Having good genes definitely help if you plan to live 85, 90 or 100-plus years — but they aren't the only thing that matters.
Canada's longest-lived seniors tend to have parents who live at least nine years longer than average and that's a lot, according to Angela Brooks-Wilson, who runs a 16-year healthy aging study at Simon Fraser University.
But lifestyle always plays a bigger role in how long you live, she said.
If you want to live to 85 and longer, it helps to stay busy.
Study participant Ivan Vance — just 90 years old — hits the gym and the courts at the Jericho Tennis Club about four times a week and really pushes himself. After the gym, he hits serves for an hour or more.
And it's singles only for Vance, when he plays.
"I get the best tennis from the top women; they are really good players," he said.
Vance calls it like he sees it, especially if he doesn't like what he sees.
Seriously though, Vance has been active his whole life.
It is always challenging to schedule the interviews with "super seniors" study participants because of their busy schedules, said Brooks-Wilson.
The late band leader Dal Richards and nonagenarian track star Olga Kotelko were also part of her super group.
Seniors in the study must be free of cancer, dementia, diabetes, cardiovascular disease and major lung disease at the time they join. They range in age from 85 — the minimum — to 109 years of age.
The researchers are examining candidate genes believed to be related to healthy aging, looking for differences between 700 super seniors and a comparison group of 500 randomly selected people in their 40s. That means they are young enough that any genetic predisposition to disease has not yet killed many of them.
Not surprisingly, very few super seniors have the APOe4 gene that is strongly associated with late-onset Alzheimer's Disease.
"What's interesting is that some do have it … and yet they are still super, so it's not a given that they will get Alzheimer's," said Brooks-Wilson, also a Distinguished Scientist with Canada's Michael Smith Genome Sciences Centre at the B.C. Cancer Agency.
Super seniors are also less likely to have a gene variant related to inflammation, which is implicated in the five major diseases that super seniors don't have by definition.
While you can't control your genome, there are powerful lifestyle choices you can make if you aim to live past 85.
Smoking tobacco is an effective way to avoid getting very old, while quitting is almost as effective at extending your life.
"We have almost no life-long smokers in the super seniors group, but about half have smoked and then quit at some time in the past," she said.
Super seniors — if they drink alcohol — have three or four drinks a week and were much more moderate in their consumption than the comparison group.
"Both moderate drinking and non-drinking are compatible with being a super senior," she noted.
Super seniors don't tend to be "super-skinny," she said. Many of them have a body mass index of about 25 — the upper end of the normal band, bordering on overweight.
Brooks-Wilson will share her research in the SFU President's Faculty lecture series on Thursday, March 15 at 5 p.m. at SFU's Burnaby campus in the Diamond Alumni Centre.
She is also anxious to recruit new super seniors. Anyone aged 85 or older who is interested in participating may call 604-675-8151, or email studycoordinator@bcgsc.ca.


text:
Q: Check All won't work in Chrome but works in Firefox I have a Check All box wherein when the user will tick it, all the items under it will be ticked. It works fine in Firefox but won't perform the Check All function in chrome.
This is the JS function:
function Check(chk, num)
{
    if(chk.value=="Check all"){
        for (i = 0; i <= num; i++){
            chk[i].checked = true ;
        }
        chk.value="UnCheck all";
    }else{

        for (i = 0; i <= num; i++){
            chk[i].checked = false ;
        }
        chk.value="Check all";
    }
}

HTML:
<form target="_blank" action="" method="post" id="myform" name="myform">
    <input type="checkbox" value="Check all" onclick="Check(document.myform.Product A, 9)" id="Fujitsu" name="Fujitsu"> Select All
    <input type="hidden" value="1" name="product_id[1]">
    <input type="checkbox" value="Product 1" id="Product 1" name="product[1]">Product A -Product 1
    <input type="hidden" value="2" name="product_id[2]">
    <input type="checkbox" value="Product 2" id="Product 2" name="product[1]">Product A -Product 2
</form>

A: For me both Firefox and Chromium crash on "document.myform.Product A".  Here is your code a little modified to work:
function Check(form, all, chk, num)
{
    if(form[all].value=="Check all"){
        for (i = 1; i <= num; i++){
            form[chk + i].checked = true ;
        }
        form[all].value="UnCheck all";
    }else{

        for (i = 1; i <= num; i++){
            form[chk + i].checked = false ;
        }
        form[all].value="Check all";
    }
}

and HTML:
<form target="_blank" action="" method="post" id="myform" name="myform">-
    <input type="checkbox" value="Check all" onclick="Check(document.myform, 'Fujitsu',  'Product_' , 2)" id="Fujitsu" name="Fujitsu"> Select All-
    <input type="hidden" value="1" name="product_id[1]">-
    <input type="checkbox" value="Product 1" id="Product_1" name="product[1]">Product A -Product 1-
    <input type="hidden" value="2" name="product_id[2]">-
    <input type="checkbox" value="Product 2" id="Product_2" name="product[1]">Product A -Product 2-
</form>

But you can do cleaner code to do the same thing:
function Check(form, action)
{
    var l = form.getElementsByTagName("input");
    for (var i = 0; i < l.length; ++i)
        if (l[i].type == "checkbox") l[i].checked = action;
}

and HTML:
<form target="_blank" action="" method="post" id="myform" name="myform">-
    <input type="checkbox" value="Check all" onclick="Check(document.myform, this.checked)" id="Fujitsu" name="Fujitsu"> Select All-
    <input type="hidden" value="1" name="product_id[1]">-
    <input type="checkbox" value="Product 1" id="Product_1" name="product[1]">Product A -Product 1-
    <input type="hidden" value="2" name="product_id[2]">-
    <input type="checkbox" value="Product 2" id="Product_2" name="product[1]">Product A -Product 2-
</form>

It would be even better if you used a library with CSS selectors like jQuery.

redpajama_set_name: RedPajamaStackExchange


text:
The Every Student Succeeds Act and Dual Language Learners
by Conor Williams
You wouldn't know it from cable news, the newspapers, or most of the rest of the national media outlets, but the Every Student Succeeds Act (ESSA) is getting very, very close to replacing No Child Left Behind. The new bill reflects conservative reticence about a strong federal role in education: it gives states considerable flexibility in identifying and improving underperforming schools.
So if you hated No Child Left Behind's broad goals for student achievement and the attached accountability incentives, I have good news! Most of that is disappearing in ESSA. States are still required to assess students every year, but the law gives them "acres of new running room" to set up their own systems for deciding what to do about the results.
In other words, if the bill passes, states will take over most of the responsibility for ensuring that underserved student populations receive equitable resources and treatment. If you trust your state to prioritize these kids — low-income students, dual language learners, children of color, etc — in a steady, measurable way, you'll like the bill fine. If — like me — you're skeptical that most states' leaders are willing to spend the political capital it takes to keep their systems focused on these children, you'll wonder how the bill ever got this far.
"This far," by the way, is pretty far indeed. The House and Senate each passed bills to replace No Child Left Behind and combined them into a single bill in conference committee negotiations just before Thanksgiving. The House passed that bill earlier today. It looks extremely likely that the Senate will follow and President Obama will sign ESSA into law. (Obligatory crow-eating: I was wrong about the bill's prospects.)
Beyond the law's general bias towards decentralizing accountability decisions to the state and local level, the law makes a few other important changes relevant to how schools serve dual language learners (DLLs).
1) Funding. The bill would authorize $756 million for Title III (the federal government's primary investment in DLLs). Is that a lot? While it's more than Title III has usually received, there are also many more DLLs in the program now than before. There were nearly 4.5 million DLLs receiving Title III services in the 2013–14 school year. If there are around that many DLLs enrolled in 2017, the $756 million would work out to about $166 per student. In 2002, Title III received $664 million to serve around 3.6 million DLLs ($184 per student). So it's not necessarily a huge boost. Interestingly, ESSA authorizes steady increases of Title III funds until 2020, when they would jump to $885 million.
In any event, we should remember that authorizing the use of these funds isn't the same as actually appropriating the money for these students. That's a separate process. For comparison: No Child Left Behind authorized up to $750 million for Title III when the law went into effect in 2002, but Congress only appropriated that much money once (in 2010). For fiscal year 2015, Title III received $737 million.
2) Accountability Systems. As I noted above, the bill would make big changes here. Title III accountability is gone. Districts would still collect data on DLLs' growth towards and attainment of English proficiency (i.e. the old Title III accountability metrics), but poor performance on these wouldn't mean anything for schools or districts' Title III dollars.
Instead, states would be required to build English proficiency into their Title I accountability systems. The theory is that including these students in a bigger funding stream would get them more attention. NCLB's Title III accountability provisions have always struggled with of being too mild to force real changes in schools — in part because they're part of a relatively small funding stream. Remember those Title III numbers I cited above? Title I was a $14.5 billion funding stream in 2015. And Bellwether Education's Chad Aldeman has suggested that ESSA would, in fact, lead to schools with high numbers of DLLs being identified for improvement at disproportionately high rates (for better or worse).
Now for the other hand. The challenge with this move is to make sure that this relatively small group of students remains prominent enough. These students got their own funding stream and accountability system in NCLB in part because they've historically been overlooked in broader efforts to improve educational equity. Recall that Title I dollars are allocated to districts and schools with high numbers of low-income students. Title I funds served 24.1 million children in the 2013–14 school year — more than five times the number of DLLs in Title III programs last year.
So: would the Department of Education really be able to get states to pay extra attention to DLLs in that much bigger Title I context? Remember, the big threat animating ESSA accountability (just as it is NCLB) would be straightforward: "the Secretary may withhold funds…until the Secretary determines that the State has fulfilled those requirements." Would it be willing (or even able, given the many ways that ESSA limits the Department's power) to pick fights over states' accountability systems when DLLs' performance is the only sticking point? We'll see.
3) Accountability Consequences. I've broken this out separately to emphasize that ESSA would leave considerable distance between states' designs of their accountability systems and what is actually required of districts and schools that are identified. As I put it in a recent column,
Each state's accountability system must incorporate students' math and reading achievement, though states have considerable sway in determining how much weight these two measures have. States may also incorporate other measures in determining whether schools are succeeding, such as attendance, student engagement, school climate measures, teacher engagement, participation in extracurriculars, and so on…Schools that finish in the bottom 5 percent of their particular system for no more than three years must be identified for improvement. Same goes for dropout factories (schools with a graduation rate below 67 percent)…Schools with any subgroup of students performing as poorly for a state-determined number of years (1? 4? 13? 25?) as the bottom 5 percent of schools are also identified as in need of improvement. The subgroups include African-American, Hispanic, [DLL], low-income, and/or Asian-American and Pacific Islander students.
There's lots of wiggle room in here. States would define how "the lowest-performing 5 percent of schools" are to be identified. They would have considerable say in determining how long schools must underperform before being identified as needing improvement.
Perhaps even more importantly, though, when a school is identified, there would be even more flexibility. ESSA would require an identified school's district to design its own "evidence-based interventions" in conjunction with community stakeholders, based on a needs assessment conducted at the school level. The improvement plan would be approved at the school, district, and state level.
Evidence-based policies and local involvement are good things. Still, there are (at least) two big challenges for this approach to accountability. First: "evidence-based" is meaningless language as far as education policymaking goes. Most new policy ideas are contested turf, where the research backing is mixed (and usually remains that way for a long, long time). There's evidence to support experimenting with basically anything — and state education agencies will be exceedingly unlikely to pick a fight with districts over an alleged lack of evidence for whatever new thing they'd like to try.
Second: "evidence-based" ideas that are dramatic enough to turn around chronically-failing schools are almost always deeply challenging to current school and district actors. But local generation and approval frequently generates improvement plans that are insufficiently aggressive to change these schools' trajectories. ESSA requires states to do something "more rigorous" with schools that aren't improving after four years of locally-driven improvements, but doesn't specify much. Under NCLB, persistent local failures result in federally-driven changes to how schools operate. Even though NCLB's mandates for struggling schools are big and unwieldy, they have the virtue of putting considerable external pressure on dysfunctional local education environments.
Here's what I think this means for DLLs in struggling schools: under NCLB, their schools also generated improvement plans. But local options in designing these plans were: 1) narrowed by NCLB's rules, and 2) backstopped by federal pressure (if the school failed to improve after five years of turnaround efforts, NCLB required major overhauls). Under ESSA, DLLs will have to count on local and, in the most persistently-struggling schools, state leadership. In other words, they'll have much more flexibility than NCLB's relatively limited options. And how they use that flexibility will make all the difference as far as DLLs are concerned.
This gets back to my assessment at the beginning: DLL stakeholders who generally trust their local leaders to prioritize DLLs' needs should be excited about this bill. DLL stakeholders who don't trust their local leaders but believe that their states can be counted on to move aggressively to put pressure on schools that aren't serving DLLs well…should be satisfied by this bill (with some reservations). DLL stakeholders who worry that their local leaders won't make tough decisions to improve how schools serve these kids, and also don't trust their states to force those leaders' hands — should be worried.
4) Data (and Accountability Again). In NCLB, DLLs who reach English proficiency leave the subgroup and are monitored for two years as former-DLLs. Under ESSA, states would be able to include the performance of recently-reclassified DLLs in the EL subgroup for the purposes of state accountability for up to four years after reclassification.
Presumably this is a decision that states would have to make and hold constant across districts and schools. If states allow variability on which recently-reclassified students are included in the DLL subgroup, it would be much easier to hide DLLs' achievement by shuffling them into or out of the EL subgroup depending on their assessment performance. This is precisely the sort of chicanery that worries folks (like me) who think that states should have limited flexibility on how they measure and report achievement data for underserved students.
There are other changes — we'll be publishing a post later this week on how the new bill changes rules for how schools, districts, and states gather and use assessment data on recently-arrived DLLs' achievement.
**Note: it's early days, and we're still picking through ESSA to make sure that we understand all of its (many) moving pieces. The foregoing is just a down payment on future analysis, and I reserve the right to have gotten some of the details and/or judgment wrong.
This post is part of New America's Dual Language Learner National Work Group. Click here for more information on this team's work
[Cross-posted at Ed Central]
Conor Williams
Conor Williams is a Senior Researcher in the Early Education Initiative at the New America Foundation. Find him on Twitter: @ConorPWilliams

redpajama_set_name: RedPajamaCommonCrawl


4 The Love of Writing: What is Horror?
A horror story is one where the author has aimed his intent to disturb the reader, to somehow penetrate the reader's psyche with fear. Horror is a genre that sustains a sense of dread. It attempts to touch the Jungian shared awareness.
The serial killer, the vampire, the returning god intent on destroying humanity, the killer dolls...are all vehicles of the horror writer.
However, I think we as writers need to stop looking at horror as a label. Instead, we should look at our ability to generate characters who are believable and our ability to put them into situations which imperil them. The more believeable a character, the greater the horror generated by that character's imminent destruction.
Find a good horror writer, and find a good writer. Some people might contradict me and point to Lovecraft. I'll grant he was not always a good writer, but when you look at the handful of material he wrote that rose above his other collected works, it was tremendous. "Shadow Over Innsmouth", "The Outsider", and "Cool Air" are examples of the writer coming first, the horror writer coming second.
So what is horror? I think the more important questions are how do we develop character? How do we tell a compelling story? How do we set a theme that stirs or set a mood that resonates?
When people ask if I'm a horror writer, I shake my head and answer: "No, I'm just a writer."
For me, horror has to have some aspect of "the other" to be effective. Something from beyond our human ken needs to interact with us. Splatterpunk (and the mass murder/snuff films like the Saw series) just don't cause me to feel that creeping dread I crave. I don't mind the stories, but they just don't get in there and work at my psyche.
I agree with Stewart. The days of putting a person and a critter in a house and letting them duke it out(so to speak) are over. As writers, we need to flesh out our characters and make people care (for good or ill) about them.


Confidential, supportive and caring private agency offering free pregnancy counseling, emotional support & adoption support services. Education, resources, home visits.
Community Gatherings for pregnant or breastfeeding mothers & families.
Unintended pregnancy consultation, free pregnancy tests, limited ultrasounds. Loving Parents Incentive Program, newborn gift pack, diapers, post-abortion support.
Free pregnancy counseling, information on all options, confidential support, adoption & voluntary foster care services, parenting resources.
Pregnancy tests, ultrasounds, free prenatal vitamins, maternity clothing, baby clothing, diapers & items. Post abortion support & options counseling. Call for an appointment. Free, confidential.
Pregnancy Support Program assists expectant mothers and new mothers with emotional support, community resources, education for pregnancy and parenting. Also works with parent wanting to make an adoption plan. Home visits available. Free.
Offers nurse home visit programs and portable cribs for parents-to-be who are City of Milwaukee residents.
Childbirth Preparation Classes. Partial or full scholarships available. Must register.
Confidential support to help expecting mothers and mothers with newborns (8 wks or younger) obtain the services they need to have a healthy pregnancy/baby as a free benefit through Wis. Medicaid (BadgerCare). PNCC/CCC services including childbirth/parenting education, nutrition/breastfeeding support, baby items, housing/employment/community resources and parenting support.
A free, statewide program that helps pregnant women, new moms, and their families quit smoking. Participants receive Wal-Mart gift cards for completing sessions.
Groups encourage, inform and promote breastfeeding.
Provides information, resources and support to pregnant women & mothers of newborns. (2 mos. or younger) who receive Medicaid/BadgerCare. Referrals given to financial resources, quality healthcare, quality childcare, computer lab, resume prep, and parenting classes.
Free pregnancy tests, confidential, layettes given 3-4 wks before due date; bring photo ID, pregnancy statement.
Offers mom-to-mom support and advocacy. Administers Circle of Hope a private, online support group for local pregnant women and moms of babies up to 12 months.
Helps women achieve alcohol-free pregnancies through screenings, education, phone counseling and text message support.
Long-term program w/ housing that guides new, single mothers towards self-sufficiency with opportunities to continue education, grow spiritually, and learn parenting skills; also financial classes, and counseling.
Head Start and Early Head Start provide weekly home visits for pregnant moms & families with children up to 5 yrs. Site-based programming for children 6 wks. up to 5 yrs. Services available for children with special needs.
Supports expectant mothers & mothers with newborns (30 days or less). AODA/mental health assistance, parenting classes, nutrition education, community activities, breastfeeding training, lifestyle management (stress relief techniques) clothing incentives, and $25 client referral program. Baby Boxes (safe sleeping space) available.
Welcome, Baby! for expectant moms, caregivers & grandparents with children under age 2.
Pregnancy counseling support & goal setting, home visits, provides resources inc. safe sleep, car seats, & other baby needs, parenting support, adoption services. Free and confidential.
Free labor & delivery classes. Attend all four sessions and receive a free pack of diapers.
Prenatal care coordination services, primary care, case management.
Free, confidential counseling re: pregnancy & post-abortion stress-related issues. Baby supplies are also distributed (diapers: size NB-5, wipes, clothing up to 24 mos.). Not a medical facility.
Prenatal Care Coordination helps women gain access to medical, social, educational and other services during pregnancy. Childbirth education classes with a free gift for attendees.
Classes for new and expecting parents.
100% free services. Pregnancy tests, ultrasounds, breastfeeding & childcare classes, fertility care, material assistance for mothers with babies & small children, and natural family planning.
Free pregnancy test, free limited OB/ultrasound (appointments required), medical & social service referrals, childbirth & parenting classes, material assistance when enrolled in Center services.
Provides ongoing prenatal support over phone; free to anyone with Medicaid.
Prenatal care coordination program free to Children's Community Health Plan members. Offers support & services needed to have a healthy pregnancy, healthy baby. Incentive program to earn baby items & gift cards, welcome mom kit, breastfeeding kit, home visits.
Free prenatal program for pregnant iCare BadgerCare Plus and Medicaid SSI members. Help to find a healthcare provider and obtain baby supplies.
Includes free home visits from nurse or social worker.


text:
package netty.napsters.client;

public interface NettyClientHandlerInterface {
	void messageHandler(String message,Response response);

	String  getName();
}

redpajama_set_name: RedPajamaGithub


text:
Covelli Centre
Covelli Centre/
EventsSeating chartsConcert tickets
Find tickets from 25 dollars to Chicago Steel at Youngstown Phantoms on Friday January 22 at 7:05 pm at Covelli Centre in Youngstown, OH
Chicago Steel at Youngstown Phantoms
$25·Covelli Centre·Youngstown, OH
Find tickets from 25 dollars to Chicago Steel at Youngstown Phantoms on Saturday January 23 at 7:05 pm at Covelli Centre in Youngstown, OH
Find tickets from 23 dollars to Chicago Steel at Youngstown Phantoms on Sunday January 24 at 4:05 pm at Covelli Centre in Youngstown, OH
Find tickets from 25 dollars to Team USA U17 at Youngstown Phantoms on Friday January 29 at 7:05 pm at Covelli Centre in Youngstown, OH
Team USA U17 at Youngstown Phantoms
Find tickets from 25 dollars to Team USA U17 at Youngstown Phantoms on Saturday January 30 at 7:05 pm at Covelli Centre in Youngstown, OH
Find tickets from 25 dollars to Team USA U17 at Youngstown Phantoms on Sunday January 31 at 4:05 pm at Covelli Centre in Youngstown, OH
Find tickets from 29 dollars to Chicago Steel at Youngstown Phantoms on Saturday February 20 at 7:05 pm at Covelli Centre in Youngstown, OH
Find tickets from 25 dollars to Muskegon Lumberjacks at Youngstown Phantoms on Friday February 26 at 7:05 pm at Covelli Centre in Youngstown, OH
Muskegon Lumberjacks at Youngstown Phantoms
Find tickets from 25 dollars to Muskegon Lumberjacks at Youngstown Phantoms on Saturday February 27 at 7:05 pm at Covelli Centre in Youngstown, OH
Find tickets from 25 dollars to Dubuque Fighting Saints at Youngstown Phantoms on Friday March 12 at 7:05 pm at Covelli Centre in Youngstown, OH
Dubuque Fighting Saints at Youngstown Phantoms
229 East Front Street, Youngstown, OH
Covelli Centre details
Covelli Centre Seating Chart Details
The Covelli Centre is a multi-purpose arena located in Youngstown, OH. As many visitors will attest, the Covelli Centre is one of the best places to catch live entertainment. The Covelli Centre is known for hosting concerts but other events have taken place here as well.
Covelli Centre Seating Maps
SeatGeek is known for its best-in-class interactive maps that make finding the perfect seat simple. Our "View from Seat" previews allow fans to see what their view at Covelli Centre will look like before making a purchase, which takes the guesswork out of buying tickets. To help make the buying decision even easier, we display a ticket Deal Score on every row of the map to rate the best bargains.
What is the seating capacity at the Covelli Centre?
The seating capacity at Covelli Centre events is around 5900 seats.


text:
Resort World Sentosa
The Raffles Hotel
Raffles Hotel is a colonial-style luxury hotel in Singapore.
Originally, a privately owned beach house, built in the 1830s, it was officially declared a national monument by the Singapore government in 1987.
It was established by Armenian hoteliers, the Sarkies Brothers in 1887, and was the first hotel in the region to have electric lights.
The hotel named after British statesman Sir Thomas Stamford Raffles, the founder of Singapore has expanded over the years with the additional wings, a veranda, ballroom, bar and billiards rooms.
The last tiger shot
In 1902, a tiger escaped from a performing circus and took refuge under the Bar and Billiards room to rest for the night.
Staff spotted the tiger and requested for the help of areas well-known sharp shooter, Mr Charles McGowan Phillips.
It was dark and it took several shots before the tiger unfortunately met its demise.
The last tiger in Singapore finally laid its head to rest under the Bar & Billiard Room.
Interesting facts about Raffles Hotel in Singapore
The Tiffin Room restaurant at the Raffles Hotel is actually the oldest in Singapore.
Long Bar is where the Singapore Sling was originally invented by Hainanese bartender Ngiam Tong Boon.
The Raffles Hotel in Singapore has been the backdrop and inspiration for many books and movies.
One of the first guests was the author Joseph Conrad, who was a seaman at the time.
© 2018 All rights reserved by CK Transport & Tour Pte Ltd | Powered by SingSuite
About Us | Terms of Use | Privacy Policy


text:
/*
 *  arch/s390/kernel/init_task.c
 *
 *  S390 version
 *
 *  Derived from "arch/i386/kernel/init_task.c"
 */

#include <linux/mm.h>
#include <linux/fs.h>
#include <linux/module.h>
#include <linux/sched.h>
#include <linux/init_task.h>
#include <linux/mqueue.h>

#include <asm/uaccess.h>
#include <asm/pgtable.h>

static struct signal_struct init_signals = INIT_SIGNALS(init_signals);
static struct sighand_struct init_sighand = INIT_SIGHAND(init_sighand);
/*
 * Initial thread structure.
 *
 * We need to make sure that this is THREAD_SIZE aligned due to the
 * way process stacks are handled. This is done by having a special
 * "init_task" linker map entry..
 */
union thread_union init_thread_union __init_task_data =
	{ INIT_THREAD_INFO(init_task) };

/*
 * Initial task structure.
 *
 * All other task structs will be allocated on slabs in fork.c
 */
struct task_struct init_task = INIT_TASK(init_task);

EXPORT_SYMBOL(init_task);


Very interesting information there. Thanks!
Does anyone know when the design change was made? That tidbit could be very useful to many who've had this job done in the past.
I know my car was seen for this problem about 3 years ago - Lord, I hope they replaced both actuators while the engine was out.
How many oil screens does W8 have?
We need to find out part number of this screen.
I believe he said it was integral to the adjuster housing.
I did some poking in ETKA and at an online dealership parts counter, and the adjuster housing part numbers 7D0 109 210 D (right bank) and 7D0 109 204 D (left bank) were superceded by 7D0 837 210 E (and -204 E), but I don't know when, or what the change was.
Next time I happen to visit my favorite parts guru, I'll ask him what he knows.
Just got my W8 back after two weeks at the dealers shop. The job actually only took one week but had to sit in the shop waiting one week as the only mechanic qualified to work on the W8 was busy with the same problem on another W8. Also I was informed that the job required the shops only set of special tools to perform thecam adjuster/filter work order. After receipt I had to return the car because the steering felt like it only had partial power steering. Apparently when they drop the engine, the power steering has to be disconnected and when reestablished there was air in the system. System was bleed and refilled and the car now handles and runs like it used to. They also completed the 40,000 mile maintenance requirement. Get ready to shell out $600 for that! Fortunately the entire bill for the cam adjuster correction was under warrantee and no charge. The good news is that both sides where replaced with redesigned parts so that this should not be a future problem on my car.
Note: The dealer provided a loaner the entire two week period. It was an 06 Jetta TDI. I was really impressed with the gas mileage and turbo assisted performance. For the period in my possession the readout was a City/Highway average of 39 mpg! When I inquired, I was informed that you can't buy a 2007 or 2008 TDI because VW couldn't meet the California diesel standards and has a problem with the warrantee of earlier diesels absent the lubrication qualities of the now provided low sulphur diesel fuel.
I think VW SOP is to replace both adjusters at the same time.
No point in pulling the engine and only doing one bank.
And I'm sure they are replacing them with the updated parts.
I'd hope that's the case, but from some of the other buggery and slipshod work that I've witnessed at my dealer's service dept, nothing would surprise me. Hence I'm going to double-check my car's history.
I call them "my" dealer because I'm friends with the parts manager, and one of the service advisers is a pretty agreeable fellow who's taken care of my concerns with bad workmanship in the past.


text:
\section{Introduction}
Genetical genomics experiments have now been routinely conducted to
measure both the genetic variants and the gene expression data on the
same subjects. Such data have provided important insights into gene
expression regulations in both model organisms and humans
[\citet{BreKru05}, \citet{Schetal03}, \citet{CheSpi02}].
Gene expression levels are treated as quantitative traits and are
subject to standard genetic analysis in order to identify the gene
expression quantitative loci (eQTL). However, the genetic architecture
for many gene expressions may be complex due to possible multiple
genetic effects and gene--gene interactions, and poorly estimated
genetic architecture may compromise the inferences of the dependency
structures of genes at the transcriptional level
[\citet{Netetal10}]. For a given gene, typical analysis of such
eQTL data is to identify the genetic loci or single nucleotide
polymorphisms (SNPs) that are linked or associated with the expression
level of this gene. Depending on the locations of the eQTLs or the
SNPs, they are often classified as distal \textit{trans}-linked loci or
proximal \textit{cis}-linked loci [\citet{KenWan03},
\citet{Kenetal06}]. Although such a single gene analysis can be
effective in identifying the associated genetic variants, gene
expressions of many genes are in fact highly correlated due to either
shared genetic variants or other unmeasured common regulators. One
important biological problem is to study the conditional independence
among these genes at the expression level.

eQTL data provide important information about gene regulation and have
been employed to infer regulatory relationships among genes
[\citet{Zhuetal04}, \citet{BinHoe05},
\citet{CheEmmSto07}]. Gene expression data have been used for
inferring the genetic regulatory networks, for example, in the
framework of Gaussian graphical models (\textit{GGM})
[\citet{SchStr05}, \citet{Segetal05}, \citet{LiGui06},
\citet{PenZhoZhu09}]. Graphical models use graphs to represent
dependencies among stochastic variables. In particular, the
\textit{GGM} assumes that the multivariate vector follows a
multivariate normal distribution with a~particular structure of the
inverse of the covariance matrix, called the concentration matrix. For
such Gaussian graphical models, it is usually assumed that the patterns
of variation in expression for a given gene can be predicted by those
of a small subset of other genes. This assumption leads to sparsity
(i.e., many zeros) in the concentration matrix and reduces the problem
to well-known neighborhood selection or covariance selection problems
[\citet{Dem72}, \citet{MeiBuh06}]. In such a concentration
graph modeling framework, the key idea is to use partial correlation as
a~measure of the independence of any two genes, rendering it
straightforward to distinguish direct from indirect interactions. Due
to high-dimensionality of the problem, regularization methods have been
developed to estimate the sparse concentration matrix where a sparsity
penalty function such as the~$L_1$ penalty or SCAD penalty is often
used on the concentration matrix [\citet{LiGui06},
\citet{FriHasTib08}, \citet{FanFenWu09}]. Among these
methods, the coordinate descent algorithm of \citet{FriHasTib08},
named \textit{glasso}, provides a computationally efficient method for
performing the Lasso-regularized estimation of the sparse concentration
matrix.

Although the standard \textit{GGM}s can be used to infer the
conditional dependency structures using gene expression data alone
from eQTL experiments, such models ignore the effects of genetic
variants on the means of the expressions, which can compromise the
estimate of the concentration matrix, leading to both false positive
and false negative identifications of the edges of the Gaussian
graphs. For example, if two genes are both regulated by the same
genetic variants, at the gene expression level, there should not be
any dependency of these two genes. However, without adjusting for
the genetic effects on gene expressions, a link between these two
genes is likely to be inferred. For eQTL data, we are interested in
identifying the conditional dependency among a set of genes after
removing the effects from shared regulations by the markers. Such a
graph can truly reflect gene regulation at the expression level.

In this paper we introduce a sparse conditional Gaussian
graphical model (\textit{cGGM}) that
simultaneously
identifies the genetic variants associated with gene expressions and
constructs a sparse Gaussian graphical model based on eQTL data.
Different from the standard \textit{GGM}s that assume constant means,
the \textit{cGGM} allows the means to depend on covariates or genetic
markers. We consider a set of regressions of gene expression in
which both regression coefficients and the error concentration
matrix have many zeros. Zeros in regression coefficients arise when
each gene expression only depends on a very small set of genetic
markers; zeros in the concentration matrix arise since the gene
regulatory network and therefore the corresponding concentration
matrix is sparse. This approach is similar in spirit to the
seemingly unrelated regression (SUR) model of \citet{Zel62} in
order to improve the estimation efficiency of the effects of genetic
variants on gene expression by considering the residual correlations
of the gene expression of many genes. In the analysis of eQTL data, we
expect sparseness in both the regression coefficients and also the
concentration matrix. We propose to develop a regularized
estimation procedure to simultaneously select the SNPs associated
with gene expression levels and to estimate the sparse concentration
matrix. Different from the original SUR model of \citet{Zel62} that
focuses on improving the estimation efficiency of the regression
coefficients, we focus more on estimating the sparse concentration
matrix adjusting for the effects of the SNPs on mean expression
levels. We develop an efficient coordinate descent algorithm to
obtain the penalized estimates and present the asymptotic results
to justify our estimates.

In the next sections we first present the formulation of the
\textit{cGGM} for both the mean gene expression levels and the concentration
matrix. We then present an efficient coordinate descent algorithm to
perform the regularized estimation of the regression coefficients
and concentration matrix. Simulation experiments and asymptotic
theory are used to justify our proposed methods. We apply the
methods to an analysis of a yeast eQTL data set. We conclude the
paper with a brief discussion. All the proofs are given in the
supplementary material [\citet{YinLi11}].

\section{The sparse \textit{cGGM} and penalized likelihood estimation}
\subsection{The sparse conditional Gaussian graphical model}
$\!\!$Suppose
we have~$n$
independent observations from a population of a vector $(\by^\prime,
\mathbf x^\prime)$, where $\by$ is a~$p\times1$ random vector of gene
expression levels of $p$ genes and $\mathbf x$ is a~$q\times1$ vector of
the numerically-coded SNP genotype data for $q$ SNPs. Furthermore,
suppose that conditioning on $\mathbf x$, $\by$ follows a multivariate
normal distribution,
\begin{equation}\label{SSUR}
\by|\mathbf x \sim\mathcal{N}(\Gamma\mathbf x, \Sigma),
\end{equation}
where $\Gamma$ is a $p\times
q$ coefficient matrix for the means and the covariance matrix
$\Sigma$ does not depend on $\mathbf x$. We are interested in both the
effects of the SNPs on gene expressions $\Gamma$ and the
conditional independence structure of~$\by$ adjusting for the
effects of $\mathbf x$, that is, the Gaussian graphical model for
$\by=(\by_1,\ldots, \by_p)$ conditional on $\mathbf x$. In applications
of gene expression data analysis, we are more interested in the
concentration matrix $\Theta=\Sigma^{-1}$ after their shared
genetic regulators are accounted for. It has a nice interpretation
in the Gaussian graphical model, as the $(i, j)$-element
is directly related to the partial
correlation between the $i$th and $j$th components of $\by$ after
their potential joint genetic regulators are adjusted. In the
Gaussian graphical model with undirected graph $(V,E)$, vertices $V$
correspond to components of the vector $\by$ and edges $E = \{e_{ij}
, 1 \le i,j \le p\}$ indicate the conditional dependence among
different components of $\by$. The edge $e_{ij}$ between $\by_i$ and
$\by_j$ exists if and only if $\theta_{ij} \ne0$, where
$\theta_{ij}$ is the $(i, j)$-element of $\Theta$. We emphasize that
in the graph representation of the random variable $\by$, the nodes
include only the genes and the markers are not part of the graph. We
call this the sparse conditional Gaussian graph model (\textit{cGGM})
of the genes.
Hence, of
particular interest is to identify zero entries in the concentration
matrix. Note that instead of assuming a constant mean as in the
standard \textit{GGM}, model (\ref{SSUR}) allows heterogeneous means.

In eQTL experiments, each row of $\Gamma$ and the concentration
matrix $\Theta$ are expected to be sparse and our goal is to
simultaneously learn the Gaussian graphical model as defined by the
$\Theta$ matrix and to identify the genetic variants associated with
gene expressions $\Gamma$ based on $n$ independent observations of
$(\by_i^\prime, \mathbf x_i^\prime), i=1,\ldots, n$. From now on,
we use
$\by_i$ to denote the vector of gene expression levels of the $p$
genes and $\mathbf x_i$ to denote the vector of the genotype codes of the
$q$ SNPs for the $i$th observation unless otherwise specified.
Finally, let $\bX=(\mathbf x_1^\prime,\ldots, \mathbf x_n^\prime)$
be the genotype
matrix and $\bar{\mathbf x}=1/n \sum_{i=1}^n \mathbf x_i$.

\subsection{Penalized likelihood estimation}
Suppose that we have $n$ independent observation $(\by_i^\prime,
\mathbf x_i^\prime)$ from the \textit{cGGM} (\ref{SSUR}). Let
$\bC_Y=1/n\sum_{i=1}^n \by_i\by_i^\prime$, $\bC_{YX}=1/n\times\sum_{i=1}^n
\by_i\mathbf x_i^\prime$ and
$\bC_X=1/n\sum_{i=1}^n \mathbf x_i\mathbf x_i^\prime$.
Then the negative of the logarithm of the likelihood function
corresponding to the \textit{cGGM} model can be written as
\[
l(\Xi)=-\log\det\Theta+
\operatorname{tr}\{\bC_Y \Theta-\bC_{YX} {\Gamma}^\prime\Theta-\Gamma
\bC_{YX}^\prime\Theta+\Gamma\bC_X{\Gamma}^\prime\Theta\},
\]
where $\Xi=(\Theta, \Gamma)$ represents the associated parameters in
the \textit{cGGM}.

The Hessian matrix of the negative log-likelihood
function $l(\Xi)$ is
\[
Hl(\Xi)=
\pmatrix{
\Theta^{-1}\otimes\Theta^{-1} & -2\bC_{YX}\otimes I_p + 2(\Gamma
\bC_X)\otimes I_p\cr
-2\bC_{YX}^\prime\otimes I_p + 2(\bC_X{\Gamma}^\prime)\otimes I_p &
2\bC_X\otimes\Theta}
\]
(see Proposition 1 in the
supplementary material [\citet{YinLi11}], Section~3). In
addition, $l(\Xi)$ is a bi-convex function of $\Gamma$ and $\Theta$.
In words, this means that for any fixed $\Theta$, $l(\Xi)$ is a
convex function of $\Gamma$, and for any $\Gamma$, $l(\Xi)$ is a~convex function of $\Theta$.
When $n> \max(p,q)$, the global minimizer of~$l(\Xi)$ is given
by
\[
\cases{
\tilde{\Theta}^{-1} = \bC_Y-\bC_{YX}\bC_X^{-1}\bC
_{YX}^\prime, \cr
\tilde{\Gamma} = \bC_{YX}\bC_X^{-1}.}
\]

Under the penalized likelihood framework, the estimate of the
$\Gamma$ and $\Sigma$ in model (\ref{SSUR}) is the solution to the
following optimization problem:
\begin{equation}\label{objadap}
\min\biggl\{\operatorname{pl}(\Xi) \equiv\,{-}\,\log
\det
\Theta\,{+}\,\operatorname{tr}(\bS_{\Gamma} \Theta)\,{+}\,\lambda\sum_{s,t} \operatorname{pen}_1(\gamma
_{st})\,{+}\,\rho
\sum_{t,t'}\operatorname{pen}_2(\theta_{tt'})\biggr\},\hspace*{-30pt}
\end{equation}
where $\operatorname{pen}_1(\cdot)$ and
$\operatorname{pen}_2(\cdot)$ denote the generic penalty functions, $\gamma_{st}$ is
the $st$th element of the $\Gamma$ matrix and $\theta_{tt'}$ is the
$tt'$th element of the $\Theta$ matrix, and
\begin{eqnarray*}
\mathbf{S}_{\Gamma} &=& \frac{1}{n}\sum_{i=1}^n(\by_i-\Gamma
\mathbf x_i)(\by_i-\Gamma\mathbf x_i)^\prime\\
&=& \bC_Y-\bC_{YX}{\Gamma}^\prime-\Gamma\bC_{YX}^\prime+\Gamma
\bC_X{\Gamma}^\prime.
\end{eqnarray*}
Here $\rho$ and $\lambda$ are the two
tuning parameters that control the sparsity of the sparse \textit
{cGGM}. We consider in this paper both the Lasso or $L_1$ penalty
function $\operatorname{pen}(x)=|x|$ [\citet{Tib96}] and the adaptive Lasso
penalty function $\operatorname{pen}(x)=|x|/|\tilde{x}|^{\gamma}$ for some
$\gamma>0$ and any consistent estimate of $x$, denoted by
$\tilde{x}$ [\citet{Zou06}]. In this paper we use $\gamma=0.5$.

\subsection{An efficient coordinate descent algorithm for the sparse
\textit{cGGM}}
We present an algorithm for the optimization problem (\ref{objadap})
with Lasso penalty function for $\operatorname{pen}_1(\cdot)$ and $\operatorname{pen}_2(\cdot)$. A
similar algorithm can be developed for the adaptive Lasso penalty
with simple modifications. Under\vadjust{\goodbreak} this penalty function, the
objective function is then
\begin{equation}\label{loglik}
\max\{\log
\det\Theta- \operatorname{tr}(\bS_{\Gamma}
\Theta)-\lambda\|\Gamma\|_1-\rho\|\Theta\|_1\}.
\end{equation}
The
subgradient equation for maximization of the log-likelihood
(\ref{loglik}) with respect to $\Theta$ is
\begin{equation}
\Theta^{-1}-\bS_{\Gamma}-\rho\Lambda= 0,
\end{equation}
where
$\Lambda_{ij}\in \operatorname{sgn}(\Theta_{ij})$. If $\Gamma$ is known,
\citet{BanElGdAs08} and \citet{FriHasTib08} have cast the
optimization problem (\ref{loglik}) as a block-wise coordinate
descent algorithm, which can be formulated as $p$ iterative Lasso
problems. Before we proceed, we first introduce some notation to
better represent the algorithm. Let $\bW$ be the estimate of
$\Sigma$. We partition $\bW$ and $\bS_{\Gamma}$ as
\[
\bW=\pmatrix{
\bW_{11} & w_{12}\vspace*{2pt}\cr
w_{12}^\top& w_{22}},\qquad
\bS_{\Gamma}=
\pmatrix{
\bS_{11} & s_{12}\vspace*{2pt}\cr s_{12}^\top
& s_{22}}.
\]
\citet{BanElGdAs08} show that the solution for $w_{12}$
satisfies
\[
w_{12}=\mathop{\arg\min}_y (y^T W_{11}^{-1}y\dvtx
\|y-s_{12}\|_{\infty} \le\rho),
\]
which by convex duality is
equivalent to solving the dual problem
\begin{equation}\label{glasso_step}
\hat\beta=\mathop{\arg\min}_{\beta}\biggl(\frac{1}{2}
\|\bW_{11}^{1/2}\beta-b\| ^2 + \rho\|\beta\|_1 \biggr),
\end{equation}
where $b=\bW_{11}^{-1/2}s_{12}$. Then
the solution for $w_{12}$ can be obtained via the solution of the
Lasso problem
and
through the relation $w_{12}=\bW_{11}\beta$. The estimate for
$\Theta$ can also be updated in this block-wise manner
very efficiently through the relationship $\bW\Theta=\mathbf{I}$
[\citet{FriHasTib08}].

After we finish an updating cycle for $\Theta$, we can proceed to
update the estimate of $\Gamma$. Since the object function of our
penalized log-likelihood is quadratic in $\Gamma$ given $\Theta$,
we can use a direct coordinate descent algorithm to get the penalized
estimate of $\Gamma$. For the ($i$, $j$)th entry of $\Gamma$,
$\gamma_{ij}$, note that for an arbitrary $q\times p$ matrix
$\mathbf{A}$, $\partial\operatorname{tr}(\Gamma A)/\partial
\gamma_{ij}=a_{ji}=e_j^\prime\mathbf{A} e_i$, where $e_j$ and $e_i$
are the corresponding base vector with $q$ and $p$ dimensions. So
the derivative of the penalized log-likelihood function
(\ref{loglik})with respect to $\gamma_{ij}$ is
\begin{equation}\label{eq_f}
2e_j^\prime(\bC_X {\Gamma}^\prime\Theta)e_i+\lambda
\operatorname{sgn}(\gamma_{ij})-2e_j^\prime(\bC_{YX}^\prime\Theta)e_i,
\end{equation}
where function $\operatorname{sgn}$ is defined as
\[
\operatorname{sgn}(t)=\cases{
1, &\quad if $t>0$,\cr
0, &\quad if $t=0$, and \cr
-1, &\quad if $t<0$.}
\]

Setting   equation (\ref{eq_f}) to zero, we get the updating
formula for $\gamma_{ij}$:
\begin{equation}\label{update_f}
\hat\gamma_{ij}=\operatorname{sgn}(g_{ij})\frac{(|g_{ij}|-\lambda
)_+}{2(e_j^\prime
\bC_X e_j)(e_i^\prime\Theta e_i)},
\end{equation}
where\vspace*{1pt}
$g_{ij}=2\{e_j^\prime(\bC_{YX}^\prime\Theta)e_i+(e_j^\prime
\bC_X e_j)(e_i^\prime\Theta e_i)\tilde{\gamma}_{ij}-e_j^\prime
(\bC_X \tilde{\Gamma}^\prime\Theta)e_i\}$ and $\tilde{\Gamma}$,
$\tilde{\gamma}_{ij}$ are the estimates in the last step of the
iteration.

Taking these two updating steps together, we have the following
coordinate descent-based regularization algorithm to fit the sparse
\textit{cGGM}:\vspace*{8pt}

\textit{The Coordinate Descent Algorithm for the sparse \textit{cGGM}.}
\begin{longlist}[(1)]
\item[(1)] Start with $\Gamma=\bC_{YX}\bC_X^{-1}$ and
$\bW=\bC_Y-\bC_{YX}\bC_X^{-1}\bC_{YX}^\prime+\rho I$. If $\bC_X$ is
not invertible, use $\Gamma=0$ and $\bW=\bC_Y+\rho I$ instead.
\item[(2)] For each $j=1, 2,\ldots, p$, solve the Lasso problem
(\ref{glasso_step}) under the current estimate of $\Gamma$. Fill in
the corresponding row and column of $\bW$
using $w_{12}=\bW_{11}\hat\beta$. Update $\hat\Theta$.
\item[(3)] For each $i=1, 2,\ldots, p$, and $j=1, 2,\ldots, q$
update each entry
$\hat\gamma_{ij}$ in $\hat\Gamma$ using the formula
(\ref{update_f}), under the current estimate for $\Theta$.
\item[(4)] Repeat step (2) and step (3) until convergence.\vspace*{1pt}
\item[(5)] Output the estimate $\hat\Theta$, $\hat\bW$ and $\hat
\Gamma$.
\end{longlist}

The adaptive version of the algorithm can be derived in the same
steps with adaptive penalty parameters and is omitted here. Note
that when $\Gamma=0$, this algorithm simply reduces to the \textit
{glasso} or the adaptive \textit{glasso} (\textit{aglasso}) algorithm of
\citet{FriHasTib08}. A similar algorithm was used in
\citet{RotLevZhu10} for sparse multivariate regressions.
Proposition 2 in the
supplementary material [\citet{YinLi11}] proves that the above
iterative algorithm for minimizing $\operatorname{pl}(\Xi)$ with respective to
$\Gamma$ and $\Theta$ converges to a stationary point of $\operatorname{pl}(\Xi)$.

While the iterative algorithm reaches a stationary point of
$\operatorname{pl}(\Xi)$, it is not guaranteed to reach the global minimum. Since
the objective function of the optimization problem (\ref{objadap})
is not always convex in $(\Gamma,\Theta)$, it is convex in either
$\Gamma$ or $\Theta$ with the other fixed. There are potentially
many stationary points due to the high-dimensional nature of the
parameter space. We also note a few straightforward properties of
the iterative procedure, namely, that each iteration monotonically
decreases the penalized negative log-likelihood and the order of
minimization is unimportant. Finally, the computational complexity
of this algorithm is $O(pq)$ plus the complexity of the \textit{glasso}.

\subsection{Tuning parameter selection}

The tuning parameters $\rho$ and $\lambda$ in the penalized
likelihood formulation (\ref{objadap}) determine the sparsity of the
\textit{cGGM} and have to be tuned. Since we focus on estimating the
sparse precision matrix and the sparse regression coefficients, we
use the Bayesian information criterion (BIC) to choose these two
parameters. The BIC is defined as
\[
\operatorname{BIC}(\hat\Theta,\hat\Gamma)=-n\log(|\hat
\Theta|)+n\operatorname{tr}(\hat\Theta
S_{\hat\Gamma})+\log(n)(s_n/2+p_n+k_n),
\]
where $p_n$ is the dimension of $\by$, $s_n$ is the number of
nonzero off-diagonal elements of $\hat\Theta$ and $k_n$ is the number of
nonzero elements of $\hat\Gamma$. The BIC has been shown to
perform well for selecting the tuning parameter of the penalized
likelihood estimator [\citet{WanLiTsa07}] and has been applied
for tuning parameter selection for \textit{GGMs} [\citet{PenZhoZhu09}].

\section{Theoretical properties}
Sections 4 and 5 in the
supplementary material [\citet{YinLi11}] state and prove
theoretical properties of the proposed penalized estimates of the
sparse \textit{cGGM}: its asymptotic distribution, the oracle
properties when $p$ and $q$ are fixed as $n\rightarrow\infty$ and
the convergence rates and sparsistency of the estimators when
$p=p_n$ and $q=q_n$ diverge as $n\rightarrow\infty$. By
sparsistency, we mean the property that all parameters that are zero
are actually estimated as zero with probability tending to one [\citet{LamFan09}].

We observe that the asymptotic bias for $\hat\Theta$ is at the same
rate as \citet{LamFan09} for sparse \textit{GGM}s, which is
$(p_n+s_n)/n$ multiplied by a~logarithm factor $\log p_n$, and goes
to zero as long as $(p_n+s_n)/n$ is at a~rate of $O\{(\log
p_n)^{-k}\}$ with some $k>1$. The total square errors for
$\hat\Gamma$ are at least of rate $k_n/n$ since each of the $k_n$
nonzero elements can be estimated with rate $n^{-1/2}$. The price we
pay for high-dimensionality is a logarithmic factor $\log(p_nq_n)$.
The estimate $\hat\Gamma$ is consistent as long as $k_n/n$ is at a
rate of $O\{(\log p_n+\log q_n)^{-l}\}$ with some $l>1$.

\section{Monte Carlo simulations}
In this section we present results from Monte Carlo simulations to
examine the performance of the proposed estimates and to compare it
with the \textit{glasso} procedure for estimating the Gaussian
graphical models using only the gene expression data. We also
compare the \textit{cGGM} with a modified version of the neighborhood
selection procedure of \citet{MeiBuh06},
where each gene is regressed on other genes and also the genetic
markers using the Lasso regression, and a link is defined between
gene $i$ and $j$ if gene $i$ is selected for gene $j$ and gene $j$
is also selected by gene $i$. We call this procedure the multiple
Lasso (\textit{mLasso}). Note that the \textit{mLasso} does not provide
an estimate of the concentration matrix. For adaptive procedures,
the MLEs of both the regression coefficients and the concentration
matrix were used for the weights when $p<n$ and $q<n$. For each
simulated data set, we chose the tuning parameters $\rho$ and
$\lambda$ based on the BIC.

To
compare the performance of different estimators for the
concentration matrix, we used the quadratic loss function
\[
\mathrm{LOSS}(\Theta, \hat\Theta)=\operatorname{tr}(\Theta^{-1}\hat
\Theta-I)^2,
\]
where $\hat\Theta$ is an estimate of the true concentration matrix
$\Theta$. We also compared $\|\Delta\|_\infty$,
$\tvb\Delta\tvb_\infty$, $\|\Delta\|$ and $\|\Delta\|_F$, where
$\Delta=\Theta-\hat\Theta$ is the difference between the true
concentration matrix and its estimate,
$\|A\|=\max\{\|Ax\|/\|x\|, x \in R^p, x\ne0\}$ is the
operator or spectral norm of a matrix $A$, $\|A\|_{\infty}$ is the
element-wise $l_{\infty}$ norm of a matrix $A$, $\tvb
A\tvb_{\infty}=\max_{1\leq i\leq p} \sum_{j=1}^q |a_{ij}|$
for $A=(a_{ij})_{p\times q}$ is\vspace*{2pt} the matrix $l_{\infty}$ norm of a
matrix $A$, and $\|A\|_F$ is the Frobenius norm, which is the
square-root of the sum of the squares of the entries of~$A$. In
order to compare how different methods recover the true graphical
structures, we considered the Hamming distance between the estimated
and the true concentration matrix, defined as $\operatorname
{DIST}(\Theta,
\hat\Theta)=\sum_{i, j} |I(\theta_{ij}\neq0)-\allowbreak I(\hat\theta
_{ij}\neq
0)|$, where $\theta_{ij}$ is the $(i, j)$th entry of $\Theta$ and
$I(\cdot)$ is the indicator function. Finally, we considered the
specificity (SPE), sensitivity(SEN) and Matthews correlation
coefficient (MCC) scores, which are defined as follows:
\begin{eqnarray*}
\mathrm{SPE}&=&\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{FP}},\qquad
\mathrm{SEN}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}},
\\
\mathrm{MCC}&=&\frac{\mathrm{TP}\times \mathrm{TN}- \mathrm{FP}\times
\mathrm{FN}}{\sqrt{(\mathrm{TP}+\mathrm{FP})(\mathrm{TP}
+\mathrm{FN})(\mathrm{TN}+\mathrm{FP})(\mathrm{TN}+\mathrm{FN})}},
\end{eqnarray*}
where TP, TN, FP and FN are the numbers of true positives, true
negatives, false positives and false negatives in identifying the
nonzero elements in the concentration matrix. Here we consider the
nonzero entry in a sparse concentration matrix as ``positive.''

\subsection{Models for concentration matrix and generation of data}
In the following simulations, we considered a general sparse
concentration matrix, where we randomly generated a link (i.e.,
nonzero elements in the concentration matrix, indicated by
$\delta_{ij}$) between variables $i$ and $j$ with a success
probability proportional to $1/p$. Similar to the simulation setup
of \citet{LiGui06}, \citet{FanFenWu09} and \citet{PenZhoZhu09}, for each link, the corresponding entry in the concentration
matrix is generated uniformly over $[-1, -0.5]\cup[0.5, 1]$. Then
for each row, every entry except the diagonal one is divided by the
sum of the absolute value of the off-diagonal entries multiplied by
1.5. Finally, the matrix is symmetrized and the diagonal entries are
fixed at 1. To generate the $p\times q$ coefficient matrix
$\Gamma=(\gamma_{ij})$, we first generated a $p\times q$ sparse
indicator matrix $\Delta=(\delta_{ij})$, where $\delta_{ij}=1$ with
a probability proportional to $1/q$. If $\delta_{ij}=1$, we
generated $\gamma_{ij}$ from $\operatorname{Unif}([v_m, 1]\cup[-1, -v_m])$,
where $v_m$ is the minimum absolute nonzero value of $\Theta$
generated.

After $\Gamma$ and $\Theta$ were generated, we generated the marker
genotypes $X=(X_1,\ldots, X_q)$ by assuming $X_i\sim\mBernoulli(1,
\frac{1}{2}),\mbox{ for }i=1,\ldots, q$. Finally, gi\-ven~$\mathbf
x$, we
generated $\by$ the multivariate normal distribution $Y|X \sim
\mathcal{N}(\Gamma X, \Sigma)$. For a given model and a given
simulation, we generated a data set of $n$ \textit{i.i.d.} random vectors
$(X, Y)$. The simulations were repeated 50 times.

\begin{table}
\caption{Comparison of the performances of the \textit{cGGM}, adaptive
\textit{cGGM} (a\textit{cGGM}), graphical Lasso (\textit{glasso}),
adaptive graphical Lasso (a\textit{glasso}) and a modified neighborhood
selection procedure using multiple Lasso (\textit{mLasso}) for models
1--3 when $p<n$ based on 50 replications, where $n$ is the sample size,
$p$ is the number of genes and $q$ is the number of markers. For each
measurement, mean is given based on 50 replications. Simulation
standard errors are given in the supplementary material [Yin and Li
(\protect\citeyear{YinLi11})]}\label{simu.tb2}
\begin{tabular*}{\tablewidth}{@{\extracolsep{\fill}}ld{2.2}cccd{1.2}d{3.2}ccc@{}}
\hline
\multicolumn{1}{c}{} & \multicolumn{5}{c}{\textbf{Estimation of}
$\bolds{\Theta}$} &
\multicolumn{4}{c@{}}{\textbf{Graph selection}}\\[-4pt]
& \multicolumn{5}{c}{\hrulefill} & \multicolumn{4}{c@{}}{\hrulefill}\\
\textbf{Method} & \multicolumn{1}{c}{\textbf{LOSS}}
& \multicolumn{1}{c}{$\bolds{\|\Delta\|_\infty}$} &
\multicolumn{1}{c}{$\bolds{\tvb\Delta\tvb_\infty}$} &
\multicolumn{1}{c}{$\bolds{\|\Delta\|}$} &
\multicolumn{1}{c}{$\bolds{\|\Delta\|_F}$} &
\multicolumn{1}{c}{\textbf{DIST}} & \multicolumn{1}{c}{\textbf{SPE}}
& \multicolumn{1}{c}{\textbf{SEN}} & \multicolumn{1}{c@{}}{\textbf{MCC}} \\
\hline
& \multicolumn{9}{c@{}}{Model 1: $(p,q,n)=(100,100,250)$, $\operatorname{pr}(\theta
_{ij}\ne0)=2/p$,
$\operatorname{pr}(\Gamma_{ij} \ne0)=3/q$}\\
[4pt]
\textit{cGGM} & 10.73 & 0.33 & 1.17 & 0.67 & 3.18 & 279.56 & 0.99 & 0.48
& 0.56 \\
\textit{acGGM} & 10.29 & 0.31 & 1.17 & 0.66 & 3.01 &313.48 & 0.99 & 0.42
& 0.50\\
\textit{glasso} & 19.17 & 0.69 & 1.89 & 1.12 & 5.19 &596.12 & 0.97 &
0.24 & 0.21\\
\textit{aglasso} & 17.93 & 0.69 & 1.89 & 1.11 & 4.98 &541.32 & 0.97 &
0.32 & 0.28 \\
\textit{mLasso} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} &\multicolumn{1}{c}{--} &\multicolumn{1}{c}{--} &309.50 & 0.99 & 0.38 & 0.48
\\[4pt]
& \multicolumn{9}{c@{}}{Model 2: $(p, q, n)=(50, 50, 250)$,
$\operatorname{pr}(\theta_{ij}\ne0)=2/p$, $\operatorname{pr}(\Gamma_{ij}
\ne0)=4/q$}\\
[4pt]
\textit{cGGM} & 5.15 & 0.37 & 1.30 & 0.72 & 2.36 & 106.88 & 0.98 &
0.69 &
0.66 \\
\textit{acGGM} & 4.62 & 0.29 & 1.14 & 0.63 & 1.97 & 83.20 & 0.99 &
0.66 &
0.71\\
\textit{glasso} & 13.95 & 0.75 & 2.12 & 1.20 & 4.57 & 391.84 & 0.87 &
0.37 & 0.18\\
\textit{aglasso} & 13.15 & 0.74 & 2.11 & 1.19 & 4.4 & 389.00 & 0.87 &
0.49 & 0.25 \\
\textit{mLasso} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} &185.68 & 0.95 & 0.60 & 0.48
\\[4pt]
& \multicolumn{9}{c@{}}{Model 3: $(p, q, n)=(25, 10, 250)$,
$\operatorname{pr}(\theta_{ij}\ne0)=2/p$,
$\operatorname{pr}(\Gamma_{ij} \ne0)=3.5/q$}\\
[4pt]
\textit{cGGM} & 1.70 & 0.24 & 0.90 & 0.52 & 1.21 & 67.08 & 0.91 & 0.76 &
0.62 \\
\textit{acGGM} & 1.58 & 0.22 & 0.87 & 0.49 & 1.12 & 56.36 & 0.94 &
0.72 &
0.65 \\
\textit{glasso} & 5.97 & 0.65 & 1.99 & 1.12 & 2.77 & 315.84 & 0.43 & 0.73
& 0.12 \\
\textit{aglasso} & 6.05 & 0.65 & 1.98 & 1.12 & 2.78 & 264.30 & 0.54 &
0.65 & 0.14\\
\textit{mLasso} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} &\multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & 111.28 & 0.84 & 0.68 & 0.44 \\
\hline
\end{tabular*}
\end{table}

\subsection{Simulation results when $p<n$ and $q<n$}
We first consider the setting when the sample size $n$ is larger
than the number of genes $p$ and the number of genetic markers $q$.
In particular, the
following three models were considered:

\begin{longlist}[Model 2:]
\item[Model 1:]
$(p,q,n)=(100, 100, 250)$, where $\operatorname{pr}(\theta_{ij}\ne
0)=2/p$,
$\operatorname{pr}(\Gamma_{ij} \ne0)=3/q$;

\item[Model 2:] $(p, q, n)=(50, 50, 250)$, where
$\operatorname{pr}(\theta_{ij}\ne0)=2/p$,
$\operatorname{pr}(\Gamma_{ij} \ne0)=4/q$;

\item[Model 3:] $(p, q, n)=(25, 10, 250)$, where
$\operatorname{pr}(\theta_{ij}\ne0)=2/p$,
$\operatorname{pr}(\Gamma_{ij} \ne0)=3.5/q$.
\end{longlist}

We present the simulation
results in Table \ref{simu.tb2}. Clearly, \textit{cGGM} provided
better estimates (in terms of the defined LOSS function and the four
metrics of ``closeness'' of the estimated and true matrices) of the
concentration matrix over \textit{glasso} for all three models considered
in all measurements. This is expected since \textit{glasso} assumes a
constant mean of the multivariate vector, which is not a
misspecified model. We also observed that the adaptive \textit{cGGM}
and adaptive \textit{glasso} both resulted in better estimates of the
concentration matrix, although the improvements were minimal. This
may be due to the fact that the MLEs of the concentration matrix
when $p$ is relatively large do not provide very informative weights
in the $L_1$ penalty functions.

In terms of graph structure selection, we first observed that
different values of the tuning parameter $\rho$ for the penalty on
the mean parameters resulted in different identifications of the
nonzero elements in the concentration matrix, indicating that the
regression parameters in the means indeed had effects on estimating
the concentration matrix. Table \ref{simu.tb2} shows that for all
three models, the \textit{cGGM} or the adaptive \textit{cGGM} resulted in
higher sensitivities, specificities and MCCs than the \textit{glasso}
or the adaptive \textit{glasso}. We observed that \textit{glasso} often
resulted in much denser graphs than the real graphs. This is
partially due to the fact that some of the links identified by \textit
{glasso} can be explained by shared common genetic variants. By
assuming constant means, in order to compensate for the model
misspecification, \textit{glasso} tends to identify many nonzero
elements in the concentration matrix and result in larger Hamming
distance between the estimate and the true concentration matrix.
The results indicate that by simultaneously considering the
effects of the covariates on the means, we can reduce both false
positives and false negatives in identifying the nonzero elements
of the concentration matrix.

The modified neighborhood selection procedure using multiple Lasso
accounts for the genetic effects in modeling the relationship among
the genes. It performed better than \textit{glasso} or adaptive \textit
{glasso} in graph structure selection, but worse than the \textit{cGGM}
or the adaptive \textit{cGGM}. This procedure, however, did not provide
an estimate of the concentration matrix.

\subsection{Simulation results when $p>n$}

In this section we consider the setting when $p>n$ and simulate
data from the following three models with values of $n$, $p$
and $q$ specified as follows:

\begin{longlist}[Model 4:]
\item[Model 4:]
$(p, q, n)\,{=}\,(1000, 200, 250)$,
$\operatorname{pr}(\Theta_{ij}\,{\ne}\,0)\,{=}\,1.5/p$,
$\operatorname{pr}(\Gamma_{ij}\,{\ne}\,0)\,{=}\,20/q$;

\item[Model 5:] $(p, q, n)\,{=}\,(800, 200, 250)$,
$\operatorname{pr}(\Theta_{ij}\,{\ne}\,0)\,{=}\,1.5/p$,
$\operatorname{pr}(\Gamma_{ij}\,{\ne}\,0)\,{=}\,25/q$;

\item[Model 6:] $(p, q, n)\,{=}\,(400, 200, 150)$,
$\operatorname{pr}(\Theta_{ij}\,{\ne}\,0)\,{=}\,2.5/p$,
$\operatorname{pr}(\Gamma_{ij}\,{\ne}\,0)\,{=}\,20/q$.
\end{longlist}

Note that for all three models, the graph structure is very sparse
due to the large number of genes considered.

Since in this setting we did not have consistent estimates of
$\Gamma$ or $\Omega$, we did not consider the adaptive \textit{cGGM} or
adaptive \textit{glasso} in our comparisons. Instead, we compared the
performance of \textit{cGGM}, \textit{glasso} and the modified
neighborhood selection procedure using multiple Lasso in terms of
estimation of the concentration matrix and graph structure
selection. The performances over 50 replications are reported in
Table \ref{simu.tbl} for the optimal tuning parameters chosen by the
\begin{table}
\caption{Comparison of the performances of the \textit{cGGM}, the
graphical Lasso (\textit{glasso}) and a modified neighbor selection
using multiple lasso (\textit{mLasso}) $\mbox{model } 4\sim \mbox{model } 6$ when $p>n$
based on 50 replications, where $n$ is the sample size, $p$ is the
number of genes and $q$ is the number of markers. For each measurement,
mean is given based on 50 replications. Simulation standard errors are
given in the supplementary material [Yin and Li
(\protect\citeyear{YinLi11})]}\label{simu.tbl}
\begin{tabular*}{\tablewidth}{@{\extracolsep{\fill}}ld{3.2}cccd{2.2}rccd{2.2}@{}}
\hline
\multicolumn{1}{c}{} & \multicolumn{5}{c}{\textbf{Estimation of}
$\bolds{\Theta}$} &
\multicolumn{4}{c@{}}{\textbf{Graph selection}}\\[-4pt]
& \multicolumn{5}{c}{\hrulefill} & \multicolumn{4}{c@{}}{\hrulefill}\\
\textbf{Method} & \multicolumn{1}{c}{\textbf{LOSS}}
& \multicolumn{1}{c}{$\bolds{\|\Delta\|_\infty}$} &
\multicolumn{1}{c}{$\bolds{\tvb\Delta\tvb_\infty}$} &
\multicolumn{1}{c}{$\bolds{\|\Delta\|}$} &
\multicolumn{1}{c}{$\bolds{\|\Delta\|_F}$} &
\multicolumn{1}{c}{\textbf{DIST}} & \multicolumn{1}{c}{\textbf{SPE}}
& \multicolumn{1}{c}{\textbf{SEN}} & \multicolumn{1}{c@{}}{\textbf{MCC}} \\
\hline
& \multicolumn{9}{c@{}}{Model 4: $(p, q, n)=(1000, 200,
250)$,
$\operatorname{pr}(\Theta_{ij}\ne0)=1.5/p$,
$\operatorname{pr}(\Gamma_{ij}\ne0)=20/q$}\\
[4pt]
\textit{cGGM} & 164.22 & 0.59 & 1.81 & 0.97 & 13.48
& 2\mbox{,}414.28 & 1.00 &
0.31 & 0.47 \\
\textit{glasso} & 257.12 & 0.71 & 2.86 & 1.31 & 19.82
& 23\mbox{,}746.98 &
0.98 & 0.08 & 0.02\\
\textit{mLasso}& \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--}
& \multicolumn{1}{c}{--} &\multicolumn{1}{c}{--}
& \multicolumn{1}{c}{--}
&3\mbox{,}886.96 & 1.00 & 0.12 & 0.16 \\
[4pt]
& \multicolumn{9}{c@{}}{Model 5: $(p, q, n)=(800, 200, 250)$,
$\operatorname{pr}(\Theta_{ij}\ne0)=1.5/p$,
$\operatorname{pr}(\Gamma_{ij}\ne0)=25/q$}\\
[4pt]
\textit{cGGM} & 142.30 & 0.75 & 2.30 & 1.20 & 12.82 & 2\mbox{,}341.28
& 1.00 & 0.21 & 0.34 \\
\textit{glasso} & 219.33 & 0.76 & 2.97 & 1.40 & 18.39
& 20\mbox{,}871.44 & 0.97 & 0.07 & 0.02 \\
\textit{mLasso} & \multicolumn{1}{c}{--} &\multicolumn{1}{c}{--}
&\multicolumn{1}{c}{--} & \multicolumn{1}{c}{--} & \multicolumn{1}{c}{--}
& 23\mbox{,}750.04 & 0.96 & 0.61 & 0.19 \\
[4pt]
& \multicolumn{9}{c@{}}{Model 6: $(p, q, n)=(400, 200, 250)$,
$\operatorname{pr}(\Theta_{ij}\neq0)=2.5/p$,
$\operatorname{pr}(\Gamma_{ij}\neq0)=20/q$}\\
[4pt]
\textit{cGGM} & 48.73 & 0.44 & 1.55 & 0.77 & 6.86 & 2\mbox{,}044.52
& 1.00 & 0.05
& 0.21\\
\textit{glasso} & 87.32 & 0.69 & 2.72 & 1.22 & 11.01 & 9\mbox{,}258.92
& 0.95 &
0.03 & -0.01 \\
\textit{mLasso}
& \multicolumn{1}{c}{--} &\multicolumn{1}{c}{--}
&\multicolumn{1}{c}{--} &\multicolumn{1}{c}{--}
&\multicolumn{1}{c}{--} & 2\mbox{,}967.30 & 0.99 & 0.08 & 0.10\\
\hline
\end{tabular*}
\end{table}
BICs. For all three models, we observed much improved estimates of
the concentration matrix from the proposed \textit{cGGM} as reflected
by both smaller $L_2$ loss functions and different norms of the
difference between the true and estimated concentration matrices.
The \textit{mLasso} procedure did not provide estimates of the
concentration matrix.

In terms of graph structure selection, since \textit{glasso} does not
adjust for potential effects of genetic markers on gene expressions,
it resulted in many wrong identifications and much lower
sensitivities and smaller MCCs than the \textit{cGGM}. Compared to
the modified neighborhood selection using multiple Lasso, estimates
from the \textit{cGGM} have smaller Hamming distance and larger MCC
than \textit{mLasso}. In general, we observed that when $p$ is larger
than the sample size, the sensitivities from all three procedures
are much lower than the settings when the sample size is larger. For
models 5 and 6, \textit{mLasso} gave higher sensitivities but lower
specificities than \textit{cGGM} or \textit{glasso}. This indicates that
recovering the graph structure in a high-dimensional setting is
statistically difficult. However, the specificities are in general
very high, agreeing with our theoretical sparsistency result of the
estimates.

\section{Analysis of yeast eQTL data}
To demonstrate the proposed methods, we present results
from the analysis of a data set generated by \citet{BreKru05}. In this experiment, 112 yeast segregants, one from each
tetrad, were grown from a cross involving parental strains BY4716
and wild isolate RM11-1a. RNA was isolated and cDNA was hybridized
to microarrays in the presence of the same BY reference material.
Each array assayed 6,216 yeast genes. Genotyping was performed using
GeneChip Yeast Genome S98 microarrays on all 112 $F_1$ segregants.
These 112 segregants were individually genotyped at 2,956 marker
positions. Since many of these markers are in high linkage
disequilibrium, we combined the markers into 585 blocks where the
markers within a block differed by at most 1 sample. For each block,
we chose the marker that had the least number of missing values as
the representative marker.

Due to small sample size and limited perturbation to the biological
system, it is not possible to construct a gene network for all 6,216
genes. We instead focused our analysis on two sets of genes that are
biologically relevant: the first set of 54 genes that belong to the
yeast MAPK signaling pathway provided by the KEGG database
[\citet{Kanetal10}], another set of 1,207 genes of the
protein--protein interaction (PPI) network obtained from a previously
compiled set by \citet{Steetal02} combined with protein physical
interactions deposited in the Munich Information center for Protein
Sequences (MIPS). Since the available eQTL data are based on
observational data, given limited sample size and limited perturbation
to the cells from the genotypes, it is statistically not feasible to
learn directed graph structures among these genes. Instead, for each of
these two data sets, our goal is to construct a conditional independent
network among these genes at the expression levels based on the sparse
conditional Gaussian graphical model in order to remove the false links
by conditioning on the genetic marker information. Such graphs can be
interpreted as a projection of true signaling or a protein interaction
network into the gene space [\citet{BraFueMen02}, \citet{Kon}].

\subsection{Results from the \textit{cGGM}
analysis of 54 MAPK pathway genes}

The yeast genome encodes multiple MAP kinase orthologs, where Fus3
mediates cellular response to peptide pheromones, Kss1 permits
adjustment to nutrient-limiting conditions and Hog1 is necessary for
survival under hyperosmotic conditions. Last, Slt2/Mpk1 is
required for repair of injuries to the cell wall. A schematic plot
of this pathway is presented in Figure \ref{KEGG}. Note that this
graph only presents our current knowledge about the MAPK signaling
pathway. Since several genes such as Ste20, Ste12 and Ste7 appear at
multiple nodes, this graph cannot be treated as the ``true graph''
for evaluating or comparing different methods. In addition, although
some of the links are directed, this graph does not meet the
statistical definition of either a directed or undirected graph.
Rather than trying to recover the MAPK pathway structure, we chose
this set of 54 genes on the MAPK pathway to make sure that these
genes are potentially dependent at the expression level.

\begin{figure}

\includegraphics{494f01.eps}

\caption{The yeast MAPK pathway from the KEGG database
\protect\href{http://www.genome.jp/kegg/pathway/sce/sce04011.html}{http://www.genome.jp/}
\href{http://www.genome.jp/kegg/pathway/sce/sce04011.html}{kegg/pathway/sce/sce\textit{04011}.html}.}
\label{KEGG}
\end{figure}

For each of the 54 genes, we first performed a linear regression
analysis for the gene expression level using each of the 585 markers
and selected those markers with a $p$-value of 0.01 or smaller. We
observed a total of 839 such associations between the 585 markers and
54 genes, indicating strong effects of genetic variants on expression
levels. We further selected 188 markers associated with the gene
expression levels of at least two out of the 54 genes, resulting in a
total of 702 such associations. In addition, many genes are associated
with multiple markers [see Figure \ref{MAPK}(a)]. This indicates that
many pairs of genes are regulated by some common genetic variants,
which, when not taken into account, can lead to false links of genes at
the expression level.

\begin{figure}
\begin{tabular}{@{}c@{}}

\includegraphics{494f02a.eps}
\\
(a)\\[4pt]

\includegraphics{494f02b.eps}
\\
(b)
\end{tabular}
\caption{Analysis of yeast MAPK pathway. \textup{(a)} Association between
188 markers and 54 genes in the MAPK pathway based on simple
regression analysis. Black color indicates significant association
at $p$-$\mbox{value}<0.01$. \textup{(b)} The undirected graph of 43 genes
constructed based on the \textit{cGGM}.}
\label{MAPK}
\end{figure}

We applied our proposed \textit{cGGM} on this set of 54 genes and 188
markers and used the BIC to choose the tuning parameters. The BIC
selected $\lambda=0.28$ and $\rho=0.54$. With these tuning
parameters, the \textit{cGGM} procedure selected 188 nonzero elements
of the concentration matrix and therefore 94 links among these 54
genes. In addition, under the \textit{cGGM} model, 677 elements of the
regression coefficients $\Gamma$ are not zero, indicating the SNPs
have important effects on the gene expression levels of these genes.
The numbers of SNPs associated with the gene expressions range
from 0 to 17 with a mean number of 4. Figure \ref{MAPK}(b) shows
the undirected graph for 43 linked genes on the MAPK pathway based
on the estimated sparse concentration matrix from the \textit{cGGM}.
This undirected graph constructed based on the \textit{cGGM} can indeed
recover lots of links among the 54 genes on this pathway. For
example, the kinase Fus3 is linked to its downstream genes Dig1,
Ste12 and Fus1. The \textit{cGGM} model also recovered most of the
links to Ste20, including Bni1, Ste11, Ste12, Ste5 and Ste7. Ste20
is also linked to Cdc42 through Bni1. Clearly, most of the links in
the upper part of the MAPK signaling pathway were recovered by \textit
{cGGM}. This part of the pathway mediates cellular response to
peptide pheromones. Similarly, the kinase Slt2/Mpk1 is linked to its
downstream genes Swi4 and Rlm1. Three other genes on this second
layer of the pathway, Fks1, Rho1 and Bck1, are also closed linked.
These linked genes are related to cell response to hypotonic shock.

As a comparison, we applied the \textit{glasso} to the gene expression of
these 54 genes without adjusting the effects of genetic markers on
gene expressions and summarized the results in Table \ref{compare}.
The optimal tuning parameter $\lambda=0.145$ was selected based on
the BIC, which resulted in selection of 341 edges among the 54 genes
(i.e., 682 nonzero elements of the concentration matrix), including
all 94 links selected by the \textit{cGGM}. The difference of the
estimated graph structures between the \textit{cGGM} and \textit{glasso}
can be at least partially explained by the genetic variants
associated with the expression levels of multiple genes. Among these
247 edges that were identified by only the \textit{glasso}, 41 pairs of
genes were associated with at least one genetic variant. The \textit
{cGGM} adjusted the genetic effects on gene expression and therefore
did not identify these edges at the expression levels. Another
reason is that the \textit{glasso} assumes a constant mean vector for
gene expression, which clearly misspecified the model and led to the
selection of more links.

\begin{table}
\caption{Comparison of the links identified by the \textit{cGGM},
modified neighborhood selection using multiple Lasso (\textit{mLasso}),
the graphical Lasso (\textit{glasso}) for the genes of the
MAPK pathway and genes of the protein--protein interaction (PPI)
network. Shown in the table is the number of links that were
identified by the procedure indexed by row but were not identified
by the procedure indexed by column due to sharing of at least one
common genetic marker}\label{compare}
\begin{tabular*}{\tablewidth}{@{\extracolsep{4in minus 4in}}lcc@{}}
\hline
&
\includegraphics{494i04.eps}

&
\includegraphics{494i05.eps}

\\
& \textbf{\textit{cGGM}} & \textbf{\textit{mLasso}} \\[-4pt]
& \multicolumn{2}{c@{}}{\hrulefill}\\
\multicolumn{1}{c}{}&\multicolumn{2}{c@{}}{\textbf{MAPK
pathway (PPI network)}}\\
\hline

\includegraphics{494i01.eps}

\textit{cGGM} & -- & 0 (0)\hphantom{0}\\

\includegraphics{494i02.eps}

\textit{mLasso} & 10 (218)\hphantom{0,}& --\\

\includegraphics{494i03.eps}

\textit{glasso} & 41 (1,569) &
2 (66)\\
\hline
\end{tabular*}
\end{table}

We also compared the graph identified by the modified neighborhood
selection procedure of using multiple Lasso. Specifically, each
gene was regressed on all other genes and 188 markers using the
Lasso. Again, the BIC was used for selecting the tuning parameter.
This procedure identified a total of 45 links among the 54 genes. In
addition, a total of 33 associations between the SNPs and gene
expressions were identified. Among these 45 links, 36 were
identified by the \textit{cGGM} and 45 were identified by \textit{glasso}.

\begin{table}
\caption{Summary of degrees of the graphs constructed by three
different methods: \textit{cGGM}, the graphical Lasso (\textit{glasso})
and a modified neighborhood selection using multiple Lasso
(\textit{mLasso}), for the genes of the MAPK pathway and genes of the
protein--protein interaction (PPI) network}
\label{degree}
\begin{tabular*}{\tablewidth}{@{\extracolsep{\fill}}lcd{2.0}d{2.2}d{2.0}
ccd{2.2}d{2.0}@{}}
\hline\multicolumn{1}{c}{} & \multicolumn{4}{c}{\textbf{MAPK pathway}} &
\multicolumn{4}{c}{\textbf{PPI network}} \\[-4pt]
& \multicolumn{4}{c}{\hrulefill} & \multicolumn{4}{c@{}}{\hrulefill}\\
\textbf{Method} & \multicolumn{1}{c}{\textbf{Min}}
& \multicolumn{1}{c}{\textbf{Max}} & \multicolumn{1}{c}{\textbf{Mean}}
& \multicolumn{1}{c}{\textbf{Median}} & \multicolumn{1}{c}{\textbf{Min}}
& \multicolumn{1}{c}{\textbf{Max}} & \multicolumn{1}{c}{\textbf{Mean}}
& \multicolumn{1}{c@{}}{\textbf{Median}}\\
\hline
\textit{cGGM} & 0 & 11 & 3.48 & 3 & 0 & 57 & 19.94 & 21\\
glasso & 5 & 19& 12.63 & 13 & 5 & 60 & 31.46 & 32\\
\textit{mLasso} & 0 & 6& 1.67 & 1 & 0 & 12 & 3.18 & 3\\
\hline
\end{tabular*}
\end{table}

Table \ref{degree} shows a summary of the degrees of the graphs
estimated by these three procedures. It is clear that \textit{glasso}
resulted in a much denser graph than the neighborhood selection and
\textit{cGGM}, and the \textit{mLasso} tends to select few links.

\subsection{Results from the \textit{cGGM} analysis of 1,207 genes on yeast
PPI network}

We next applied the \textit{cGGM} to the yeast protein--protein
interaction network data obtained from a previously compiled set by
\citet{Steetal02} combined with protein physical interactions
deposited in MIPS. We further selected 1,207 genes with variance
greater than 0.05. Based on the most recent yeast protein--protein
interaction database BioGRID [\citet{Staetal11}], there are a
total of 7,619 links among these 1,207 genes. The BIC chose
$\lambda=0.34$ and $\rho=0.43$, which resulted in selection of 12,036
links out of a total of 727,821 possible links, which gives a sparsity
of 1.65\%. Results from comparisons with the two other procedures are
shown in Table \ref{compare}. The \textit {glasso} without adjusting
for the effects of genetic markers resulted in a total of 18,987 edges
with an optimal tuning parameter $\lambda=0.22$. There were 9,854 links
that were selected by both procedures. Again \textit{glasso} selected a~lot more links than the \textit{cGGM}; among the links that were
identified by the \textit{glasso} only, 1,569 pairs are associated with at
least one common genetic marker (see Table \ref{compare}), further
explaining that some of the links identified by gene expression data
alone can be due to shared comment genetic variants.

The modified neighborhood selection procedure \textit{mLasso}
identified only 1,917 edges with $\lambda=0.42$, out of which 1,750
were identified by the \textit{cGGM} and 1,916 were identified by the
\textit{glasso}. There was a common set of 1,749 links that were identified
by all three procedures. A summary of the degrees of the graphs
estimated by these three procedures is given in Table \ref{degree}.
We observe that the \textit{glasso} gave a much denser graph than the other
two procedures, agreeing with what we observed in simulation
studies.

If we treat the PPI of the BioGRID database as the true network
among these genes, the true positive rates from \textit{cGGM}, \textit
{glasso} and the modified neighborhood selection procedure were 0.067,
0.071 and 0.019, respectively, and the false positive rates were
0.016, 0.026 and 0.0025, respectively. The MCC scores from \textit
{cGGM}, \textit{glasso} and the modified neighborhood selection
procedure were 0.041, 0.030 and 0.033, respectively. One reason for
having low true positive rates is that many of the protein--protein
interactions cannot be reflected at the gene expression level.
Figure \ref{hist}(a) shows the histogram of the correlations of
\begin{figure}
\begin{tabular}{@{}cc@{}}

\includegraphics{494f03a.eps}
 & \includegraphics{494f03b.eps}\\
(a) & (b)\\[4pt]

\includegraphics{494f03c.eps}
 & \includegraphics{494f03d.eps}\\
(c) & (d)
\end{tabular}
\caption{Histograms of marginal correlations for pairs of linked genes
based on BioGRID \textup{(a)} and linked genes identified by
\textit{cGGM} \textup{(b)}, \textit{glasso} \textup{(c)} and a modified
neighborhood selection procedure (\textit{mLasso}) \textup{(d)}.}
\label{hist}
\end{figure}
genes that are linked on the BioGRID PPI network, indicating that
many linked gene pairs have very small marginal correlations. The
Gaussian graphical models are not able to recover these links.
Figure~\ref{hist} plots (b)--(d) show the marginal correlations of
the genes pairs that were identified by \textit{cGGM}, \textit{glasso} and
\textit{mGlasso}, clearly indicating that the linked genes identified
by the \textit{cGGM} have higher marginal correlations. In contrast,
some linked genes identified by \textit{glasso} have quite small
marginal correlations. Another reason is that the PPI represents the
marginal pair-wise interactions among the proteins rather than the
conditional interactions.\looseness=1

\section{Conclusions and discussion}
We have presented a sparse conditional Gaussian graphical model for
estimating the sparse gene expression network based on eQTL data in
order to account for genetic effects on gene expressions. Since
genetic variants are associated with expression levels of many
genes, it is important to consider such heterogeneity in estimating
the gene expression networks using the Gaussian graphical models. We
have demonstrated by simulation studies that the proposed sparse
\textit{cGGM} can estimate the underlying gene expression networks more
accurately than the standard \textit{GGM}. For the yeast eQTL data set
we analyzed, the standard Gaussian graphical model without adjusting
for possible genetic effects on gene expressions identified many
possible false links that result in very dense graphs and make the
interpretation of the resulting networks difficult. On the other
hand, our proposed \textit{cGGM} resulted in a much sparser and
biologically more interpretable network. We expect similarly good
performance on data from other published sources, such as from
\citet{Schetal03} and \citet{CheSpi02}.

Due to the limits of the gene expression data, one should not expect
to recover completely the true signaling networks since many
dependencies among these genes can be observed only at the protein
or metabolite level. In any global biochemical network such
signaling network or protein interaction network, genes do not
interact directly with other genes; instead, gene induction or
repression occurs through the activation of certain proteins, which
are products of certain genes [\citet{BraFueMen02}, \citet{Kon}]. Similarly, gene transcription can also be affected by
protein-metabolite complexes. Despite these limitations of the gene
expression, it is still useful to abstract the actions of proteins
and metabolites and represent genes acting on other genes in a gene
network [\citet{Kon}]. This gene network is what we aim to learn
based on the proposed \textit{cGGM}. As we observed from our analysis
of the yeast eQTL data, such graphs or gene networks constructed
from the \textit{cGGM} can indeed explain the data and provide certain
biological insights into gene interactions. Such graphs can be
interpreted as a projection of true signaling or protein interaction
network into the gene space [\citet{BraFueMen02}, \citet{Kon}].

We have focused in this paper on estimating the sparse conditional
Gaussian graphical model for gene expression data by adjusting for the
genetic effects on gene expressions. However, we expect that by
explicitly modeling the covariance structure among the gene
expressions, we should also improve the identification of the genetic
variants associated with the gene expressions
[\citet{RotLevZhu10}]. This is in fact the original motivation of
the SUR models proposed by \citet{Zel62}. It would be interesting
to investigate theoretically as to how modeling the concentration
matrix can lead to improvement in estimation and identification of the
genetic variants associated with the gene expression traits.

We used the Gaussian graphical models for studying the conditional
independence among genes at the transcriptional level. Such
undirected graphs do not provide information on causal dependency.
Data from genetic genomics experiments have been proposed to
construct the gene networks represented by directed causal graphs.
For example, \citet{LiuDeLHoe08} and \citet{BinHoe05}
used structural equation modeling and a genetic algorithm to
construct causal genetic networks among genetic loci and gene
expressions. \citet{CNetal10} developed an efficient Markov
chain Monte Carlo algorithm for joint inference of causal network
and genetic architecture for correlated phenotypes. Although
genetical genomics data can indeed provide opportunity for inferring
the causal networks at the transcriptional level, these causal
graphical model-based approaches can often only handle a small number
of transcripts because the number of possible directed graphs is
super-exponential in the number of genes considered
[\citet{ChiHecMee03}]. Regularization methods may provide alternative
approaches to joint modeling of genetic effects on gene expressions
and causal graphs among genes at the expression level.

\section*{Acknowledgments}

We thank the three reviewers and the Editor for many insightful
comments that have greatly improved the presentation of this paper.

\begin{supplement}[id=suppA]
\stitle{Supplemental materials for ``A sparse conditional Gaussian
graphical model for analysis of
genetical genomics data''\\}
\slink[doi,text={10.1214/11-\break
AOAS494SUPP}]{10.1214/11-AOAS494SUPP}
\slink[url]{http://lib.stat.cmu.edu/aoas/494/supplement.pdf}
\sdatatype{.pdf}
\sdescription{The online supplemental materials
include the simulation standard errors of Tables \ref{simu.tb2}
and \ref{simu.tbl}, two
propositions on the Hessian matrix of the likelihood function and
the convergence of the algorithm and the theoretical properties of
the proposed penalized estimates of the sparse \textit{cGGM}: its
asymptotic distribution, the oracle properties when~$p$ and $q$ are
fixed as $n\rightarrow\infty$ and the convergence rates and
sparsistency of the estimators when $p=p_n$ and $q=q_n$ diverge as
$n\rightarrow\infty$. All the proofs are also given in the
supplemental materials.}
\end{supplement}

redpajama_set_name: RedPajamaArXiv


text:
No. 6: Outfielder Jhailyn Ortiz
If there's one Phillies prospect to just dream on, that would definitely be Jhailyn Ortiz. He signed as a 16-year-old for $4 million with an immense amount of raw power but some concern in regards to how he would face live pitching. In his first professional season at 17 years old in the GCL, Ortiz showed that power with eight home runs and 18 extra-base hits in 47 games, but his average was a meager .231.
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This year in short-season Williamsport, Ortiz continued to hit for power while showing a drastic improvement in his hit tool. He had a .302 average and showed the ability to hit both fastballs and off-speed pitches. Ortiz employed his power in both directions, hitting plenty of home runs and doubles to right field.
Ortiz will always be a high-strikeout hitter with a 25.1 percent strikeout rate.
It should be noted that he had an above-average 9.6 percent walk rate this year. Combined with his power output, his high strikeout total shouldn't be too much of a worry.
Next: Roy Halladay lived life as an ace
Ortiz is bound for Low-A Lakewood next year as a 19-year-old. It will be a big test to see how much he can still hit as he moves up the minor-league ladder. If he can maintain the steady approach he showed this year, there shouldn't be too much of an issue.