variables $\sigma$, $\phi$, $\beta$, we give a plot of the last $5,000$ sample points together with the histogram and the autocorrelation function from the last $100,000$ points. When resampling from the past, the resampling schedule used is $B+\lceil k\rceil^\alpha$, $B=125,000$ and $\alpha=1.25$. For the third sampler with resampling from an auxiliary process, each of the two chains is run for $125,000$ iterations. The results of the variable $\sigma$ (resp. $\phi$ and $\beta$) are given in in Graph 2 (resp. Graph 3 and Graph 4). On each graphics, the first column gives the result of the plain Gibbs sampler, the second column gives the results of the Gibbs sampler with resampling from the past and the results of the third sampler are in the third column.

Clearly, resampling from the past significantly improve on the Gibbs sampler. To quantify the gain, we compute, following \citep{kimetal97} the inefficiency of each sampler on each of the three variables. For a Markov chain with transition kernel $P$ and invariant distribution $\pi$, the inefficiency at $f$ is:
\begin{equation}
I(f)=1+2\sum_{k=1}^\infty\rho_k(f),\end{equation}
where $\rho_k(f)=Cov_\pi\left(f(X_k),f(X_0)\right)/Var_\pi\left(f(X_0)\right)=\pi\left(\bar fP^k\bar f\right)/\pi\left(\bar f^2\right)$.  Basically, it is the cost of using a dependent process to sample from $\pi$. To estimate $I(f)$, we use, following \cite{kimetal97}:
\begin{equation}
\hat I(f)=1+\frac{2B}{B-1}\sum_{i=1}^BK\left(\frac{i}{B}\right)\hat\rho_i(f),\end{equation}
where $\hat\rho_i(f)$ is the usual estimate of the autocorrelation at lag $i$ for $f$ and $K$ the so-called Parzen kernel. We use $B=5,000$. The result is given in Table 1.

By resampling from the past or from an auxiliary process, we obtain a sampler that outperforms \citep{shephardetpitt97} and is as efficient as the offset mixture method of \citep{kimetal97}.

\begin{table}
\begin{center}
\small
\begin{tabular}{lccc}
\hline
&$\sigma$&$\phi$&$\beta$\\
\hline
Plain Gibbs& $448.12$&$211.55$ & $1.54$\\
Gibbs with resampling & $10.96$& $4.92$ & $0.97$\\
Gibbs with Aux. Proc. & $12.24$& $9.91$ & $1.39$\\
\hline
\end{tabular}
\end{center}
\caption{Inefficiencies of the samplers for the Sterling dataset.}
\end{table}

\subsection{Bayesian phylogeny reconstruction}
Since Darwin's theory of evolution, methods to reconstruct the evolutionary relationships between different species have become important. We are concerned here with the statistical inference of phylogenetic trees based on molecular sequences. Recently, more realistic models have been considered in this field owing to the MCMC machinery. We show here that MCMC samplers for phylogeny reconstruction can be improved upon with resampling from the past.

The statistical model is not standard, so we summarize it first. For more details on phylogenetic trees, we refer the reader to \citep{felsenstein04}. Suppose we have $n$ aligned deoxyribonucleic acid (DNA) sequences $(y_1,\ldots,y_n)$ each of length $m$, where sequence $i$ is from organism $i$. That is, $y_i=(y_i(1),\ldots,y_i(m))$ where $y_i(j)$ can be one of the four nucleotide basis $A$ (Adenine), $G$ (Guanine), $C$ (Cytosine) or $T$ (Thymine). Based on these sequences, we would like to infere the phylogenetic tree or evolutionary relationships between these organisms. To be precise, we recall that a binary tree $\tau$ for $n$ species is a connected graph $(V,E)$ with vertex set $V$ and edges $E$, with no cycle, such that $V=\{\rho\}\cup\mathcal{I}\cup\mathcal{T}$, where $\rho$ (the root) has degre $2$; any $v\in\mathcal{I}$ has degre $3$ and any $v\in\mathcal{T}$ has degre $1$. $\mathcal{I}$ has $n-2$ elements called the internal nodes and $\mathcal{T}$ (the leaves or the tips) represent the $n$ species. A phylogenetic tree for $n$ species is a couple $\psi=(\tau,b)$, where $\tau$ is a binary tree for the $n$ species and $b\in (0,\infty)^{\abs{E}}$, where $\abs{E}=2n-1$ is the cardinality of $E$. For $e\in E$, $b_e$ represents the length of edge $e$, the so-called branch length. We restrict our attention to phylogenetic trees with ``contemporary tips'', where the sum of the branch length $b_e$ on the directed path from the root to any tip is constant (equal to $1$ hereafter). Such phylogenetic trees are said to be with a ``molecular clock'' as the $b_e$ can now be interpreted as time. Let $\Psi$ be the set of all phylogenetic trees for $n$ species. For $i\in V\setminus\{\rho\}$, denote $p(i)$ the parent of $i$, that is the vertex $p(i)$ such that $(p(i),i)\in E$.

The model of phylogenetic reconstruction we are interested in assumes that there are some missing DNA sequences $(y_j)_{\{j\in\{\rho\}\cup\mathcal{I}\}}$ such that the joint conditional distribution of $(y_j)_{V}$ given the phylogenetic tree $\psi$ writes:
\begin{equation}\label{phylomodel1}
f((y_i)_{\{i\in V\}}\vert\psi)=f(y_\rho)\prod_{i\in V\setminus\{\rho\}}f\left(y_i\vert y_{p(i)},\psi\right).\end{equation}

In addition we make the simplifying assumption that each site evolves independently:
\begin{eqnarray}\label{phylomodel2}
f(y_\rho)&=&\prod_{j=1}^mf(y_\rho(j)),\;\mbox{ and }\\
f\left(y_i\vert y_{p(i)},\psi\right)&=&\prod_{j=1}^m f\left(y_i(j)\vert y_{p(i)}(j),b_{(p(i),i)}\right).\end{eqnarray}

And finally, we assume that there exist $(\pi_l)_{l\in \{A,G,C,T\}}$, $\pi_l\geq 0$, $\sum\pi_l=1$, parameters $\theta,\kappa\in(0,\infty)$ and a $4\times 4$ Markov process generator $Q=Q(\theta,\kappa,\pi_A,\pi_G,\pi_C,\pi_T)$ such that:
\begin{eqnarray}\label{phylomodel3}
f(y_\rho(j)=l)&=&\pi_l,\;l\in\{A,G,C,T\}\mbox{ and }\\
f\left(y_i(j)=m\vert y_{p(i)}(j)=l,b_{(p(i),i)}=b\right)&=&exp(bQ)_{lm},\;\;l,m\in\{A,G,C,T\}.\end{eqnarray}

The matrix $Q$ specifies the model of DNA evolution. We use the F84 model as in \citep{largetetsimon99}. The parameters of the statistical model are then $(\psi,\theta,\kappa,\pi_A,\pi_G,\pi_C,\pi_T)$. To simplify the sampler, we fix $\pi_A,\pi_G,\pi_C,\pi_T$ to their empirical values in the data. We assume that $\psi$ has a uniform prior distribution on $\Psi$ and we assume that $\theta$ and $\kappa$ each has a uniform prior on $(0,M)$, $M=200$. Let $\pi\left(\psi,\theta,\kappa\vert (y)_{i\in\mathcal{T}}\right)$ be the posterior distribution of the model. Clearly, $\pi\left(\psi,\theta,\kappa\vert (y)_{i\in\mathcal{T}}\right)\propto f\left((y)_{i\in\mathcal{T}}\vert \psi,\theta,\kappa\right)$ and this likelihood is obtained by integrating out the missing variables $(y_i)_{i\in\{\rho\}\cup\mathcal{I}}$ from (\ref{phylomodel1}). A fast computation of this likelihood is available with the pruning method of Felsenstein \citep{felsenstein04}. To sample from this posterior distribution, we follow essentially \citep{largetetsimon99}. We update $\theta$ and $\kappa$ together, given the phylogenetic tree $\phi$, using a random walk Metropolis move. Next, given $\theta,\kappa$, we update the phylogenetic tree $\psi$ with the \textit{global move with a molecular clock} of \citep{largetetsimon99}.

We compare this plain MCMC sampler with the samplers obtained with the two methods discussed in this paper. For the simulations, we use the \textit{primate dataset} discussed in \citep{yangetrannala97}. The dataset has $n=9$ species and the phylogeny reconstruction is based on aligned sequences of length $m=888$. The three samplers are simulated for $N=500,000$ iterations. For each sampler and for each of the variables $\theta$, $\kappa$, we give a plot of the last $5,000$ sample points together with the histogram and the autocorrelation function from the last $150,000$ iterations. When resampling from the past, the resampling schedule used is $B+\lceil k\rceil^\alpha$, $B=100,000$ and $\alpha=1.3$. For the third sampler with resampling from an auxiliary process, each of the two chains is run for $250,000$ iterations. The auxiliary process is a MCMC chain with stationary distribution $\pi^{(0)}=\pi^{1/T}$, with $T=2$. The results of the variable $\theta$ (resp. $\kappa$) are given in in Graph 5 (resp. Graph 6). On each graphics, the first column gives the result of the plain MCMC sampler, the second column gives the results of the MCMC sampler with resampling from the past and the results of the third sampler are in the third column. In accordance with \citep{largetetsimon99}, the outputs of the three samplers overwhelmingly (with an estimated posterior distribution over $0.95$) select the phylogenetic tree topology plotted in figure 7 as the most probable for this primate dataset.

Here again, resampling from the past significantly improve on the plain MCMC sampler. Table 2 gives the efficiency gains.

\begin{table}
\begin{center}
\small
\begin{tabular}{lcc}
\hline
&$\theta$&$\kappa$\\
\hline
Plain MCMC& $1510.23$&$1271.87$\\
MCMC with resampling & $13.95$& $24.37$\\
MCMC with Aux. Proc. & $9.18$& $8.15$\\
\hline
\end{tabular}
\end{center}
\caption{Inefficiencies of the samplers for the primates dataset}
\end{table}
\bigskip

\section{Proofs of Theorem \ref{thm1} and \ref{thm2}}\label{proof}
We start with Theorem \ref{thm1}. Without any loss of generality we assume that $B$, the burn-in period is $0$.
\subsection{Proof of Theorem \ref{thm1}}
The following lemma is a consequence of (A).
\begin{lemma}\label{lem1}
Assume (A). There exists a constant $C_1\in (0,\infty)$ such that for any signed measure $\mu$ on $(\mathcal{X},\mathcal{B})$ such that $\mu(\mathcal{X})=0$ and for any $n\geq 0$,
\begin{equation}\norm{\mu P^n}_V\leq C_1\rho^n\norm{\mu}_V.\end{equation}
\end{lemma}

\begin{proof}[Proof of Theorem \ref{thm1}] Fix $n$ such that $a_k\leq n<a_{k+1}$, $k\geq 2$. For $f\in L_V$ such that $\abs{f}_V\leq 1$, define $\bar f=f-\pi(f)$. We have:
\begin{eqnarray}\mathbb{E}\left(\bar f(X_n)\vert X_0=x\right)&=&\mathbb{E}\left[\mathbb{E}\left(f(X_n)\vert X_{a_k}\right)\vert X_0=x\right]\nonumber\\
&=&\mathbb{E}\left(P^{n-a_k}\bar f(X_{a_k})\vert X_0=x\right)\\
&=&\left(\mathcal{L}^{(a_k)}-\pi\right)\left[P^{n-a_k}\bar f\,\right](x),\end{eqnarray}
where $\mathcal{L}^{(a_k)}(x,A)=\Pr\left(X_{a_k}\in A\vert X_0=x\right)$.  Therefore, since\\ $\nnorm{\mathcal{L}^{(n)}-\pi}_V=\sup_{x\in\mathcal{X}}\frac{\sup_{\abs{f}_V\leq 1}\abs{\mathbb{E}\left(\bar f(X_n)\vert X_0=x\right)}}{V(x)}$, it follows from Lemma \ref{lem1}, that:
\begin{equation}\label{bound1proofthm1}\nnorm{\mathcal{L}^{(n)}-\pi}_V\leq C_1\rho^{n-a_k}\nnorm{\mathcal{L}^{(a_k)}-\pi}_V.\end{equation}

Also, for $f\in L_V$ with $\abs{f}_V\leq 1$, we have:
\begin{eqnarray}
\mathcal{L}^{(a_k)}\bar f(x)&=&\mathbb{E}\left[\frac{1}{a_k}\sum_{j=0}^{a_k-1}\bar f(X_j)\vert X_0=x\right]\nonumber\\
&=&\frac{a_{k-1}}{a_k}\mathcal{L}^{(a_{k-1})}\bar f(x)+\frac{1}{a_k}\sum_{j=a_{k-1}}^{a_k-1}\mathbb{E}\left(\bar f(X_j)\vert X_0=x\right)\nonumber\\
&=&\frac{a_{k-1}}{a_k}\mathcal{L}^{(a_{k-1})}\bar f(x)+\frac{1}{a_k}\sum_{j=a_{k-1}}^{a_k-1}\left(\mathcal{L}^{(a_{k-1})}-\pi\right)P^{j-a_{k-1}}\bar f(x).\end{eqnarray}

Then proceding as above and using Lemma \ref{lem1} again we get:
\begin{equation}\label{boundproof2thm1}\nnorm{\mathcal{L}^{(a_k)}-\pi}_V\leq \exp\left(-u_{k}\right)\nnorm{\mathcal{L}^{(a_{k-1})}-\pi}_V,\end{equation}
with $u_k=\log(a_k)-\log(a_{k-1}+c)$, $c=\frac{1}{1-\rho}$. If we define $u_1=-a_1\log(\rho)$ and $\delta_k=\sum_{i=1}^ku_k$, we get $\nnorm{\mathcal{L}^{(a_k)}-\pi}_V\leq C_2\exp(-\delta_k)$ for some finite constant $C_2$, which, together with (\ref{bound1proofthm1}) yields:
\begin{equation}\nnorm{\mathcal{L}^{(n)}-\pi}_V=O\left(\rho^{n-a_k}\exp(-\delta_k)\right),\end{equation}
for $a_k\leq n<a_{k+1}$, as wanted.

\end{proof}

\subsection{Proof of Theorem \ref{thm2}}
Let $\{X_n\}$ be the process generated by the importance-resampling scheme.  We prove Theorem \ref{thm2} as a consequence of Theorems 3.1 and 3.2 of \citep{atchadeetrosenthal03}. Denote $\mathcal{F}_n$ the $\sigma$-algebra generated by $(X_0,\ldots,X_n)$. For $x\in\mathcal{X}$ and $A\in\mathcal{B}$, define $P_n(x,A)=\Pr\left(X_n\in A\vert X_{n-1}=x\right)=\Pr\left(X_n\in A\vert \mathcal{F}_{n-1},X_{n-1}=x\right)$. We have:
\begin{equation}
P_n(x,A)=\theta P(x,A)+(1-\theta)\mu_n(A),\end{equation}
where $\mu_n(A)=\mathbb{E}\left[\frac{\sum_{k=0}^{n-1}\omega(X_k^{(0)})\textbf{1}_A(X_k^{(0)})}{\sum_{j=0}^{n-1}\omega(X_j^{(0)})}\right]$.

Define $M_r=\sup_n\mathbb{E}\left(V^{r}(X_n^{(0)})\right)$, $r\geq 0$. It follows from (A0) that $M_r\leq M_1<\infty$ for all $r\in [0,1]$. For $p\geq 0$, we write $\omega_i=\omega(X_i^{(0)})$, $s_n=\sum_{k=0}^{n-1}\omega_k$, $V_i^\alpha=V^{\alpha}(X^{(0)}_i)$ and $\mu_n^{(p)}=\mathbb{E}\left[\frac{\sum_{i=0}^{n-1}\omega_iV_i^\alpha}{s_n}\right]^p$. The next lemma is crutial.
\begin{lemma}\label{lem21} For $p\in[1,\frac{1}{4\alpha}]$, $\max_{0\leq i\leq n-1}\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\right]^p=O\left(\frac{1}{n^p}\right)$ and $\mu_n^{(p)}=O(1)$ as $n\to\infty$.\end{lemma}
\begin{proof}
By the Minkowski inequality, we only need to prove that $\max_{0\leq i\leq n-1}\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\right]^p=O\left(\frac{1}{n^p}\right)$.

Write $c=\lambda(h)$ and $c_0=\lambda(h^{(0)})$. For $0\leq i\leq n-1$ and $\kappa\in(0,c/c_0)$, we have:
\begin{equation*}\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\right]^p=\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\textbf{1}_{\{s_n\geq n(c/c_0-\kappa)\}}\right]^p+\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\textbf{1}_{\{s_n<n(c/c_0-\kappa)\}}\right]^p.\end{equation*}

\[\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\textbf{1}_{\{s_n\geq n(c/c_0-\kappa)\}}\right]^p\leq \frac{1}{n^p(c/c_0-\kappa)^p}\mathbb{E}\left[\omega_iV_i^\alpha\right]^p\leq \frac{\abs{\omega}_{V^{\alpha}}M_1}{n^p(c/c_0-\kappa)^p}.\]

By the Cauchy-Schwarz inequality, we can bound the second term as follows:
\begin{eqnarray*}
\mathbb{E}\left[\frac{\omega_iV_i^\alpha}{s_n}\textbf{1}_{\{s_n<n(c/c_0-\kappa)\}}\right]^p&\leq&\mathbb{E}^{1/2}\left[\frac{\omega_iV_i^\alpha}{s_n}\right]^{2p}\left(\Pr\left[\frac{1}{n}\sum_{i=0}^{n-1}\left(\omega_i-\frac{c}{c_0}\right)<-\kappa\right]\right)^{1/2}\\
&\leq&\mathbb{E}^{1/2}\left[V_i^{2p\alpha}\right]\left(\Pr\left[\frac{1}{n}\sum_{i=0}^{n-1}\left(\omega_i-\frac{c}{c_0}\right)<-\kappa\right]\right)^{1/2}\\
&\leq&\frac{M_1^{1/2}}{n^{2p}\kappa^{4p}}\mathbb{E}^{1/2}\left(\sum_{i=0}^{n-1}\left(\omega_i-\frac{c}{c_0}\right)\right)^{4p},\end{eqnarray*}

where for the last line, the Markov inequality was used. Now we use the classical Poisson equation and martingale approximation technique. Since $\omega\leq V^{\alpha}$, the Poisson equation $\omega-c/c_0=g-P^{(0)}g$ has a solution $g$ which satisfies $\abs{g}\leq V^{\alpha}$. With this solution, for $n>1$, we can rewrite $\sum_{i=0}^{n-1}\omega_i-c/c_0=M_n+W_n$ where $W_n=g(X_0^{(0)})-P^{(0)}g(X_{n-1}^{(0)})$, $M_n=\sum_{i=1}^{n-1}g(X^{(0)}_i)-P^{(0)}g(X^{(0)}_{i-1})$ and $(M_n)$ is a martingale. Therefore with the Minkowski inequality, we get: $\mathbb{E}^{1/2}\left(\sum_{i=0}^{n-1}(\omega_i-c/c_0)\right)^{4p}\leq \left[\mathbb{E}^{1/4p}\left(M_n\right)^{4p}+\mathbb{E}^{1/4p}\left(W_n\right)^{4p}\right]^{2p}$. Since $\abs{g}_{V^\alpha}<\infty$ and $4p\alpha\leq 1$, it follows from Assumption (A0) that $\sup_{i,j}\mathbb{E}\left(g(X_i^{(0)})-P^{(0)}g(X_{j}^{(0)})\right)^{4p}<\infty$. Therefore $\left(\mathbb{E}^{1/4p}\left(W_n\right)^{4p}\right)$ is bounded. Using Burkholder's inequality (see e.g. \citep{halletheyde80}), we have the bound:
\begin{eqnarray*}\mathbb{E}\left(M_n\right)^{4p}&\leq& K_3\mathbb{E}\left(\sum_{i=1}^{n-1}\left(g(X_i^{(0)})-P^{(0)}g(X_{i-1}^{(0)})\right)^2\right)^{2p}\\
&\leq&K_3\left[\sum_{i=1}^{n-1}\mathbb{E}^{1/2p}\left(g(X_i^{(0)})-P^{(0)}g(X_{i-1}^{(0)})\right)^{4p}\right]^{2p}\\
&\leq&K_4n^{2p},\end{eqnarray*}
for some finite constants $K_3,K_4$. This implies that $\mathbb{E}^{1/2}\left(\sum_{i=0}^{n-1}(\omega_i-c/c_0)\right)^{4p}=O(n^p)$ which finishes the proof.

\end{proof}

\begin{lemma}\label{lem2}
For all $n\geq 1$, $P_n$ has an invariant distribution $\pi_n$, and for all $k\geq 0$,
\begin{equation}
\nnorm{P_n^k-\pi_n}_{V^{\alpha}}\leq C\theta^k\rho^k,\end{equation}
where the constant $C\in(0,\infty)$ does not depend on $n$ or $k$. Moreover
\begin{equation}\pi_n(f)\longrightarrow\pi(f),\;\mbox{ as } n\to\infty,\end{equation}
for any measurable function $f$, with $\abs{f}_{V^\alpha}<\infty$. \end{lemma}
\begin{proof}
One can directly check that the invariant distribution of $P_n$ is $\pi_n$ where:
\begin{equation}\pi_n(A)=(1-\theta)\mu_n\left(\sum_{i=0}^\infty \theta^iP^i(x,A)\right).\end{equation}

And by recurrence, we can check that for $k\geq 0$ and $g\in L_{V^{\alpha}}$:
\begin{equation}
P_n^kg-\pi_n(g)=\theta^kP^k\bar g-(1-\theta)\mu_n\left(\sum_{i=k}^\infty\theta^iP^i\bar g\right).\end{equation}

Therefore $\nnorm{P_n^k-\pi_n}_{V^{\alpha}}\leq \theta^k\rho^k\left(1+\frac{1-\theta}{1-\theta\rho}\sup_n\mu_n(V^{\alpha})\right)$ and according to Lemma \ref{lem21},\\ $\sup_n\mu_n(V^{\alpha})$ is finite.

For $f\in L_{V^{\alpha}}$, we write $\zeta(f)=(1-\theta)\sum_{i=0}^\infty\theta^iP^if\in L_{V^{\alpha}}$.  We have $\abs{\pi_n(f)-\pi(f)}=\abs{\mu_n\left(\zeta(\bar f)\right)}$, where $\bar f=f-\pi(f)$. Note that $\pi(\zeta(\bar f))=0$. We recall:
\begin{equation}\label{eqlem2}\mu_n\left(\bar f\right)=\mathbb{E}\left[\frac{\sum_{k=0}^{n-1}\omega(X_k^{(0)})\bar f(X_k^{(0)})}{\sum_{j=0}^{n-1}\omega(X_j^{(0)})}\right].\end{equation}
 From the strong law of large numbers for $\{X^{(0)}\}$, the expression under the expectation in (\ref{eqlem2}) converges a.s. to $0$ as $n\to\infty$. On the other hand, for $p\in (1,1/4\alpha)$,
\begin{equation}\mathbb{E}\abs{\frac{\sum_{k=0}^{n-1}\omega(X_k^{(0)})\bar f(X_k^{(0)})}{\sum_{j=0}^{n-1}\omega(X_j^{(0)})}}^p\leq \mu_n^{(p)},\end{equation}
and $(\mu_n^{(p)})$ is a bounded sequence. Therefore the sequence $\left(\frac{\sum_{k=0}^{n-1}\omega(X_k^{(0)})\bar f(X_k^{(0)})}{\sum_{j=0}^{n-1}\omega(X_j^{(0)})}\right)$ is uniformly integrable and it follows that $\mu_n(\bar f)\to 0$ as $n\to\infty$.
\end{proof}

\begin{lemma}\label{lem3}
\begin{equation}\nnorm{P_n-P_{n-1}}_{V^{\alpha}}+\norm{\pi_n-\pi_{n-1}}_{V^{\alpha}}=O\left(\frac{1}{n}\right).\end{equation}
\end{lemma}
\begin{proof}
For $n\geq 1$, we have: $\nnorm{P_n-P_{n-1}}_{V^{\alpha}}+\norm{\pi_n-\pi_{n-1}}_{V^{\alpha}}\leq 2(1-\theta)\mathbb{E}\left[\frac{\omega_{n-1}V_{n-1}^{\alpha}}{\sum_{k=0}^{n-1}\omega_k}\right]$ and the lemma follows from Lemma \ref{lem21}.
\end{proof}
\bigskip

\begin{proof}[Proof of Theorem \ref{thm2}]
Follows from Lemmas \ref{lem2} and \ref{lem3} and Theorems 3.1, 3.2 of \cite{atchadeetrosenthal03}.
\end{proof}

\bibliographystyle{ims}

redpajama_set_name: RedPajamaArXiv


text:
Home West Ham News Mills Exclusive: West Ham star man may become 'Burden' after big development
Mills Exclusive: West Ham star man may become 'Burden' after big development
Connor Whitley speaking to Danny Mills
23rd November 2020 at 4:00pm
Danny Mills has warned West Ham United not to offer Michail Antonio a five-year contract as he could become a burden.
Speaking exclusively to Football Insider correspondent Connor Whitley, the former Leeds United and England full-back delivered his verdict as contract negotiations stalled over the length of a new deal.
This site revealed earlier this month the Hammers were planning to offer their star forward, 30, a new two-year deal with the option of a third year.
His current contract runs out in the summer but the club have an option to extend it for a further 12 months.
ExWHUEmployee claimed on the West Ham Way podcast that talks have hit an impasse over the length of a new deal with Antonio keen to end his career in East London.
"There's always a balance to be had in these sort of situations," Mills told Football Insider.
"I think he's done exceptionally well, he's been magnificent for West Ham, and I'm sure they appreciate him.
"I'm sure he wants a long contract and I'm sure West Ham are going to go 'well, you're 30 now, when you get to the end of this one, you'll be 32 so how long can we offer him? How long is it going to be this good for?'
"Yes, they want to reward him for what he's done but it has to also still work within the structure and the sensible nature of the club.
"There's no point offering him a five-year contract and after two years, it might start to be a burden. It's a difficult one.
"The player is doing unbelievably well at the minute and deserves a new deal but it's about the length of that."
In other West Ham news, a top pundit cannot believe what David Moyes has said about Declan Rice.
Previous article'How's That Happened?' – Whelan 'Really Worried' by what he's seen at Aston Villa
Next article'Bielsa won't tolerate it' – Exclusive: Pundit on what he's seen from Leeds youngsters
Ibrox Exclusive: Finance guru drops 'Amazing' £35m Rangers reveal & Mike Ashley claim
'100%' – Exclusive: Ex-Derby coach on Leeds maybe signing Louie Sibley after big update
'It's Classic Tin Ear From Celtic' – Exclusive: Finance expert rips into board


text:
• Register Now for the
2007 Buyer's Guide
Will the Real ROI Please Stand Up?
Mobile organizations increasingly use CRM software to realize ROI.
By Arielle Emmett
Bert Burkholder of AGSCO in Grand Forks, N.D., tells a story of how one change in a customer relationship management (CRM) system saved his fertilizer company 26,000 man hours of labor and tens of thousands of dollars each year in lost chemicals inventory.
In the past, the AGSCO sales team of 40 men and women routinely visited customer farms, writing down all chemical sales orders on little slips of paper. The customers were given a carbon copy, and the sales team would assemble back in the office, dialing into the Internet through a Citrix server and typing in the sales activity for the day. The administrative process took three to five hours each day. Moreover, papers kept getting lost, along with the returnable stainless steel chemical containers.
Then AGSCO's IT department implemented a mobile CRM sales solution. Instead of keying in transactions and inventory, the sales force now has an automated process that uploads sales orders in about a minute. The company chose a device-agnostic mobile data management solution, OneBridge from Sybase/iAnywhere, that allows direct integration with the company's Microsoft Dynamic GP accounting and inventory system. OneBridge provides integrated email, contacts, calendars and slimmed-down sales transactions. "The solution allows us to scan the serial numbers of [our] chemical containers," Burkholder says. When it comes to capturing sales information, it makes syncing effortless." Thanks to the solution, AGSCO has seen not only manpower reductions but almost 100 percent decreases in lost inventory.
Is Mobile ROI a Moving Target?
The AGSCO mobile CRM case isn't unique. However, the industry is divided about the numbers and meaning of mobile CRM return on investment (ROI) in a world where hardware, software, networks and company expectations are shifting so rapidly.
"There are really two classes of return on investment for mobile CRM," says William Clark, a VP in research communication at Gartner. "The first is a 'softer,' subjective set of benefits." Soft benefits include things like greater personal satisfaction with work and increased convenience—for example, the ability to populate databases with the results of an email or voice call, or to contact multiple users in a sales team using a mobile CRM e-cast. "These benefits are running at less than 50 percent ROI annualized," Clark asserts. "A second and more interesting [class of ROI] is in mobile field service. Technicians can be traveling out in bands or within the four walls of an institution. Yet depending on a lot of variables, typically what we see exceeds 200 percent ROI annualized, and that makes a very compelling investment."
Increases in operational efficiencies account for much of the benefit. Field technicians whose work processes are automated and synced to backend systems, whether wirelessly or in near real time, can save on paperwork, inventory calls, and routing and dispatch mistakes while adding an extra job or two each day to their assignment lists. The net result is more trouble tickets completed per day or, if necessary, a reduction in costs and time to complete the same number of jobs.
"That translates into ROI, and it's very easy to calculate," says Mark Ferrentino, a VP of engineering at Vettro, a five-year-old company specializing in mobile, on-demand CRM applications for field service and sales force automation. "A few years ago, we were fighting to convince people that mobility was something they needed to invest in; now, people are already convinced."
Addressing Pent-Up Need
Mobility is a hot topic among CTOs and CIOs. In North America, the number of RIM BlackBerry users has quadrupled in the last two years and driven mobile CRM right along with Windows Mobile 5.0, the Pocket PC, the Palm Treo 650 and 700, and J2ME handsets, according to Ferrentino.
Among large mobility vendors such as Panasonic, which sells its Toughbook laptop line to mobile field forces, sales have doubled between 2002 and 2005, says Mike McMahon, director of workforce automation at Panasonic Computer Solutions. "The number one reason [for the sales boom] is the advance of mobility in the workforce management space. Five to seven years ago, ROI typically was a three-year payback process [based on loaded labor rates, i.e., $55 to $95/hour for field service technicians in telecoms]. Now the ROI payback has shrunk to three to five months because the [computer] hardware, software and wireless technologies have become much more dependable and mission critical," McMahon believes.
Field forces demonstrate a pent-up need for mobile data, according to a 2005 study by the Aberdeen Group. Such applications as on-demand access to work order details and scheduling, locating and identifying spare parts and warranties, and quickly obtaining customer histories are main areas for growth. In 2004, no more than 30 percent of the companies Aberdeen surveyed could provide real-time data access to their field forces in any individual data category, while at least half the companies indicated they required it. Among mobile CRM groups already deployed, Aberdeen found a 27 percent average improvement in worker productivity, a 19 percent increase in customer satisfaction and double-digit improvements in overall profitability and service revenues.
Multiple m-CRM Models
Does one model fit all? Obviously not. Key mobile/CRM enterprise suppliers, among them Siebel/Oracle, SAP, Sybase/iAnywhere, Salesforce.com, Nokia and even smaller mobile players such as Dexterra and Vettro, each have distinct approaches to ROI. No one interviewed for this article—not even analyst groups—would commit to any comparative ROI figures for specific vendor product or mobile CRM service offerings. Instead, the claims are summarized as variable, user-based, circumstantial and based on parameters unique to particular companies or industries.
One common factor among many mobile CRM offerings today is that they are based on something known as "service-oriented architecture," i.e., a centralized distribution model from a server that can deliver applications to devices over the air. In other words, solutions are no longer device-centric or jury-rigged for individual wireless applications, contends Tien Tzuo, the senior VP of product management at Salesforce.com.
"If you look back at the software infrastructures of 1999 and 2000, each company had to be responsible for wirelessly enabling its [mobile data]," he says. "But today with service-oriented architecture, that's not really true. You can build your applications and customize them on an applications exchange platform (he cites the Salesforce.com www.appexchange.com Web site, which uses service-oriented architecture). Once loaded, those applications will automatically appear on your [mobile] device."
By transitioning to service-oriented architecture, Salesforce.com and other CRM suppliers have been able to get more companies up and running quickly.
Variable Solutions
Large-scale, embedded CRM infrastructures present unique challenges for vendors seeking a mobile component. For example, CRM giant Siebel (now part of Oracle), while fully invested in more than 3.5 million users, now offers three different CRM integration solutions to satisfy more than 30 percent of its customers requiring mobile data access. The solutions touch customers using remote laptop clients, handheld PDAs and wireless clients, says Guy Waterman, senior director of product strategy for mobile solutions at Oracle, which handles Siebel operations. Siebel handheld solutions are also packaged by individual industries and by application. Moreover, the Siebel CRM model does not require an always-on connection. Many of the solutions are occasionally connected, meaning the databases of field workers are synchronized or updated in the background only at certain times and intervals.
Siebel does offer a browser-based mobile CRM solution known as Siebel Wireless, which provides real-time wireless access to inventory connected to back-office systems. The solution offers "a zero footprint on a mobile device," Waterman says.
Less Is More?
Not everyone deploys mobile CRM with several layers of complexity. To Mike Ikotin, a VP of products marketing at Dexterra, a company specializing in mobile CRM solutions, the key to worker acceptance is a less-is-more approach. "The field worker works differently from a person in the office, and that's the key difference to success in mobile CRM," he claims. Mobile workers need a skinnied-down interface that's easy to read and integrates with critical apps in the field. Ikotin calls this "the outside-in approach." The approach accents an opportunistic connection rather than a persistently connected mobile CRM model. By opportunistic, Ikotin means that workers are only connected when they need to be, and the system automatically pushes information to them. Updates can be obtained either wirelessly or in a cradle connection. In this way, the system avoids information overload or the temptation to replicate too much information in the same form as the monster backend CRM system.
Ikotin points out that mobile CRM is becoming less expensive and more personalized. Dexterra, for example, offers a category of mobile application that lets users take modules or components of functionality and put them together to build a mobile solution. For greeting card company John Sands, Dexterra's order and fulfillment solution has produced a 15 percent decrease in ordering time along with an 85 percent user adoption rate among its sales force.
Despite generally moving targets for ROI, many believe the tipping point for mobile CRM is at hand. Organizations are increasingly recognizing ROI benefits—quantified, qualitative or both. And, says Chris Leffel, a senior product manager with iAnywhere, customers are asking for more than mobile email or Internet access; many want vertical applications and extended databases.
"Productivity as a factor in ROI is always hardest to compute," Leffel says. "What you can measure is the quality of information in the field that's delivered to the back end. While no size fits all, customer perceptions of ROI continue to drive the marketplace. Leffel concludes, "It's really about finding what makes sense for each customer and building your ROI case around that." //
Arielle Emmett is a freelance writer in Pennsylvania.


Wat Khao Khamphaeng Uthong is even further into the western part of Suphanburi province. We didn't see a soul when we visited, so we could not learn more about this temple which shows some Khmer elements in its design. Inside the Ubosot is a large white marble Buddha statue.


text:
Cristina García Banegas
The day finally arrived!
The great concert celebrating Cristina's 50 years in music was a great success, with a full house, even in the midst of the pandemic.
The days before the concert had their corresponding share of chaos, with the continuous count of available places given the limited capacity and the limited staff so that everything flowed without problems. Anyway, when the day came, everything went according to plan, and people were able to enjoy the event with Cristina and from their homes.
On Monday, after her well-deserved rest, Cristina took the time to leave us a few words about the special celebration of this milestone in her career:
"(...) This concert was scheduled for March 21, which also coincided with Johann Sebastian Bach's birth date, and it was 270 years (...) after his death. And we were able to announce it in advance, but by March 14th, 15th, we knew that it would not be possible.
Time passed by, and there was an opening, to a certain degree, to carry out activities trying not to gather big crowds and such, so I asked at the Parish and Father Raúl (...), said yes.
(...) As I have too much activity every week, I had to decide a few days ago what repertoire (...) I was going to do, and the program that I had in mind, of course, was Beatles Love Bach because I had never presented it in Montevideo. I had played something very similar in the Paysandú Basilica at the end of 2019. So I wanted to do it, but at the same time, I didn't know if I would have the time to put together the program. (...) I said to myself: Well, at the end of the concert I want to add All You Need Is Love, as a final message, which (...) is not on the album. And I thought I needed a soloist, and I chose (...) Álvaro Cedrés, who is an excellent singer, and he immediately accepted. (...) There, I thought it would be very nice if he also sang the song For No One, which is linked to the aria of the G string (...) by Bach. (...) Later, I also had the idea to add (...) the song A Whiter Shade of Pale by Procol Harum (...) because it is also written on (...) a bass voice very similar to the aria by Bach and the song For No One.
(...) During the concert, I was happy and at the same time very attentive because this instrument from the Tapes parish, although it is very dear to me and has accompanied me since the beginning of my studies, has some defects. Several were solved thanks to the competence of Jaime Camps and the help of the new future organ builder Nicolás López Marino (...), and it is a joy for us because we can think that the organ building school will continue in Uruguay. (...) The pneumatic system does not work 100% well, and then the keyboards and the pedalboard have a response, sometimes quite finicky. It means that one passes the foot over it barely touching it (...) and sounds a little, and of course, that (...) is heard. (...) We plan to improve the instrument soon.
(...) It was really moving, reaching the end with All You Need Is Love and the surprise for the public, especially from the De Profundis choir that from their chairs they accompanied with the choir of this song while Álvaro Cedrés sang the melody. (...) And that encouraged people to start clapping their hands, and well, a party started. But calmly, with joy, and with gratitude.
(...) The concert was recorded with two cameras and will have a professional sound take.
(...) And last but not least, my regards and most sincere thanks to the parish priest Raúl Díaz who accompanied this project from the moment I asked him if he thought it was okay for me to do my 50th-anniversary celebration concert on his instrument."
During the concert, many copies of Beatles Love Bach and Cristina's new album, Preludi e Concerti, recorded in the San Domenico Church, Rieti, Italy were also sold. You can still get your copy by communicating over private messages.
This would be it for now, see you next Thursday!
Final Details!


After the failed coup, in which he had already backed Peter Dutton while pledging support to Malcolm Turnbull, Mathias Cormann's reputation is now in tatters, writes Michael Galvin.
BARELY AN HOUR after the Liberal Party high noon showdown on Friday, the first "player" to give an extended interview on ABC News was Senator Mathias Cormann.
Cormann seemed desperate to explain himself and did so at length. As the dust settled in the following hours, it became clear why he was so desperate to get ahead of the story.
Anyone who watched the 15-minute interview would have been struck by a couple of things.
Firstly, Cormann still seemed obsessed with what had happened three days earlier, when Turnbull called a snap leadership poll and declared all positions vacant. At the time, there were reports that Cormann was miffed because he was not forewarned of Turnbull's plan. Apparently, only Deputy Liberal Leader Julie Bishop knew what Turnbull was going to do.
From what Cormann said on Friday, "miffed" is too mild a word. He seemed obsessed with being taken by surprise by Turnbull on Tuesday. He repeated the word "surprise" no less than four times in the Friday interview — a telling sign Turnbull had hurt him mightily and personally.
This sense of personal affront was reinforced throughout the rest of the Friday interview, in which the honourable Senator went on at great length about how difficult these decisions had been for him, personally.
Cormann has been working on his image for a while now. Patient with the assorted nutters on the Senate crossbench, a shared affinity and mutual respect for Labor Senator Penny Wong and so on. Gradually, he had moved on from his early caricaturish image as a dull, conservative zealot and had reinvented himself as something of an "honest broker".
When he walked into the ABC interview barely an hour after the Friday vote, he must have known that this particular game of his was up. Why? Because if he and the other two show ponies (Senator Michaelia Cash and Senator Mitch Fifield) had not switched in a public display of disunity the day before, the spill motion would have been defeated and Turnbull would still be Prime Minister.
Hence his desperate rush to get to the media first and pour out how much pain he had suffered personally in all of this. A valiant effort, but a failed one. Cormann's reputation is back to where it started — a dull conservative zealot incapable of original thought.
When it was revealed a few hours later that the three reluctant "switcheroos" – Cormann, Fifield and Cash – had actually signed Dutton's petition when it still needed another 20 or so more names, Cormann's interview straight after the ballot was revealed for what it was. Not only a pathetic display of self-pity and personal pique, but a pack of lies and a desperate attempt to save his own reputation. Cormann was part of the push to dump Turnbull — not an anguished bystander who was forced to act honourably in dishonourable circumstances.
Shame, Cormann, shame. Walking confidently with Dutton to the Party room meeting, you showed your true colours and your reputation is rightly now in tatters.
Sadly, for those of us who hope that this period of rightwing madness will go away as soon as Abbott falls under a bus, or finds some useful way to spend his time away from public sight, there will be no such relief in the medium term. The younger lot – Cormann, Dutton and the new boys, like Member for Deakin Michael Sukkar, Member for Hume Angus Taylor, Member for Canning Andrew Hastie, Member for Barker Tony Pasin and Senator Zed Seselja – are just as bad.
They are first-class wreckers but cannot competently execute their own coup. Their keystone cops performance this week would have been funny under other circumstances. But this time around, it was just pathetic and sad.


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Ten Things
Jaguars News | Jacksonville Jaguars - jaguars.com
Single-game tickets for all Jaguars home games are now on sale. Tickets can be ordered online at jaguars.com, or by phone by calling 1-877-4-JAGS-TIX (credit card only). Tickets can be ordered on the telephone from 8:00 a.m. to 6:00 p.m. Monday through Saturday. Ticket prices are $25, $35, $45, $50, $65, $95 and $215 per ticket, depending upon location and availability.
The Jaguars will open their 2002 home schedule on Friday, August 16, when they host the Tampa Bay Buccaneers at 7:00 p.m. at ALLTEL Stadium. The regular season begins on September 8 when the Jaguars host the Indianapolis Colts.
Official: Jaguars sign WR Laquon Treadwell
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Although the Dow Jones EuroStoxx 50 was only introduced in February 1998, its prices were calculated retroactively back to the year 1986.
The EuroStoxx 50 consists of the shares of the 50 largest companies in the Eurozone and represents their growth. For this reason, the EuroStoxx 50 and its growth are also regarded as an indicator for the Eurozone share market as a whole. The securities contained in the EuroStoxx 50 are weighted according to their market capitalization and free float. Two variants of the EuroStoxx 50 are calculated: Firstly, there is the price index, comparable with the SMI, the index level of which displays the average of the shares contained within it and which does not take dividend payments into account. Secondly, there is the dividend-corrected performance index, similar to the SMIC.
The inclusion of a company in the EuroStoxx 50 does not depend on defined criteria and does not take place on specified dates. Instead, a joint venture between the Swiss Stock Exchange SWG Group, Deutsche Börse AG and Dow Jones & Company decides whether a share is to be included or excluded.
The second largest European stock market barometer besides the EuroStoxx 50 is the Stoxx 50. It lists the shares of the 50 largest companies from all over Europe. It also includes companies from Switzerland and the UK – non-euro countries whose companies cannot be included in the EuroStoxx 50 based on the above principles.