Note: Today, 2 July 2015, Constance Bommelaer delivered the following remarks to the United Nations "Informal Interactive Stakeholder Consultation", convened by the President of the UN General Assembly, as part of the planning for the 10-year review of the World Summit on the Information Society (WSIS). For more information about the WSIS+10 process, please see Constance's earlier blog post as well as our WSIS page. A video recording of her remarks is included at the end of this post.
It is my honor to be here with you today, to share the perspective of the Internet Society on progress made in the implementation of the WSIS outcomes.
The organization that I represent, the Internet Society, finds its origins in the technical community that first began collaborating over 40 years ago and which brought the Internet. As a global organization of 71,000 members and 108 chapters in 92 countries, our organization has been engaged in all stages of the WSIS.
We've come a long way since the Tunis Agenda recognized the respective roles and responsibilities of governments, civil society, business and the technical community in shaping the evolution of the Internet. In just the past 10 years, we have made impressive progress in implementing the goals laid out in Geneva, and then Tunis.
First of all, a more cohesive Internet community has emerged. I remember 15 years ago when working for the French government, sitting on the other side of the fence – we had little knowledge of the community of pioneers that brought the Internet. Today bridges have been built between all groups, learning from each other.
Concretely, the number of policymakers participating to technical meetings where Internet standards are developed – such as the IETF – is increasing. But also, inter-governmental organizations are progressively opening the door to stakeholders.
Concretely, the elaboration and endorsement of the ITU and UNESCO WSIS review outcomes, by all stakeholders, in 2013 and 2014, have become milestones in the collective memory of the Internet community.
Concretely, public-private partnerships for infrastructure development and capacity building have helped bring more than 3 billion people online.
But access is not the ultimate goal, it is only a means to an end: sustainable development and human empowerment.
And here are the ultimate challenges: We need the Internet to be an enabler for Human Rights. We need more leading women in the technology field, for the Internet to contribute to gender equality. We need innovation to transcend frontiers, for the next Facebook to come from a developing country. We need a secure Internet that users can trust.
There are many examples of the benefits of collaborative governance. I'll share just one: the Internet Governance Forum (IGF), this unique platform that allows all stakeholders to come together to share insights. This year, participants are tackling important challenges such as developing Policy Options for Connecting the Next Billion, or Best Practices to counter abuse against women online. The multiplication of IGF-type initiatives, on all continents, demonstrates the viability of the model. This is why, we strongly call for the renewal of its mandate beyond 2015 and welcome Mexico's generous offer to host IGF 2016.
Today, the principle of collaborative governance appears to be more relevant than ever. The world's increasing reliance on ICTs commands to broaden the partnership to enroll ICT sector foundations, development agencies, SMEs from emerging regions and many others who have a critical stake in the Internet's development.
Of course, collaborative governance, with all stakeholders at the table, is not always easy; it takes timeand hard discussions. But the results are also often more robust, efficient and legitimate as a consequence.
In the same spirit, we believe that preparations for the WSIS+10 High-Level event in December, should be as inclusive as possible. In this regard, I would like to thank again the President of the UN General Assembly and the two co-facilitators, as well as all delegates, for having us here today.
Note: Thank you to Joly MacFie of the Internet Society New York Chapter for capturing the video segment.


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Home / Companies / News / IL&FS case: Bombay HC dismisses MCA plea to ban Deloitte and KPMG for five years
IL&FS case: Bombay HC dismisses MCA plea to ban Deloitte and KPMG for five years
(Photo: Reuters)
2 min read . Updated: 21 Apr 2020, 05:14 PM IST PTI
Bombay High Court on Tuesday quashed all prosecution against the two firms that had been pending before NCLT and a special court in the city, over alleged financial irregularities
Mumbai: Granting relief to audit firms BSR and Associates, and Deloitte Haskins and Sells, both former auditors of IL&FS Financial Services, the Bombay High Court on Tuesday quashed all prosecution against the two firms that had been pending before the National Company Law Tribunal and a special court in the city, over alleged financial irregularities.
BSR, part of KPMG India, and Deloitte had moved HC last year challenging the validity of the Union government's plea before the NCLT seeking their removal as auditors of IL&FS.
Such removal under section 140 (5) of the Companies Act would also bring along a ban on the audit firms for five years.
The Union Ministry of Corporate Affairs had sought such removal and also initiated criminal proceedings against the firms for their role in alleged financial irregularities at the now bankrupt IL&FS Group.
In August last year, the NCLT had found merit in the Union government's pea, and subsequently approved the proposed removal of both firms.
The firms however, approached HC arguing that they had already resigned as auditors of IL&FS much before the Ministry sought their removal.
They had, therefore, challenged the constitutional validity of section 140 (5) of the Act.
The section deals with removal and resignation of auditors and imposes a five year ban on an auditing firm that is proven to have "acted in a fraudulent manner", or to have "abetted or colluded in any fraud".
On Tuesday, a bench of Chief Justice BP Dharmadhikari and Justice NR Borkar quashed the prosecution of both firms before the NCLT.
While the bench upheld the constitutional validity of section 140 (5), it held that the provisions of the section did not apply to former auditors who had resigned.
The bench also quashed a criminal complaint filed against the two firms by Serious Fraud Investigation Office (SFIO), a Central agency, in the above case of financial irregularities.
The bench said the SFIO complaint filed before a special court was "bad in law".
In June last year, the Ministry of Corporate Affairs had moved the NCLT against BSR and some of the then external auditors of IL&FS alleging professional misconduct.
At the time, it had also directed the SFIO to initiate probe and disciplinary action against such audit firms.
The SFIO had subsequently claimed BSR and some other audit firms had acted in breach of auditing standards and that they had failed to detect financial inconsistencies at IL&FS.
Advocate Sujay Kantawala, who was a part of the legal team for BSR, said on Tuesday, the Union government sought a stay for eight weeks on HC's order quashing such prosecution.
While the counsels for BSR and Deloitte opposed the government's request, HC granted such stay on its own order.
Kantwala stated that HC granted such stay saying that denying time to the government for an appeal would not be "fair in todays troubled times".
He added that Tuesday's order quashing prosecution would have major implications on the corporate world and would act as a precedent in preventing "harassment of innocent firms".

redpajama_set_name: RedPajamaCommonCrawl


You never know what a coin might amount to.
Take a closer look before you dump that handful of pennies and nickels into the tip jar — you don't need to find a Revolutionary War-era coin to make a fortune from your change.
They're harder to find each year, but there are several valuable coins floating around that aren't all that old. They're often valuable for vastly different reasons — like the World War II-era coins minted from atypical metals, or double-printed pennies — but each one is easy to miss if you're not paying attention.
Check out these eight coins that are worth a lot more than their intended value.
Find an average Wisconsin state quarter from 2004, and that will get you one-fourth of a bag of chips. Find one with either the high or low leaf error, and you can get a whole lot more.
The 50 State Quarters series ran from 1999 until 2008, with special designs representing each state. Wisconsin's quarter came out in 2004; the reverse design features a cow, a wheel of cheese and a partially husked ear of corn lurking in the back.
It would be too easy to make a corny joke about this coin. Too cheesy?
However, some the coins have an extra line below the front left leaf, which looks like another leaf entirely. There are two varieties you should be looking out for: the high leaf and low leaf.
This penny has a double-printed obverse (heads side) that makes the "LIBERTY" and "IN GOD WE TRUST" look blurry. The error has happened before, in 1969 and 1972, and those versions of the coins are much more valuable.
During World War II, the United States needed to save as much nickel as possible for military uses. Consequently, it started minting nickels made of 35% silver. Melting down pennies and nickels is a federal offense, but the coin might still fetch you enough for a decent lunch, if it's in good condition.
Pennies were made from steel in 1943 only.
Pennies were made from steel during wartime, for the same reasons nickels were made partially from silver — steel pennies helped preserve copper for World War II. However, the switch only lasted one year.
Easy to notice, but hard to find.
In 1948, the U.S. mint began circulating half-dollar coins with images of Ben Franklin and an eagle — which is funny, considering Franklin opposed the bald eagle's nomination as the nation's bird, in favor of a wild turkey.
Franklin's portrait on the coin was replaced by John F. Kennedy in 1964, following the president's 1963 assassination.
Between 1932 and 1964, quarters were 90% silver and 10% copper. These silver quarters look like any pre-state quarter 25-cent piece, but are worth a lot more if they're in the right condition.
Remember: Always clean your machine.
While it might seem like a mint employee's rogue political statement, these coins are actually just the result of grease preventing a clean pressing.
These Washington dollars are missing key inscriptions.
In 2007, the U.S. Mint began printing a series of dollar coins featuring presidents. Many of the early coins, especially those with George Washington, have errant or missing lettering along the edge of the coin.


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"TW3" in Criminology
February 1, 2020 22:08 / Leave a comment
In the 1960s, or so I am told, there was a very popular weekly television programme called That Was The Week That Was, informally known as TW3. This satirical programme reflected on events of the week that had just gone, through commentary, comedy and music. Although the programme ended before I was born, it's always struck me as a nice way to end the week and I plan to (very loosely) follow that idea here.
This week was particularly hectic in Criminology, here are just some of the highlights. On Monday, I was interviewed by a college student for their journalism project, a rather surreal experience, after all, 'Who cares what I think?'
On Tuesday, @manosdaskalou and I, together with a group of enthusiastic third years, visited the Supreme Court in London. This trip enabled a discussion which sought to unpack the issue of diversity (or rather the lack of) within justice. Students and staff discussed a variety of ideas to work out why so many white men are at the heart of justice decisions. A difficult challenge at the best of times but given a new and urgent impetus when sat in a courtroom. It is difficult, if not impossible, to remain objective and impartial when confronted with the evidence of 12 Supreme Judges, only two of which are women, and all are white. Arguments around the supposed representativeness of justice, falter when the evidence is so very stark. Furthermore, with the educational information provided by our tour guide, it becomes obvious that there are many barriers for those who are neither white nor male to make their way through the legal ranks.
Wednesday saw the culmination of Beyond Justice, a module focused on social justice and taught entirely in prison. As in previous years, we have a small ceremony with certificate presentation for all students. This involves quite a cast, including various dignitaries, as well as all the students and their friends and family. This is always a bittersweet event, part celebration, part goodbye. Over the months, the prison classroom leaves its oppressive carceral environment behind, instead providing an intense and profound tight-knit learning community. No doubt @manosdaskalou and I will return to the prison, but that tight-knit community has now dissipated in time and space.
On Thursday, a similarly bitter-sweet experience was my last focused session this year on CRI3003 Violence: From Domestic to Institutional. Since October, the class has discussed many different topics relating to institutional violence focused on different cases including the deaths of Victoria Climbié, Blair Peach, Jean Charles de Menezes, as well as the horror of Grenfell. We have welcomed guest speakers from social work, policing and the fire service. Discussions have been mature, informed and extremely sensitive and again a real sense of a learning community has ensued. It's also been my first experience of teaching an all-female cohort which has informed the discussion in a variety of meaningful ways. Although I haven't abandoned the class, colleagues @manosdaskalou and @jesjames50 will take the reins for a while and focus on exploring interpersonal violence. I'll be back before the end of the academic year so we can reflect together on our understanding of the complexity of violence.
Finally, Friday saw the second ever #BigCriminologyQuiz and the first of the new decade. At the end of the first one, the participants requested that the next one be based on criminology and music. Challenge completed with help from @manosdaskalou, @treventoursu, @svr2727, @5teveh and @jesjames50. This week's teams have requested a film/tv theme for the next quiz so we'll definitely have our work cut out! But it's amazing to see how much criminological knowledge can be shared, even when you're eating snacks and laughing. [i]
So, what can I take from my criminological week:
Some of the best criminological discussions happen when people are relaxed
Getting out of the classroom enables and empowers different voices to be heard
Getting out of the classroom allows people to focus on each and share their knowledge, recognising that
A classroom is not four walls within a university, but can be anywhere (a coach, a courtroom a prison, or even the pub!)
A new environment and a new experience opens the way for discord and dissent, always a necessity for profound discussion within Criminology
When you open your eyes and your mind you start to see the world very differently
It is possible (if you try very hard) to ignore the reality of Friday 31 January 23:00 ☹
It is possible to be an academic, tour guide, mistress of ceremonies and quiz mistress, all in the same week!
Here's looking forward to next week….not least Thursday's Changemaker Awards where I seem to have scored a nomination with my #PartnerinCriminology @manosdaskalou.
[i] The first quiz was won by a team made up of 1st and 2nd years. This week's quiz was won by a group of third years. The next promises to be a battle royale 😊 These quizzes have exposed, just how competitive criminologists can be….
20 years of Criminology
It was at the start of a new millennium that people worried about what the so-called millennium will do to our lives. The fear was that the bug will usher a new dark age where technology will be lost. Whilst the impending Armageddon never happened, the University College Northampton, as the University of Northampton was called then, was preparing to welcome the first cohort of Criminology students.
The first cohort of students joined us in September 2000 and since then 20 years of cohorts have joined since. During these years we have seen the rise of University fees, the expansion of the internet and google search and of course the emergence of social media. The original award was focused on sociolegal aspects, predominantly the sociology of deviance, whilst in the years since the changes demonstrate the departmental and the disciplinary changes that have happened.
Early on, as criminology was beginning to find its voice institutionally, the team developed two rules that have since defined the focus of the discipline. The first is that the subject will be taught in a multi-disciplinary approach, widely inclusive of all the main disciplines involved in the study of crime; so alongside sociology, you will find psychology, law, history, philosophy to name but a few. The impetus was to present these disciplines on an equal footing and providing opportunity to those joining the course, to discover their own voice in criminology. The second rule was to give the students the opportunity to explore contentious topics and draw their own perspective. Since the first year of running it, these rules have become the bedrock of UoN Criminology.
The course since the early years has grown and gone through all those developmental stages, childhood, adolescence and now eventually we have reached adulthood. During these stages, we managed to forge a distinctiveness of what criminology looks like; introducing for example a research placement to allow the students to explore the theory in practice. In later years we created courses that reflect Criminology in the 21st Century always relating to the big questions and forever arming learners with the skills to ask the impossible questions.
Through all these years students join with an interest in studying crime and by the time they leave us, to move onto the next chapter of their lives, they have become hard core criminologists. This is always something that we consider one of the course's greatest contribution to the local community.
In an ordinary day, like any other day in the local court one may see an usher, next to a probation officer, next to a police officer, next to a drugs rehabilitation officer, all of them our graduates making up the local criminal justice system. A demonstration of the reach and the importance of the university as an institution and the services it provides to the local community. More recently we developed a module that we teach in prison comprised by university and prison students. This is a clear sign of the maturity and the journey we have done so far…
As the 21st century entered, twin towers fell, bus and tube trains exploded, consequent wars were made, riots in the capital, the banking crisis, the austerity, bridge attacks, Brexit, extinction rebellion, buildings burning, planes coming down, forest fires and #metoo, and we just barely cover 20 years. These and many more events keep criminological discourse relevant, increase the profile of the subject and most importantly further the conversation we are having in our society as to where we are heading.
As I raise my glass to salute the first 20 years of Criminology at the University of Northampton, I am confident that the next 20 years will be even more exciting. For those who have been with us so far a massive thank you, for those to come we are looking forward to discussing some of the many issues with you. We are passionate about criminology and we want you to infect you with our passion.
As they say in prison, the first 20 years are difficult the rest you just glide through…
Beyond education…
In a previous blog I wrote about the importance of going through HE as a life changing process. The hard skills of learning about a discipline and the issues, debates around it, is merely part of the fun. The soft skills of being a member of a community of people educated at tertiary level, in some cases, outweigh the others, especially for those who never in their lives expected to walk through the gates of HE. For many who do not have a history in higher education it is an incredibly difficult act, to move from differentiating between meritocracy to elitism, especially for those who have been disadvantaged all their lives; they find the academic community exclusive, arrogant, class-minded and most damning, not for them.
The history of higher education in the UK is very interesting and connected with social aspiration and mobility. Our University, along with dozens of others, is marked as a new institution that was created in a moment of realisation that universities should not be exclusive and for the few. In conversation with our students I mentioned how as a department and an institution we train the people who move the wheels of everyday life. The nurses in A&E, the teachers in primary education, the probation officers, the paramedics, the police officers and all those professionals who matter, because they facilitate social functioning. It is rather important that all our students understand that our mission statement will become their employment identity and their professional conduct will be reflective of our ability to move our society forward, engaging with difficult issues, challenging stereotypes and promoting an ethos of tolerance, so important in a society where violence is rising.
This week we had our second celebration of our prison taught module. For the last time the "class of 2019" got together and as I saw them, I was reminded of the very first session we had. In that session we explored if criminology is a science or an art. The discussion was long, and quite unexpected. In the first instance, the majority seem to agree that it is a social science, but somehow the more questions were asked, the more difficult it became to give an answer. What fascinates me in such a class, is the expectation that there is a clear fixed answer that should settle any debate. It is little by little that the realisation dawns; there are different answers and instead of worrying about information, we become concerned with knowledge. This is the long and sometimes rocky road of higher education.
Our cohort completed their studies demonstrating a level of dedication and interest for education that was inspiring. For half of them this is their first step into the world of HE whilst the other half are close to heading out of the University's door. It is a great accomplishment for both groups but for the first who may feel they have a long way to go, I will offer the words of a greater teacher and an inspiring voice in my psyche, Cavafy's 'The First Step'
Even this first step
is a long way above the ordinary world.
To stand on this step
you must be in your own right
a member of the city of ideas.
And it is a hard, unusual thing
to be enrolled as a citizen of that city.
Its councils are full of Legislators
no charlatan can fool.
To have come this far is no small achievement:
what you have done already is a glorious thing
Thank you for entering this world. You earn it and from now on do not let others doubt you. You can do it if you want to. Education is there for those who desire it.
C.P. Cavafy, (1992) Collected Poems, Translated by Edmund Keeley and Philip Sherrard, Edited by George Savidis, Revised Edition, Princeton University Press, Princeton.
Out early on good behaviour
February 18, 2018 11:38 / 3 Comments on Out early on good behaviour
Dr Stephen O'Brien is the Dean for the Faculty of Health and Society at the University of Northampton
The other week I had the opportunity to visit one of our local prisons with academic colleagues from our Criminology team within the Faculty of Health and Society at the University of Northampton. The prison in question is a category C closed facility and it was my very first visit to such an institution. The context for my visit was to follow up and review the work completed by students, prisoners and staff in the joint delivery of an academic module which forms part of our undergraduate Criminology course. The module entitled "Beyond Justice" explores key philosophical, social and political issues associated with the concept of justice and the journeys that individuals travel within the criminal justice system in the UK. This innovative approach to collaborative education involving the delivery of the module to students of the university and prisoners was long in its gestation. The module itself had been delivered over several weeks in the Autumn term of 2017. What was very apparent from the start of this planned visit was how successful the venture had been; ground-breaking in many respects with clear impact for all involved. Indeed, it has been way more successful than anyone could have imagined when the staff embarked on the planning process. The project is an excellent example of the University's Changemaker agenda with its emphasis upon mobilising University assets to address real life social challenges.
My particular visit was more than a simple review and celebration of good Changemaker work well done. It was to advance the working relationship with the Prison in the signing of a memorandum of understanding which outlined further work that would be developed on the back of this successful project. This will include; future classes for university/prison students, academic advancement of prison staff, the use of prison staff expertise in the university, research and consultancy. My visit was therefore a fruitful one. In the run up to the visit I had to endure all the usual jokes one would expect. Would they let me in? More importantly would they let me out? Clearly there was an absolute need to be on my best behaviour, keep my nose clean and certainly mind my Ps and Qs especially if I was to be "released". Despite this ribbing I approached the visit with anticipation and an open mind. To be honest I was unsure what to expect. My only previous conceptual experience of this aspect of the criminal justice system was many years ago when I was working as a mental health nurse in a traditional NHS psychiatric hospital. This was in the early 1980s with its throwback to a period of mental health care based on primarily protecting the public from the mad in society. Whilst there had been some shifts in thinking there was still a strong element of the "custodial" in the treatment and care regimen adopted. Public safety was paramount and many patients had been in the hospital for tens of years with an ensuing sense of incarceration and institutionalisation. These concepts are well described in the seminal work of Barton (1976) who described the consequences of long term incarceration as a form of neurosis; a psychiatric disorder in which a person confined for a long period in a hospital, mental hospital, or prison assumes a dependent role, passively accepts the paternalist approach of those in charge, and develops symptoms and signs associated with restricted horizons, such as increasing passivity and lack of motivation. To be fair mental health services had been transitioning slowly since the 1960s with a move from the custodial to the therapeutic. The associated strategy of rehabilitation and the decant of patients from what was an old asylum to a more community based services were well underway. In many respects the speed of this change was proving problematic with community support struggling to catch up and cope with the numbers moving out of the institutions.
My only other personal experience was when I spent a night in the cells of my local police station following an "incident" in the town centre. This was a case of being in the wrong place at the wrong time. (I know everyone says that, but in this case it is a genuine explanation). However, this did give me a sense of what being locked up felt like albeit for a few hours one night. When being shown one of the single occupancy cells at the prison those feelings came flooding back. However, the thought of being there for several months or years would have considerably more impact. The accommodation was in fact worse than I had imagined. I reflected on this afterwards in light of what can sometimes be the prevailing narrative that prison is in some way a cushy number. The roof over your head, access to a TV and a warm bed along with three square meals a day is often dressed up as a comfortable daily life. The reality of incarceration is far from this view. A few days later I watched Trevor MacDonald report from Indiana State Prison in the USA as part of ITV's crime and punishment season. In comparison to that you could argue the UK version is comfortable but I have no doubt either experience would be, for me, an extreme challenge.
There were further echoes of my mental health experiences as I was shown the rehabilitation facilities with opportunities for prisoners to experience real world work as part of their transition back into society. I was impressed with the community engagement and the foresight of some big high street companies to get involved in retraining and education. This aspect of the visit was much better than I imagined and there is evidence that this is working. It is a strict rehabilitation regime where any poor behaviour or departure from the planned activity results in failure and loss of the opportunity. This did make me reflect on our own project and its contribution to prisoner rehabilitation. In education, success and failure are norms and the process engenders much more tolerance of what we see as mistakes along the way. The great thing about this project is the achievement of all in terms of both the learning process and outcome. Those outcomes will be celebrated later this month when we return to the prison for a special celebration event. That will be the moment not only to celebrate success but to look to the future and the further work the University and the Prison can do together. On that occasion as on this I do expect to be released early for good behaviour.
Barton, R., (1976) Institutional Neurosis: 3rd edition, Butterworth-Heinemann, London.
(The Absence of) Technology in the Classroom
Following on from Manos' 'Reflections from a pilot' I shall continue in a similar vein. The pilot has formed part of our academic thoughts and discussions for some months and now it has finished we are in reflective mode. Much of what we have experienced throughout the pilot was striking and will give us food for thought for some time to come. For this entry, I am going to focus on an aspect that I had not really considered, or at least, not very much beyond the prosaic.
We knew before the pilot that prison and technology do not make comfortable bedfellows. Whilst on the outside, technology permeates virtually every aspect of our waking lives, the same cannot be said for those incarcerated. From the moment you step inside the prison gate, signs remind you of what you cannot bring into the carceral environment; top of the list are mobile phones, computers, USBs and recording devices. This meant that in very basic terms there could be no powerpoint, video clips or recordings of lectures. It also meant that we could not rely upon the internal learners having a shared knowledge of current affairs beyond that which was available in newspapers or on radio or television. All the above could be perceived as inadequacies and deprivations, however, we found a number of positives side-effects of these supposed failings.
In the university classroom, technology is commonplace; smartboards, computer lecterns, laptops, tablets and smartphones. All of this technology can enable learning on many levels, but can also provide irresistible diversion from the task at hand. Whilst the intention may be educational; for example taking notes on a laptop, the temptation to drift into social media, email and so can prove to be seductive. Conversely, the prison classroom contains little to attract attention, beyond some posters on the wall and the view from the windows which offered nothing of real interest. From the outset, and throughout the entire pilot, it appeared that the absence of technology heightened concentration. This was observable through increased eye-contact, body language and engagement with both academic discussions and general conversations across all learners. Furthermore, the absence of technological distraction impelled students to self-reliance in way (for the external learners, at least) they were largely unused to and generally unprepared for.
It should be acknowledged that this increase in engagement may also have been impacted by the strangeness of the prison environment (for the external students) and the anxiety involved in meeting new people (for all students). Nevertheless, engagement did not seem to decrease despite increasing familiarity with both the surroundings and participants.
All of the above is not to say that technology has no place in education; the ease of access to educational materials and the ability to engage in academic discourse globally demonstrate its power. What I would suggest it does is offer us all an opportunity to reflect upon our own use (and dare I say, reliance) upon technology as a replacement for deep learning.
Reflections from a Pilot
March 3, 2017 18:14 / 5 Comments on Reflections from a Pilot
Firstly, I would like to apologise for the use of the first person. I have made an entire career of telling my students to use the third person. However, writing a blog is generally informal and a bit more personal.
Throughout my years in academia there are a number of things I continue to find incredibly edifying; transferring research interests into teaching is one of them, even better when that is done outside of the traditional educational environment. The idea of education in prison is definitely not new, with roots in the old reformers (notably in the UK; Elizabeth Fry), with a clear focus on combating illiteracy. This was a product of penal policy that reflected a different social reality. In the 21st century, we have to re-imagine penal policy, alongside education, which can cater for the changed nature of our world.
Our recent pilot, was designed to explore some new approaches to education in both the prison and the university* . The idea was to bring university students and prisoners together and teach them the same topics encouraging them to engage with each other in discussions. This was envisaged as a process whereby all participants would be equal learners; leaving all other identities behind. The main thinking behind the approach taken was predicated on universal notions; the respect for humanity and the opportunity to express oneself uninhibited among equals. With this in mind, teaching in prisons should not be any different to teaching at University, provided that all learners feel safe and they are ready to engage. In the planning stages, my concerns were primarily on the way equality could be maintained. In addition, the levels of engagement and the material covered were also issues that created some trepidation. The knowledge that this pilot would be the blueprint for the design of a new level 6 module made the undertaking even more exciting.
The pilot involved 9 hours of teaching in prison with additional sessions before and after in order to familiarise all learners with each other, the environment and the learning process. Through the three teaching sessions, we all observed the transformative effect of education. From early suspicion and reluctance among learners to the confident elaboration of complex arguments. It took one simple statement to get the learning process going. This is when the pilot became a new lens through which I saw education, in prison with all my students, as a thriving learning environment.
*Some years ago I told a prison governor of a young offenders' institution that the commonalities of our institutions were greater than the differences. Before, you protest at the analogy, consider the points of reference: the age group in a young offenders is 18-21, they are living away from home, have to learn to live with others and are trying, in the process, to better themselves. The obvious and significant difference is incarceration; the loss of freedom and the criminal identity that sticks onto them like the mark of Cain.


Thank you for supporting TMLS. We are excited to see you at the banquet on April 5th.
Join us to celebrate the year at the 2019 Thurgood Marshall Legal Society Annual Banquet! The banquet will be held at the AT&T Conference Center on April 5, 2019. Our keynote speaker is Justice Adrienne Nelson of the Oregon Supreme Court and member of the UT Law Class of 1993.
Tickets include a three-course dinner (your choice of beef tenderloin or salmon entree) as well as access to our open bar. Cocktail hour begins at 6 pm and dinner begins at 7 pm.


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Bertrand St-Arnaud at the National Order of Quebec ceremony in June 2013.
Bertrand St-Arnaud (born 13 September 1958) was a politician in the Canadian province of Quebec, who was elected to represent the riding of Chambly in the National Assembly of Quebec in the 2008 provincial election. He was defeated in the 2014 Quebec general election by Coalition Avenir Quebec candidate Jean-Francois Roberge. He is a member of the Parti Québécois.
St-Arnaud first obtained a license degree in law from the Université de Montréal and later added a master's degree in political sciences from the Université Laval. He also made studies in Europe with a degree from the University of Lund in Sweden.
He practised law from 1987 to 2000 and in 2005. He was also the press secretary for the Cabinet of the Premier of Quebec in 1985 and would work for the intergovernmental affairs department as well as for the Library of the National Assembly of Quebec and the Cabinet director for the Minister of International Relations from 2000 to 2003.
This article about a Member of the National Assembly of Quebec from the Parti Québécois is a stub. You can help Wikipedia by expanding it.
This page was last edited on 20 February 2017, at 05:19 (UTC).


text:
The Case for Mentoring as a Pathway to Promote Student Interest in STEM
Kathrin Schilling, Ph.D.
Associate Research Scientist Geochemistry, Columbia University
Emily Bohonos
Science Teacher, Elijah Stroud Middle School, Brooklyn, N.Y.
By Adrienne Umali, M.S.B.S., M.S.Ed., NYAS Staff
Regardless of the field you're in, it is likely that if you looked back at your career path, you could identify at least one person who has helped guide you to where you are today. Whether this person was a teacher, family member, coach, or supervisor, mentorship has always been an incredibly important part of not only exposing individuals to new ideas and opportunities, but in encouraging them to their full potential.
When the 2018 Program for International Student Assessment (PISA) scores in math and science showed the United States ranked 13th, behind several Asian and European nations, it was once again demonstrated that the U.S. needs to raise its investment in science, technology, engineering and math (STEM) to remain globally competitive. These fields are core to almost every industry, but a 2017 poll found that only 38 percent of middle and high school teachers see their students as being "naturally interested" in STEM.
Most students rarely have the opportunity to meet a working scientist, so developing programs that expose students to science professionals is proving to be a critical way to cultivate a love of STEM in the next generation. It's what brought Emily Bohonos, a middle school science teacher in Brooklyn, N.Y., to join the New York Academy of Science's Scientist-in-Residence (SiR) program.
SiR brings together scientists and NYC middle and high school teachers for a year-long collaboration that aims to jumpstart student interest in STEM through real-world projects and the opportunity to "humanize" a scientist.
Bohonos along with her partner Kathrin Schilling, Ph.D., an associate research scientist of Geochemistry from Columbia University, have spent the last few months creating a project focused on something that most students already have an interest in: food. Building off of Schillings' expertise — she has degrees in geology, soil science and microbiology — the two are challenging students to research diet variations around the world and create experiments that explore the effects of different conditions on plant growth. Their project pushes students to practice thinking critically, creatively, and globally.
Want to Become a Mentor?
...the U.S. needs to raise its investment in science, technology, engineering and math (STEM) to remain globally competitive.
Schilling loves sharing her passion for science with students and is thrilled when she sees them thinking outside of the box. The benefits of programs like this, however, are not limited to added content expertise — they also provide tangible examples of people who have found success in STEM.
In fact, Schilling notes that many of the questions she gets are far removed from her area of expertise. With the title of "Dr.", the students see her as an expert in all science-related fields, a factor she recognizes may be one of the reasons that science can seem inaccessible to some students. "It feels like you have to be a genius in every field [to be a scientist] and we are definitely not." Schilling admits that she herself wasn't a great student until she was able to start specializing in her post-secondary education.
To this end, Bohonos creates time during each lesson to allow students to interact one-on-one with their Resident Scientist and get to know her on a personal level. In this way, students can hopefully begin to see STEM as a career path not just limited to those who have already been labeled as "smart". Fostering this type of environment is particularly critical at schools like Bohonos', where students of color make up almost 90 percent of the student body, a group which still remains significantly underrepresented in the number of individuals receiving undergraduate STEM degrees.
Mentoring takes time and it comes with its own challenges, but despite this, Schilling remains optimistic about her role in fostering a positive outlook regarding STEM. "Even if I can change the mind of just a few [students] it's more than before the program.


Practice these Reading & Writing Files under Java Programming walk-in interview Questions/ examination questions with best tricks and short cuts with solution. Student (candidate) who want to crack the walk in interview, competitive exams and want to find short cuts and tricks to solve questions on Reading & Writing Files for following purpose.
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1. Which of these exception is thrown by close() and read() methods?
Both close() and read() method throw IOException.
2. Which of these exception is thrown in cases when the file specified for writing it not found?
In cases when the file specified is not found, then FileNotFoundException is thrown by java run-time system, earlier versions of java used to throw IOException but after Java 2.0 they throw FileNotFoundException.
3. Which of these methods are used to read in from file?
Each time read() is called, it reads a single byte from the file and returns the byte as an integer value. read() returns -1 when the end of the file is encountered.
4. Which of these class contains the methods used to write in a file?
5. Which of these methods is used to write() into a file?
6. Which of these values is returned by read() method is end of file (EOF) is encountered?


Plans for an auto dealership and mini-storage facility at C-470 and West Alameda Parkway near Dinosaur Ridge are meeting with significant opposition.
More than 10,000 people have signed an online petition objecting to a proposal to rezone properties northwest and southeast of the intersection. And an informal community group has been formed to challenge the proposed development in the scenic Rooney Valley.


text:
PCMA's Convening Leaders Annual Meeting Breaks Attendance Records in Chicago
Rachel Wimberly
It may have been cold in Chicago in the second week of January, but that didn't stop a record amount of attendees from coming to the Windy City for the Professional Convention Management Association's Convening Leaders annual meeting.
From Jan. 11-14, there were 4,128 convention managers and suppliers who packed McCormick Place West, taking part in educational sessions, keynotes and a bevy of networking and charity events throughout the city.
The 2015 event topped the 2014 record-breaking one in Boston, which drew nearly 4,000 attendees.
"This year's program was designed to challenge the most respected leaders in the industry to embrace the spirit of innovation and risk-taking," said Deborah Sexton, president and CEO, PCMA.
She added, "Our audience showed that, without a doubt, they are ready to accept that challenge and elevate the next generation of meetings, conferences and events."
There were wide range of keynotes, including long-distance swimmer Diana Nyad talking about what it took to swim from the U.S. to Cuba, to Dan Pallotta, founder and chief humanity officer for Advertising for Humanity, advising the audience to rethink the way they give to charities.
Besides the high-caliber keynotes, there also were education sessions that spanned everything from the idea of "Un-Marketing: Stop Marketing. Start Engaging" to "Be Proactive Not Reactive to Global Meeting Trends in 2015".
"We aimed to give our attendees more than education credits," Kelly Peacy, senior vice president, Education and Events, PCMA, said.
She added, "The roadmap served as a path from inspiring big-picture general session concepts to specific intimate courses with personal and practical takeaways. When our attendees return home, we want them to be able to take what they learned at Convening Leaders and immediately adapt it to their own organizations."
There also were some other learning opportunities offered outside of the education tracks, including the PCMA Learning Lounge that featured, among other activities, Q&A sessions with keynotes and thought leaders and TechCentral at which attendees could learn about new technology.
Beyond the more than 4,000 attendees who made it to the face-to-face event, there also were another 1,000-plus form 33 countries who took part in the PCMA Convening Leaders Hybrid Event.
"We made no little plans with our hybrid meeting," Mary Reynolds Kane, senior director, experience marketing, PCMA, says. "This year, we streamed 13 sessions over three days for a full taste of what Convening Leaders offers."
Reynolds Kane and the PCMA hybrid meeting team infused a virtual networking element to each day of the program, too, with an online happy hour at the end of each day that allowed virtual participants to stay logged on and continue their chat discussions.
PCMA has a major focus on giving back, so there also were plenty of chances to do just that at the annual meeting as well.
Just a few of the events included more than 1,200 attendees taking part in the 22nd year of PCMA's Party with a Purpose that benefitted Future Founders, Network for the Needy® & PCMA Education Foundation and PCMA's Hospitality Helping Hands Program that drew 120 individuals to help out at the Greater Chicago Food Depository.
Next year's PCMA Convening Leaders already is in the works, set for Jan. 10-13 in Vancouver, B.C.
PCMA's Convening Leaders Breaks Attendance Records in Nashville
The 62nd edition of Professional Convention Management Association's Convening Leaders, which took place Jan. 7-10 at Music City Center in Nashville, Tenn., welcomed 4,457…
PCMA's Convening Leaders Kicks Off Jan. 11-14 in Chicago with Dynamic Schedule of Events
Several thousand convention managers and suppliers to the industry will be heading to the Windy City's McCormick Place Jan. 11-14 to take part in the Professional Convention…
IAEE's Expo! Expo! Annual Meeting & Exhibitions Breaks Attendance, Showfloor Records in Baltimore
"Charm City" lived up to its name, and then some, when more than 2,500 attendees flocked to Baltimore, Md., last week for the International Association of Exhibitions' Expo!…
ASAE's Technology Conference & Expo Breaks Attendance Records
When 1,292 attendees came to the 10th Technology Conference & Expo, held by the American Society of Association Executives Dec. 14-16 at the Gaylord National Resort…
Hong Kong Convention and Exhibition Centre Breaks Attendance Record with 6.4 Million Annual Visitors
In fiscal year 2014-2015 (July 2014 to June 2015), a total of 1,113 events were held at the Hong Kong Convention and Exhibition Centre, including 111 exhibitions and 38…


text:
\section{Introduction}\label{sec:intro}
In this work we follow up on a recent preprint~\cite{kim2020efficient}.
The main motivation for the questions in~\cite{kim2020efficient} is to understand
 how much kinship information can be learned from DNA.
 More concretely~\cite{kim2020efficient} studies the inference problem of recovering ancestral kinship relationships of a population of \textit{extant} (present-day) individuals using only their genetic data for a mathematical generative model of pedigrees and DNA sequences on them. The goal is to use this extant genetic data to recover the \textit{pedigree} of the extant population, under our model.

To study this question, the paper~\cite{kim2020efficient} introduces
an idealized model for generating pedigree data.
The population model they use is a standard random mating model, but the genetic inheritance model assumes that inheritance blocks are of fixed length.
This removes the additional difficulty of ``phasing" which allows for a rigorous analysis.

The main contribution of~\cite{kim2020efficient} is to show that under certain conditions, the algorithm proposed in the paper, named {\sc Rec-Gen}, approximately recovers the true, unknown pedigree as well as its genetic content.

In this paper we take the theoretical analysis in~\cite{kim2020efficient} and study to what extent can it be applied in more realistic settings.

There is a tension between different aspects of the assumptions in~\cite{kim2020efficient}.
On one hand, they require a very big pedigree to avoid inbreeding. On
the other, the algorithm Rec-Gen has cubic running time. While in the
limit as the pedigree size goes to infinity, this tension disappears,
we find that applying the algorithm on simulated data results either
in poor accuracy or an infeasible running time.

Our main contributions in this paper are:
\begin{itemize}
\item
As a first step, we improve the running time of the algorithm to essentially quadratic for data generated by the model.
\item
We then observe that even the faster version of the algorithm does not do well in any simulations in recovering the pedigree beyond 2 generations.
\item
We claim that this is due to the inbreeding present in any setting where the algorithm can be run, even on simulated data.
\item
To support the claim we show that a main step of the algorithm, called ancestral reconstruction, performs accurately in a setting with no inbreeding but performs poorly in random mating populations.
\item
Finally, to overcome the poor behavior of REC-GEN we introduce a Belief-Propagation based heuristic that accounts for the inbreeding and performs much better in our simulations.
\end{itemize}

\section{Model Description}

We model populations as in~\cite{kim2020efficient}. Here, we briefly
restate the definition of a \emph{coupled pedigree}, the structure
manipulated by the \textsc{Rec-Gen} algorithm (definition 3.4
in~\cite{kim2020efficient}) and introduce notation relevant to the
description of our modified algorithm.

A $(N,B,T,\xi)$-\emph{uncoupled pedigree} $\mathcal{U}$ is a directed acyclic
graph $(V, E)$ in which vertices $v \in V$ represent individuals and
edges $e = (u, v) \in E$ represent the relationship that $u$ is a
\emph{parent} of $v$. The set of vertices $V$ can be partitioned into
$T + 1$ subsets $V_0,\dots,V_T$ so that each $v \in V_i$,
$0 \le i < T$ has exactly two in-edges, both of which are from
vertices in $V_{i + 1}$. The sets $V_i$ represent \emph{generations},
where $V_0$ is the \emph{extant population} and $V_T$ is the
\emph{founding population}. The size of the founding population
$|V_T|$ equals $N$. The vertices $V$ also satisfy \emph{monogamy} ---
within each generation $V_i$, $i > 0$, the vertices $V_i$ can be
partitioned into pairs $(v_1, v_2)$ such that if $u$ is a child of
$v_1$ if and only if $u$ is a child of $v_2$; such pairs are called
\emph{couples}. The number of children of each couple is randomly
drawn from the distribution $\xi$.

Each vertex $v$ has associated genetic information in the form of $B$
\emph{blocks}, each of which contains a symbol sampled from some
alphabet $\Sigma$. The symbol at block $b$ of the genome of vertex
$v$ is denoted $s_v(b)$.

The $(N,B,T,\xi)$-\emph{coupled pedigree} $\mathcal{P}$ induced by an
uncoupled pedigree $\mathcal{U}$ is formed by merging each couple into
a single vertex --- the resulting vertices are called \emph{coupled
nodes}. Now each $v$ in a generation other than the extant represents
a pair of individuals, and an edge from a coupled node $u$ to a
coupled node $v$ represents that $u$ is the parent of one of the
individuals in couple $u$. All vertices in $\mathcal{P}$ have
in-degree two, except vertices in the extant population, which remain
uncoupled and have in-degree 1. The genetic information $s_v(b)$ of a
coupled node $v$ is the set of all symbols that are in
block $b$ for some individual in the couple represented by $v$.

When we say that some graph is a pedigree in this paper without
specifying whether the pedigree is coupled or uncoupled, we are
referencing coupled pedigrees.

\section{{\sc Rec-Gen}}\label{sec:kim2020efficient}

The \textsc{Rec-Gen} reconstruction algorithm presented in
\cite{kim2020efficient} proceeds in three main phases. In each generation,
siblinghood detection (Algorithm \nameref{algo:test-siblings})
reconstructs relationships in the current generation, outputting a
siblinghood hypergraph in which triple $u, v, w$ forms a hyperedge if
they are likely to be siblings. Algorithm
\nameref{algo:construct-parents} processes maximal cliques in the
outputted hypergraph, populating the parent generation. Symbol
collection (Algorithm \nameref{algo:collect-symbols}) reconstructs the
genetic information of the parent generation. For reference, the
original algorithm pseudocode from \cite{kim2020efficient} is provided in
Appendix \ref{sec:pseudocode}.

\subsection{Runtime Analysis}\label{sec:runtime}

Na\"ive implementations of Algorithms~\nameref{algo:test-siblings}
and~\nameref{algo:collect-symbols} both run in $\Omega(BN_0^3)$ time.
Algorithm~\nameref{algo:test-siblings} counts the number of shared
blocks in all triples, which can require $\Omega(BN_0^3)$ in the worst
case.

To na\"ively find a triple of extant vertices sharing a gene in block
$b$ with $u$ as their joint-LCA for some $u$ in generation $t$ of the
pedigree for Algorithm~\nameref{algo:collect-symbols}, it may be
necessary to inspect all triples of extant descendants of $u$ in each
block $b$, which is also $\Omega(BN_0^3)$.

We wish to improve both of these processes to $O(BN_0^2)$, as
described in Sections~\ref{sec:fast-sib} and~\ref{sec:fast-symb}.

\subsection{Faster Siblinghood Detection}\label{sec:fast-sib}

The greatest bottleneck in the runtime of \textsc{Rec-Gen} is the
siblinghood detection step, which for each generation $t$ is cubic in
the size of that generation $N_t$. To reduce the runtime from
$O\left( N_t^3B \right)$ to $O\left( N_t^2B\right)$, we begin by
processing all pairs of vertices, marking pairs that share some
threshold $\theta=0.4$ of their blocks as \emph{sibling candidates}.
We then only consider triples of vertices formed from sibling
candidates when generating the siblinghood hypergraph. Pseudocode of
the alternate algorithm \nameref{algo:fast-test-siblings} follows:

\begin{algorithm}[H]
\caption{
    Perform statistical tests to detect siblinghood
}
\begin{algorithmic}[1]
\algolabel{\textsc{Fast-Test-Siblinghood}}{algo:fast-test-siblings}
\Procedure{Fast-Test-Siblinghood}{depth $(k-1)$ pedigree $\hat{\cP}$}
    \State $C \gets \varnothing$
    \State $V \gets$ vertices of $\hat{\cP}$ at level $k-1$
    \ForAll{distinct pairs $\{u,v\} \in 2^V$}
        \If{
            $\geq 0.4|B|$ blocks $b$ such that
            $\hat{s}_{u}(b) \cap \hat{s}_{v}(b) \neq \varnothing$
        }
            \State $C \gets C \cup \{u,v\}$
        \EndIf
    \EndFor
    \State $E \gets \varnothing$
    \ForAll{pairs $\{u,v\} \in C$}
        \ForAll{
            $w \in V$ at level $k-1$ such that
            $w \neq u \land w \neq v$
        }
            \If{
                $\geq 0.21|B|$ blocks $b$ such that
                $
                    \hat{s}_{u}(b) \cap
                    \hat{s}_{v}(b) \cap
                    \hat{s}_{w}(b) \neq \varnothing
                $
            }
                \State $E \gets E \cup \{u,v,w\}$
            \EndIf
        \EndFor
    \EndFor
    \State $\hat G \gets (V, E)$
    \State \Return $\hat{G}$
\EndProcedure
\end{algorithmic}
\end{algorithm}

\subsection{Faster Symbol Collection}\label{sec:fast-symb}

To decrease the complexity of executing the \textsc{Rec-Gen}
symbol-collection phase on $v$, we avoid explicitly searching for
extant triples that have $v$ as their joint-\textsf{LCA}. Instead, we
make the simplifying assumption that any three extant vertices $x,y,z$
descended from distinct children of $v$ have $v$ as a
joint-\textsf{LCA}. Now, we can use the following modified algorithm
to achieve an effect equivalent to the original
\nameref{algo:collect-symbols} of \cite{kim2020efficient}:
\begin{itemize}
    \item Let $\hat{G}_u(b)$ for a child $u$ of $v$ and block $b$ be
        the set of genes $g$ such that there exists an extant
        descendant $x$ of $u$ such that $\hat{s}_u(b) = \{g\}$.
    \item Compute $\hat{G}_u(b)$ for all children $u$ of $v$.
    \item Let $\hat{s}_v(b)$ be the two genes that are present in the
        greatest number of computed sets $\hat{G}_u(b)$.
\end{itemize}
Pseudocode of this modified process can be seen in Algorithm
\nameref{algo:fast-symbols}.

\cite{kim2020efficient} proves that, conditioned on the nonoccurence of
undesirable inbreeding events, the existence of a joint-\textsf{LCA}
$v$ for three nodes $x,y,z$ entails that $v$ is their unique
\textsf{LCA}. Therefore, if most extant nodes have a
joint-\textsf{LCA}, then the algorithm described above is equivalent
to the initial description of symbol-collection in \cite{kim2020efficient}.
Empirically, very few ($<1\%$ of) extant triples in simulated
pedigrees are descended from unique children of a vertex that is not
their joint-\textsf{LCA}.

Generating $\hat{G}_u$ requires time that is linear in the number of
nodes in the descendants pedigree of $u$. Since $\alpha > 2$, this is
on expectation bounded above by a linear function of the number of
extant descendants of $u$. Each extant individual $v$ has at most
$2^t$ ancestors in generation $t$. Therefore, the sum of the number of
extant descendants of $u$ over all $u$ in generation $t$ is at most
$2^tN_0$, where $N_0$ is the size of the extant population, so that
the runtime of invoking Algorithm~\nameref{algo:fast-symbols} for all
$u$ at generation $t$ is $O(B \cdot (2^tN_0 + |G|))$. Since
$\alpha > 2$,
$2^t \subseteq O(\alpha^t) \subseteq O(\mathbb{E}[N_t]/N_T)$, so that
the total runtime of Algorithm~\nameref{algo:fast-symbols} is
$O(B \cdot \mathbb{E}[N_t]N_0/N_T) \subseteq O(BN_0^2)$.

\begin{algorithm}[H]
\caption{
    Empirically reconstruct the symbols of top-level node $v$ in
    $\cP$.
}
\begin{algorithmic}[1]
\algolabel{\textsc{Fast Collect-Symbols}}{algo:fast-symbols}
\Procedure{Fast Collect-Symbols}{$v, \hat{\cP}$}
    \ForAll{blocks $b \in [B]$}
        \State $c_g \gets 0 \;\forall\; g$
        \ForAll{children $u$ of $v$}
            \State $\hat{G}_u(b) \gets \varnothing$
            \ForAll{extant $x$ descended from $u$}
                \State $\hat{G}_u(b) \gets \hat{G}_u(b) \cup \hat{s}_x(b)$
            \EndFor
            \ForAll{$g \in \hat{G}_u(b)$}
                \State $c_g \gets c_g + 1$
            \EndFor
        \EndFor
        \State $\sigma_1 \gets g\text{ with highest }c_g$
        \State $\sigma_2 \gets g\text{ with second-highest }c_g$
        \State Record the symbols $\sigma_1, \sigma_2$ for block $b$ in $v$.
    \EndFor
\EndProcedure
\end{algorithmic}
\end{algorithm}

\section{Simulations}\label{sec:simulations}

We assess the empirical accuracy of \textsc{Rec-Gen} and other
algorithms presented later in this work by running them on simulated
pedigrees. We generate pedigrees satisfying the stochastic model in
\cite{kim2020efficient}, as described in section \ref{sec:gen-ped}. The extant
populations of the pedigrees can be used as input for our
implementations of the reconstructive algorithms, and a grader
program evaluates the accuracy of the result as described in
section \ref{sec:grader-prog}.

\subsection{Generating Pedigrees}\label{sec:gen-ped}

Our pedigree generator program accepts arguments $N,B,T,\alpha,d$
(where $N,B,T,\alpha$ are integer parameters and $d$ is a Boolean
parameter) and creates $(N,B,T,\xi)$-coupled pedigrees, where $\xi$ is
Poisson-distributed with parameter $\alpha$ if $d$ is False and is a
constant distribution with value $\alpha$ otherwise.

We begin by creating $N$ individual nodes numbered from 1 to $N$;
these are the founding individuals, and make up generation $T$ of the
generated pedigree $\cP$. The $i$th individual has gene $i$ in all
$B$ blocks of its genome; note that this satisfies the property that
no two founders share a gene in any block.

Now, given the individuals in generation $t > 0$, we produce the
couples in generation $t$ and generate the individuals in generation
$t - 1$ in the following manner:
\begin{itemize}
    \item Assign to each individual in generation $t$ a real-valued
        \emph{mating index} sampled from a uniform distribution over
        the unit interval.
    \item Sort the individuals in generation $t$ in order of
        increasing mating index; let this order be
        $v_{t,1},\dots,v_{t,N_t}$. For each pair of elements of the
        form $c_i = (v_{t,2i-1},v_{t,2i})$ for positive integers
        $i$, add the coupled node formed by $c_i$ to generation $t$
        of $\mathcal P$.
    \item For each coupled node $c_i$ in generation $t$, let $f_i$ be
        $\alpha$ if $d$ is true; otherwise sample $f_i$ from a
        Poisson distribution with parameter $\alpha$. Add $f_i$
        individuals that have couple $c_i$ as their parent to
        generation $t - 1$ and assign each a genome of $B$ blocks,
        where each gene is sampled from the genes of $c_i$ at that
        block with equal probability.
\end{itemize}

At $t = 0$, the individual nodes are mated with themselves to form
the special unmated coupled nodes of the extant population.

\subsection{Assessing Reconstruction Accuracy}\label{sec:grader-prog}

Our grader program takes as input a parameter $\alpha \in [0, 1)$ and
two pedigrees with identical extant populations and the same numbers
of generations | an original pedigree $\cP$ and its reconstruction
$\cP'$. It outputs a partial mapping between the coupled nodes of
$\cP$ and $\cP'$, where a coupled node $v \in \cP$ of the original
pedigree is mapped to a coupled node $v' \in \cP'$ of the
reconstructed pedigree only if $v'$ is an \emph{$\alpha$-successful}
reconstruction of $v$. $\alpha$-successful reconstructions are
defined recursively in the following manner:
\begin{itemize}
    \item In generation 0 (the extant population) a vertex
        $v' \in \cP'$ is an $\alpha$-successful reconstruction of
        $v \in \cP$ if and only if $v$ and $v'$ are the same coupled
        node.
    \item In generation $t > 0$, let $c(v, v')$ for
        $v \in \cP, v' \in \cP'$ denote the number of pairs $u$ and
        $u'$ from generation $t - 1$ of $\cP$ and $\cP'$,
        respectively, for which $u$ is a child of $v$, $u'$ is a
        child of $v'$, and $u'$ is an $\alpha$-successful
        reconstruction of $u$. Also, let $f$ be the number of
        children of $v$ and $f'$ be the number of children of $v'$.
        Then $v'$ is an $\alpha$-successful reconstruction of $v$ if
        and only if $c(v, v') > \alpha f$ and $c(v, v') > \alpha f'$.
\end{itemize}
In the case that multiple vertices $v' \in \cP'$ are an
$\alpha$-successful reconstruction of some $v \in \cP$, the grader
program maps $v$ to the one that maximizes $c(v, v')$. If the program
maps some $v'$ to $v$, we consider $v$ successfully reconstructed.

The grader also outputs the
following statistics for each generation $t$:
\begin{itemize}
    \item The number and percent of successfully reconstructed
        vertices
    \item The number and percent of successfully reconstructed edges
        (these are the sum of $c(v, v')$ over reconstructed $v$ and
        the ratio of that sum to the sum of $f$ over all $v$ in $t$)
    \item The number of reconstructed blocks, where a block
        $g$ in position $b$ of $v$ is considered reconstructed if
        $v'$ also has $g$ in position $b$\footnote{In case that $v$
        has two identical genes in some position, they are both
        considered reconstructed only if $v'$ also has two copies of
        that gene; otherwise, only one is considered reconstructed.
        Note, however, that this should not happen regularly, as it
        is an indication of inbreeding.}, as well as the percent of
        blocks reconstructed out of all blocks in generation
        $t$ and out of blocks belonging to reconstructed nodes in
        generation $t$.
\end{itemize}

When using the grader to study the behavior of the reconstruction of
symbols, we typically apply a generous $\alpha = 0.5$ threshold, so
as not to exclude information about weakly reconstructed vertices.
For the accuracy metrics presented throughout this paper, we usually
use $\alpha = 0.75$ or $\alpha = 0.99$.

\section{Simulation Results for {\sc Rec-Gen}}\label{sec:kim2020efficient-sim}

\subsection{Results for\texorpdfstring{
    $\boldsymbol{T = 3}$}{T = 3}
}\label{sec:kim2020efficient-sim-t3}

Experiments using simulated data as described in Section
\ref{sec:gen-ped} indicate that, even in pedigrees with relatively
small founding populations ($N=50$) and fertility rates ($\alpha=6$),
\textsc{Rec-Gen} reliably reconstructs two generations above the
extant (the `parent' and `grandparent' generations) in pedigrees with
$T=3$. However, performance at the third generation declines sharply,
and in individual simulations with $T=4$ (not included in the batched
results in this section; see Section \ref{sec:kim2020efficient-sim-t4}),
\textsc{Rec-Gen} fails to recover even a single vertex of the founding
population. Figures~\ref{fig:vert-t3-a99}
through~\ref{fig:block-t3-a75} graph the average vertices and blocks
reconstructed over $\alpha$ for three generation pedigrees with $N=50$
and $B=5000$ for two values of the reconstruction accuracy threshold:
$0.75$ and $0.99$.

As one would expect, reconstruction accuracy generally improves as
$\alpha$ increases (an exception is for the high accuracy threshold
$0.99$ in the case of constant fertilities --- when there is a larger
number of children, even an algorithm that reconstructs each with
higher probability may reconstruct all of them with lower
probability). Additionally, \textsc{Rec-Gen} performs better for the
case of constant fertilities than for the case of Poisson-distributed
fertilities. Since \textsc{Rec-Gen} performs poorly for vertices with
low fertility (and is incapable of reconstructing vertices with
fertility less than 3), we attribute the relatively poor performance
of \textsc{Rec-Gen} for the Poisson case as compared to the
deterministic case to the incidence of low-fertility nodes.

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t3-a99.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t3-a99-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent vertices 0.99-successfully reconstructed in
        each generation of $T=3$ pedigrees, plotted over fertility
    }\label{fig:vert-t3-a99}
\end{figure}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t3-a99.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t3-a99-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent blocks 0.99-successfully reconstructed in
        each generation of $T=3$ pedigrees, plotted over fertility
    }\label{fig:block-t3-a99}
\end{figure}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t3-a75.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t3-a75-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent vertices 0.75-successfully reconstructed in
        each generation of $T=3$ pedigrees, plotted over fertility
    }\label{fig:vert-t3-a75}
\end{figure}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t3-a75.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t3-a75-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent blocks 0.75-successfully reconstructed in
        each generation of $T=3$ pedigrees, plotted over fertility
    }\label{fig:block-t3-a75}
\end{figure}

\subsection{Decline at\texorpdfstring{
    $\boldsymbol{T = 4}$}{T = 4}
}\label{sec:kim2020efficient-sim-t4}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{decline-constant.png}
        \caption{Constant threshold}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{decline-fixed.png}
        \caption{Adjusted threshold}
    \end{subfigure}
    \caption{
        Vertices 0.5-reconstructed by \textsc{Rec-Gen} for a $T=4$
        pedigree, with both the default $21\%$ siblinghood threshold
        (a) and a manually optimized siblinghood threshold (b). Note
        that 0 nodes are reconstructed in generation 4 in (a).
    }
    \label{fig:node-decay}
\end{figure}

As demonstrated in Figure~\ref{fig:node-decay} (a), \textsc{Rec-Gen}
appears to encounter major difficulties by the fourth generation,
failing to recover even a single founding node in our simulations.
This failure seems to be precipitated by a rapid decline in accuracy
of reconstructed blocks, as shown in Figure~\ref{fig:block-decay}.
Recall that Algorithm~\nameref{algo:collect-symbols} requires that
triples share at least $21\%$ of their blocks to be identified as
siblings. In generations 0 and 1, the distribution of shared
reconstructed blocks for sibling triples lies entirely above the
$21\%$ threshold. By generation 2, it shifts slightly to the left so
that some siblings are not recognized (and, as a result, not all of
the generation 3 is reconstructed). In generation 3, there are two
clusters in the distribution of shared triples: one at 0\% and one
around 10\%. The cluster at 0\% is the result of the members of
generation 3 who were not reconstructed at all; the rest of the
distribution consists of the remaining triples, which still share
distinctly more blocks than non-sibling triples, but fewer than 21\%.

When we manually set the siblinghood threshold to decay with each
generation to match the accumulation of errors, we can extend the
number of generations for which \textsc{Rec-Gen} is able to
accurately reconstruct the topology. Figure~\ref{fig:block-decay} (b)
demonstrates the improvement in accuracy when using the siblinghood
thresholds 21\%, 21\%, 17\%, 4\% for generations 0, 1, 2, and 3
respectively.

This experiment implies that the step that introduces the most error
into \textsc{Rec-Gen} is the symbol-collection step. In reality, we
cannot easily manually adjust the siblinghood threshold, because the
optimal threshold varies from pedigree to pedigree and may be
difficult to determine without knowledge of the true pedigree
topology. We can further assume that these errors are largely the
result of failure of the combinatorial \textsc{Rec-Gen} algorithm to
correctly handle inbreeding. We confirm this assumption by running
\textsc{Rec-Gen} on a large pedigree constructed as though it were a
section sampled from an infinitely wide pedigree --- indeed,
\textsc{Rec-Gen} has almost perfect accuracy in this case, as expected
(the only errors were the result of blocks that were not passed down
to any descendants, which can happen with frequency $1/2^\alpha$). We
therefore wish to improve the robustness of the symbol-collection step
against inbreeding.

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-sib-0.png}
        \caption{Generation 0 (Extant)}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-sib-1.png}
        \caption{Generation 1 (Parents)}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-sib-2.png}
        \caption{Generation 2 (Grandparents)}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-sib-3.png}
        \caption{Generation 3 (Founder's children)}
    \end{subfigure}
    \caption {
        Distribution of percent reconstructed blocks shared in all
        triples for a $T=4$ pedigree. Note the sharp decline at
        generation 3.
    }\label{fig:block-decay}
\end{figure}

\section{Belief Propagation}\label{sec:bp}

To improve the empirical accuracy of the symbol collection step, we
replace the original combinatorial Algorithm
\nameref{algo:collect-symbols} with a single pass of a
Belief-Propagation (BP) algorithm for recovering the genetic
information of pedigrees. BP is a message-passing algorithm for
inference that is most successful in locally tree-like models.
\cite{mezard2009information} gives the BP equations in the following setting:
\begin{itemize}
    \item $\V x$ is a tuple of $N$ variables
        $\left( x_1, \dots, x_N \right)$ assuming values from the
        finite alphabet $\cX$.
    \item There are $M$ constraints in the form of the marginals
        $\psi_1, \dots, \psi_M$ governing the distribution of values
        assumed by $\V x$, so that the probability distribution of $x$
        satisfies
        \[
            p(\V x) \cong \prod_{a = 1}^M \psi_a\left(
                \V x_{\partial a}
            \right)
        \]
        where
        $
            \V x_{\partial a} = \left\{
                x_i : i \in \partial a
            \right\}
        $
        and $\partial a \subseteq [N]$ is the set of variable indices
        constrained by $\psi_a$ (here, the notation $x \cong y$
        denotes that the two functions $x,y : \cX \to \mathbb{R}$ are
        equal down to a constant factor).
\end{itemize}
In this context, the relationships between variables can be modelled
by a bipartite graph in which each vertex representing a variable
$x_i$ has an edge to each `factor vertex' representing a constraint
$\psi_a : i \in \partial a$; this graph is called the
\emph{factor graph}. The BP equations that permit approximation of the
marginal distribution of each variable govern `messages' sent over the
edges of the factor graph at each time step $t + 1$:
\begin{itemize}
    \item Message from the $j$th variable to the $a$th factor:
        \[
            \nu_{j \to a}^{(t + 1)}\left( x_j \right) \cong
                \prod_{b \in \delta j \setminus a}
                \widehat\nu_{b \to j}^{(t)}\left( x_j \right)
        \]
    \item Message from the $a$th constraint to the $j$th variable:
        \[
            \widehat\nu_{a \to j}^{(t)}(x_j) \cong
                \sum_{\V x_{\partial a \setminus j}} \psi_a\left(
                    \V x_{\partial a}
                \right) \prod_{k \in \partial a \setminus j}
                    \nu_{k \to a}^{(t)}\left( x_k \right)
        \]
\end{itemize}
The estimate for the marginal distribution of variable $i$ at time
$t$ is
\[
    \nu_i^{(t)}\left( x_i \right) \cong
        \prod_{a \in \partial i} \widehat\nu_{a \to i}^{(t - 1)}
        \left(
            x_i
        \right)
\]
If the factor graph is a tree, then BP is known to be exact | that is,
the values $\nu_i$ converge, and they converge precisely to the true
marginals of the variables. Moreover, the exact marginals can be
computed with BP in linear time in the tree case, as $\nu_i$ assume
the values of the marginals of $x_i$ after two passes through the
tree, as described in \cite{mezard2009information}.

For our modified symbol-collection step, we effectively complete one
BP sweep (half of the tree algorithm) independently for each position
in the genome. Let $G$ be the set of all genes, $\ch{v}$ be the tuple
of children of vertex $v$, $0 < \varepsilon < 1$ be some constant that
represents the probability of an error in the topology of the
reconstruction, $\V g_v$ be the variable the value of which is the
pair of genes in a given block of vertex $v$, and
$\pr{v}$ be a function from unordered pairs from $G$ to the unit
interval, the BP estimate of the marginal distribution of $\V g_v$.

For each extant vertex $v$ with gene $g$, we introduce a constraint
\[
    \psi \cong \mathbb{I}_{\V g_v = (g, g)}
\]
For each nonextant vertex $v$, we introduce a constraint indicating
that a child of $v$ is an anomaly in the topology (shares no genes
with $v$) with probability $\varepsilon$:
\[
    \psi \cong
        \varepsilon^{\scalebox{0.75}{$
            |\{u \in \ch{v} :
            \V g_v \cap \V g_u = \varnothing\}|
        $}}
\]
Then the computed values of $\pr{v}$ are as follows. For extant
couples $v$ with gene $g$, we have
\[
    \pr{v}(g_1, g_2) \cong \mathbb{I}_{g_1 = g_2 = g}
\]
And for nonextant couples $v$
\[
    \pr{v}(g_1, g_2) \cong
        \sum_{\V{g}\in (G^2)^{|\ch{v}|}}
        \varepsilon^{\scalebox{0.75}{$
            |\{i \in [1, |\ch{v}|] :
            \{g_1, g_2\} \cap \V{g}_i = \varnothing\}|
        $}}
        \prod_{i \in [1,|\ch{v}|]} \pr{\ch{v}_i}(\V{g}_u)
\]
We record the gene pair with the highest probability according to
$\pr v$ as the genes reconstructed for couple $v$.

Computing $\pr{v}$ directly would be computationally inefficient |
worse than $O\left( |G|^{2\alpha} \right)$ on expectation, as
$|\ch{v}|$ is Poisson-distributed with parameter $\alpha$. We can
substantially improve this runtime by computing the probability
distribution by summing over the number of children indicating
topology errors, rather than over all possible assignments of genes.
To do this, we construct a DP table $\DP(g_1, g_2)_{i,j}$ that stores,
for the first $i$ children, the probability that $j$ of them indicate
topology errors. The recursive definition follows:
\[
    \DP(g_1, g_2)_{i,j} = \left\{\;\begin{aligned}
        & \mathbb{I}_{j = 0} & i = 0 \\
        & \DP(g_1, g_2)_{i-1,j-1}\sum_{(h_1, h_2) \in G^2}
            \mathbb{I}_{\{h_1, h_2\} \cap \{g_1, g_2\} = \emptyset}
            \pr{\ch{v}_i}(h_1, h_2)\;+ & \\
        & + \DP(g_1, g_2)_{i-1,j}\sum_{(h_1, h_2) \in G^2}
            \mathbb{I}_{\{h_1, h_2\} \cap \{g_1, g_2\} \neq \emptyset}
            \pr{\ch{v}_i}(h_1, h_2) & i > 0
    \end{aligned}\right.
\]
Once we have computed the values of this table for $i = |\ch v|$, we
can compute $\pr v$ by taking the following sum:
\[
    \pr{v}(g_1, g_2) \cong \sum_{j = 0}^{|\ch{v}|} \varepsilon^j \cdot \DP(g_1, g_2)_{|\ch{v}|, j}
\]
Constructing the DP table takes $O\left( \alpha|G|^4 \right)$ time per
block, which dominates the runtime of computing the marginals by this
method. We can further reduce the runtime by directly maintaining the
marginal probability that some single gene appears in each node (in
addition to the probability estimate over pairs of genes $\pr v$):
\[
    S_v(g) = \sum_{g' \in G}\pr{v}(g, g')
\]
Then we can compute the DP as below:
\[
    \DP(g_1, g_2)_{i,j} = \left\{\;\begin{aligned}
        & \mathbb{I}_{j = 0} & i = 0 \\
        & \DP(g_1, g_2)_{i-1,j}\left(
            S_v(g_1) + \mathbb{I}_{g_1 \neq g_2}
            (S_v(g_2) - \pr{\ch{v}_i}(g_1, g_2))
        \right) \;+ \\
        & + \DP(g_1, g_2)_{i-1,j-1}\left(
            1 - (S_v(g_1) + \mathbb{I}_{g_1 \neq g_2}
            (S_v(g_2) - \pr{\ch{v}_i}(g_1, g_2)))
        \right) & i > 0
    \end{aligned}\right.
\]
Computing the DP table in this manner requires only
$O\left( \alpha|G|^2 \right)$ time.

However, as presented, the BP sweep for symbol collection has a memory
complexity of $O\left( |G|^2 \right)$ per block per node, which in
practice is prohibitive even for pedigrees with relatively small
founding populations. To reduce the memory complexity by a factor of
$|G|$, we make the simplifying assumption that
the probability that some vertex $v$ has at least one of a pair of
genes $g_1, g_2$ approximately equals
$S_v\left( g_1 \right) + S_v\left( g_2 \right)$; this permits us to
store only the marginal probabilities over single genes, rather than
the entire distribution over pairs of genes.

The DP values are then calculated as follows:
\[
    \DP(g_1, g_2)_{i,j} = \left\{\;\begin{aligned}
        & \mathbb{I}_{j = 0} & i = 0 \\
        & \DP(g_1, g_2)_{i-1,j}\left(
            S_v(g_1) + \mathbb{I}_{g_1 \neq g_2} S_v(g_2)
        \right) \;+ \\
        & + \DP(g_1, g_2)_{i-1,j-1}\left(
            1 - (S_v(g_1) + \mathbb{I}_{g_1 \neq g_2} S_v(g_2)
        \right) & i > 0
    \end{aligned}\right.
\]

On small pedigrees, this assumption does not produce a decrease in
reconstruction accuracy. We also show that simulations on large
pedigrees, which are impractical with the $O\left( |G|^2 \right)$
per-block memory complexity, perform well.

We also implement a relatively simple parsimony-based symbol
collection step, which greedily takes the genes that entail the fewest
topology errors. The behavior of the parsimony implementation should
match the behavior of the limit as $\epsilon$ approaches 0 of the BP
implementation.

\section{Simulation Results for BP}\label{sec:bp-sim}

Experiments using simulated data generated as described in
Section~\ref{sec:gen-ped} indicate that using BP or Parsimony instead
of the combinatorial symbol-collection step of \textsc{Rec-Gen}
significantly improves accuracy and permits substantial recovery of
the founding populations of $T=4$ pedigrees without manual
intervention in the siblinghood threshold.
Figures~\ref{fig:vert-t4-a75} through~\ref{fig:block-t4-a50} show the
reconstruction accuracy of BP with two values of $\epsilon$ (0.01 and
0.001), parsimony, and the original \textsc{Rec-Gen} symbol-collection
step. Parsimony and both instances of BP have similar accuracy, which
past the grandparent generation is significantly better than that of
the original \textsc{Rec-Gen}. BP with $\epsilon=0.01$ tends to
slightly outperform BP with $\epsilon=0.001$ and parsimony. These
results indicate that BP is more robust against inbreeding than the
combinatorial \textsc{Rec-Gen}, and that parsimony is a simple but
reliable approximation of the BP.

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t4-a75.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t4-a75-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent vertices 0.75-successfully reconstructed using
        each of four different procedures for symbol collection in
        each generation of $T=4$ pedigrees
    }\label{fig:vert-t4-a75}
\end{figure}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t4-a75.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t4-a75-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent blocks 0.75-successfully reconstructed using
        each of four different procedures for symbol collection in
        each generation of $T=4$ pedigrees
    }\label{fig:block-t4-a75}
\end{figure}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t4-a50.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{vert-t4-a50-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent vertices 0.50-successfully reconstructed using
        each of four different procedures for symbol collection in
        each generation of $T=4$ pedigrees
    }\label{fig:vert-t4-a50}
\end{figure}

\begin{figure}
    \centering
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t4-a50.png}
        \caption{Poisson-distributed fertilities}
    \end{subfigure}
    \begin{subfigure}{.45\textwidth}
        \centering
        \includegraphics[width=\textwidth]{block-t4-a50-d.png}
        \caption{Constant fertilities}
    \end{subfigure}
    \caption {
        Average percent blocks 0.50-successfully reconstructed using
        each of four different procedures for symbol collection in
        each generation of $T=4$ pedigrees
    }\label{fig:block-t4-a50}
\end{figure}

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