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Members of the SWAT team who apprehended Boston bombing suspect #2 from the boat he was hiding in spoke to Anderson Cooper in their first national interview. They provided extensive details on what happened during the tense standoff.
It's important to note that the police officers from the Massachusetts Bay Transportation Authority SWAT team insist they are not heroes and refuse to take credit for capturing Dzhokhar Tsarnaev on Friday night. They say his arrest was a team effort involving several agencies.
"He was bleeding pretty bad," Officer Saro Thompson told Anderson about the 19-year-old suspect. While Officer Jeff Campbell told Anderson Tsarnaev was "weak" from the blood loss and wobbling. The SWAT team says after they put the suspect in handcuffs, they didn't know if the boat had explosives on board so they "all ran like hell" to get away from it.
Tsarnaev's arrest capped off a tragic and terrifying week in Boston. The twin bombings during Monday's Boston Marathon turned "a beautiful day into chaotic hell," said Officer Campbell.
The drama continued early Friday morning when members of the SWAT team were involved in a massive shootout with the bombing suspects, after they allegedly carjacked a man in Cambridge, which led to a car chase into Watertown. "It was almost like we were in a movie… it was surreal," Sgt. Detective Sean Reynolds told Anderson. When the bullets stopped flying, bombing suspect #1, Tamerlan Tsarnaev was dead. The 26-year-old was Dzhokhar's brother.
MBTA Transit Police Officer Richard "Dick" Donohue was shot and severely injured during a gun battle with the suspects. If you'd like to help his family, you can find more information at http://www.officerricharddonohue.com/
Post by: Anderson Cooper
Filed under: Boston Marathon Attack
Anderson Cooper goes beyond the headlines to tell stories from many points of view, so you can make up your own mind about the news. Tune in weeknights at 8 and 10 ET on CNN.
Questions or comments? Send an email
Want to know more? Go behind the scenes with AC361°


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Thursday, May 23rd, 2013. CD12.
At my dildo-cam appointment this morning, I was pleasantly surprised to find that I have one plump follie (who I have subsequently named Dudley, if you're interested) measuring around 20mm. I also have a couple of little guys on the left measuring 15 and 13mm, but the doc was doubtful that they'd catch up much before Saturday.
Oh right. I suppose I should let you know what we're doing…
So we also decided to go forward with an IUI on Saturday. This cycle hasn't been ideal in my mind, but the doctor thought it looked pretty great. I would have liked more than one mature follicle, but hey – it only takes one, right?
The husband and I will drive up on Saturday morning for his "appointment", and then go have a nice breakfast in Ann Arbor somewhere. After that, we'll go back for my baby-batter injection, lie on the table with my hips in the air for 20 minutes, and then head out to the cottage for some rest and relaxation.
And then in two weeks, we'll be pregnant. RIGHT?!
Fingers are crossed for that part, anyway.
One thing I'm a little concerned about is the timing of the IUI… And yes, I knoooooow that I shouldn't question the doctors, especially since they were right the last time I freaked out about my sad, lagging follies and thin-ish uterine lining (which caught up to 12.5, by the way!), but it's really hard not to question their 36 hour rule.
I am supposed to trigger tonight around bedtime, and the IUI is scheduled for around 9am on Saturday morning… In past IUI cycles, I've triggered anywhere from 12 to 36 hours before the IUI. The shorter timeframes were because my labs apparently showed that I was trying to ovulate on my own, but I always feel like I ovulate around 24 hours after my trigger.
I could be totally wrong, of course, and may or may not be basing much of this assumption on my BBT, which I have been told is not accurate once you've triggered.
Still though… Can anyone out there ease my mind about trigger timing? Are the broad majority of women triggering and then ovulating 36 hours after – no earlier, no later? That does not seem plausible to me, but it's what I'm being led to assume.
Either way, the husband and I will ensure that our bases are covered, timing-wise. We'll take matters into our own hands (heh) at home tonight, IUI on Saturday morning, and we'll attempt a bit more "intervention" Saturday night and Sunday.
You know, just to be sure Dudley doesn't get away.
So anyway, that's what's going on all up in my business.
What's new with you? 🙂

subset: commoncrawl


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The Mean Value Theorem
Here's a nice technical result we may have call for from time to time: a higher-dimensional version of the differential mean value theorem. Remember that this says that if we've got a function continuous on the closed interval and differentiable on its interior, there is some point in the middle where the derivative of the function is the same as the average — the mean — rate of change of the function over the interval. In more than one dimension we're going to modify this a bit to make it clearer what it means.
First of all, instead of talking about the closed interval , we're going to use the closed straight line segment. That is, the collection of all the points between and in a straight line, and including the endpoints. We first look at the total displacement from one point to the other. Then we start at and move some portion of this displacement towards . That is, the closed line segment consists of all points of the form for in the closed interval . Setting gives us the point , and gives us the point . Similarly, the open line segment consists of all points of the form for in the open interval .
Next, we have to be clear about the average rate of change. As we move from to , the value of the function changes by . It takes a displacement of to get there, so on average the rate of change is
Finally, we don't just have a single value for the instantaneous rate of change, we have a differential . But we can use it to find directional derivatives. Specifically, we'll consider the derivative of in the direction pointing from to . We'll pick out this direction with the unit vector we get by normalizing the displacement
So the mean value theorem will tell us that if is differentiable in some open region that contains the whole closed line segment . Then there is some point in the open line segment so that the average rate of change of from to is equal to the directional derivative of at in the direction pointing from to :
or, more simply
We'll get at this by changing to a function of one variable so we can bring the one-dimensional version to bear. To that end, we define for in the closed interval . Then , and we can also show that is differentiable everywhere inside the interval. Indeed, we can evaluate the difference quotient
Taking the limit as approaches , we find
which exists since is differentiable.
So our old differential mean-value theorem tells us that there is some so that
where is a point in the open line segment .
4 Comments »
[…] theorem that resembles the mean value theorem. And we'll even use an approach like we did for the extension of that result to higher […]
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[…] the ball is convex, the line segment is completely contained within , and so we can bring the mean value theorem to bear. For each component function we can […]
Pingback by Another Lemma on Nonzero Jacobians « The Unapologetic Mathematician | November 17, 2009 |
[…] also in for sufficiently small . Then writing and we find . The mean value theorem then tells us […]
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JPMorgan Chase earnings beat consensus
JP Morgan Chase, the nation's second-largest bank by market value, reported second-quarter earnings of $1.46 a share, vs. $1.29 expected by analysts.
Nevertheless, its earnings and revenue declined from the same period last year. Earnings fell to $5.99 billion vs. $6.5 billion a year earlier, and revenue fell to $25.35 billion.
The massive bank's stock rose 1.71% in pre-market trading on the news.
Like other large banks, JPMorgan Chase faced legal headwinds. The company paid $500 million in legal fees in the second quarter, or about 13 cents a share. Unlike Citigroup, which reported earnings Monday, "They are further along in the legal situation," says Erik Oja, banking industry analyst for S&P capital IQ.
Like Citibank, JPMorgan Chase also saw growth in its key business: Core lending rose 8% from the same time a year ago, and commercial banking rose 9%. But both big banks saw their revenue from trading fall. JPMorgan Chase logged $3.5 billion in bond trading in the second quarter, down 12% from a year previous. Stock trading revenue was down 10%.
Wall Street's expectation for the bank were low: The stock is priced at about 10 times earnings, says Oja, "A few years ago, they were the strongest of the big three banks; now they are the weakest," Oja says.


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Currency hedging cost Japanese companies such as Honda Motor the chance to fully cash in on a weak yen last quarter, raising the risk that investor expectations could outrun earnings.
The near 20 percent fall in the currency since October has been a primary driver of the longest weekly run of gains for the benchmark Nikkei index since 1959.
But exporters may have been caught out by the magnitude of the yen's fall and bought too early, currency traders said.
"The rally is completely driven by hopes rather than facts," said Soichiro Monji, chief strategist at Daiwa SB Investments.
(Read More: Just How Low Will the Yen Go)
"We knew the yen's impact would be limited in October-December. Still I had thought the earnings would be a little bit better."
Analysts say a 1 percent decline in the value of the yen typically boosts corporate Japan's profits by about 1 percent. Auto, steel and electronics firms, all major exporters, reap the biggest benefit.
So they should be doing well in the fallout from Abenomics. New Prime Minister Shinzo Abe's drive for aggressive monetary easing and fiscal stimulus helped push the yen to a 2-1/2 year low of 92.29 to the dollar on Friday.
Japanese shares are trading at more than 13 times forecast earnings, versus 11.6 at the end of September.
But warning signs come from firms like Honda, which booked an unrealised loss on currency derivatives of 54.5 billion yen ($598.5 million) in the fourth quarter, mostly in currency products.
(Read More: )
Honda's chief financial officer Fumihiko Ike told reporters that the company hedged currency trades three month ahead, a common practice among Japanese exporters that means their fourth quarter sales were booked at yen levels near a record high.
Still Cautious
The cheaper yen will likely start filtering through to bottom lines from the January-March quarter, but many Japanese companies remain cautious about earnings.
Honda trimmed its annual net profit forecast unexpectedly, citing poorer-than-expected demand in China and Europe.
Camera and printer maker Canon, which derives 80 percent of its revenue from overseas and is seen as one of the most competitive Japanese firms, reported a fall in quarterly profits in October-December.
Although Canon forecast a 26.6 percent increase in operating profits to 410 billion yen this year, that fell short of analysts' 452.1 billion yen outlook.
Still, the 33-month high for the on Friday is also based on hopes that a weaker yen will revitalise the Japanese economy, not just exports
"No hedge fund wants to miss the debasement of the yen, and the majority sees the Japanese equity market as the most likely best performer in H1," Bank of America-Merrill Lynch said in a note.
But a weaker currency also carries domestic risks, especially in terms of energy costs in a country where almost all fuel is imported.
"A weaker yen will boost our profits but if the yen falls too much, that's also negative because we require a lot of electricity," said Makoto Kubo, executive vice president of Toshiba, which produces flash memory chips among other things.
"It's difficult to say what is the best level but 90 yen per dollar is not so bad."


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Next gen visuals. Old-fashioned gameplay. The PlayStation 4 action-adventure Knack looks better than most video games you've played, but there's a good chance you've played a game like Knack before.
It's not that I want to knock Knack. It's a launch game. Launch games seldom offer more than what Knack offers. You get a game you can show off to friends. You get a game that hints at what new gaming hardware can do. You get a game that feels ready to be supplanted by a richer sequel—or, really, any other game in 2014 or 2015—made by people who are more used to making games for brand-new hardware.
Knack is also a throwback. It's the kind of colorful third-person action game that you don't see from major game creators outside of Nintendo very often. Certainly, the PlayStation has moved on from the PS2 heydey of Jak & Daxter, Ratchet & Clank, and Sly Cooper. Throwbacks are fine, if your character is cool enough and your gameplay is fun enough. Knack's is, if barely.
Knack stars a character of the same name. He is, oddly, a sort of weapon of mass destruction, a brawling beast nurtured and directed by a kindly professor who enlists Knack for a military mission and who turns out to have a Lord of the Rings-style weakness for ultimate power. Happily, the professor's assistant is a boy who is wise beyond his years and, luckily, there's a human vs. goblin war for Knack to punch through. The main bad guy is a human military industrialist who looks a bit like Tony Stark. This is a cartoon world of mean robots and enemy soldiers who disappear rather than die, a world of lost loves who wear pink and an evil henchwoman whose mech suit sports high heels. There's a nice dollop of moral ambiguity to the human-goblin conflict, but most of these characters speak in clichés and possible Star Wars homages.
The character of Knack is nevertheless mightily impressive. Initially, and at the start of many of the game's levels, he's just an orb surrounded by a head, arms, hands, legs and feet. All of his parts are magical relics—little pyramids and cubes and the like. The gimmick of the game is that you, as Knack, can walk around, sucking more relics into your body and swelling Knack from Pygmy size to King Kong. At his maximum size, Knack is a bipedal swarm of relics that the game's creative director Mark Cerny says must be rendered by some 500,000 polygons.
This is Knack at pretty large size, but not quite his max:
I can't help but marvel at Knack's look. What I can do with Knack is less of a marvel. I can punch. I can jump. I can dodge. Knack the game is straightforward character action, a brawler with a tiny bit of platform jumping. Across the game's 13 chapters, you'll enter clearing after clearing, street after street and rooftop after rooftop, encountering enemies who are just standing there waiting for you to punch them or to punch back. Knack can jump, punch and dodge in any direction. He also has a trio of special super attacks that are metered by the energy he collects from yellow crystals scattered throughout the game. His enemies have swords or shields. They toss grenades or shoot balls of energy.
It's all quite standard. If you play the game long enough, it's almost meditative in its repetition and consistency of that flow.
From zone to zone, you'll encounter an enemy or four, do the requisite dodges and jump attacks needed to beat them and then you'll move on. This is, I guess, how many games are designed—killing room after killing room, one after the other. Knack just lays it all bare by not arming Knack with all that many moves and by presenting a game world that is so crisp, so high resolution that you can literally see this design playing out toward the horizon. More primitive, technologically-challenged games would only show you one clearing of enemies at a time, but look past the area where you're brawling and you can see the next area and its waiting enemies. You might even see the one beyond that and the one that you'd won't get to until you horseshoe halfway around the level.
The game does look great. The grass! The trees! The purple crystal bridges! They all look sharp in a resolution and framerate that just can't hold up when you see it in a YouTube clip compared to when you see it live on a PS4.
As good as the environment looks, I wanted Knack's own visual detail, his body of floating relics, to amount to more than a special effect. Too infrequently, that's all it is. Mostly, Knack just gets bigger as you stomp through a level and collect loose relics. Enemies get bigger, too, which diminishes the effect of becoming so large. Only in the game's final chapter did I get to experience an abundance of something I expected to encounter throughout the game: the ability to more or less stomp on certain kinds of enemies who, minutes and many relics earlier, had towered over me.
Knack is at its best when the concept of Knack as a being made of loose objects becomes a gameplay element. In a few areas, for example, Knack can build himself up with logs. Wood Knack is a mighty brawler. His problem is that he's also flammable and therefore no friend to archers armed with flaming arrows. When Wood Knack catches fire, he starts losing body mass piece by piece. Occasionally, Wood Knack will have to walk past a fireplace. When he does, he will catch fire. This can't be avoided and it essentially puts his health bar in gradual decline. As that happens and as pieces burn away, Knack becomes smaller, which in turn makes enemies tougher to fight. That felt fresh, but it is an idea that Knack barely explores.
The game also includes a promising sequence involving a metal Knack and some overhead magnets, another opportunity to play with the idea of a body made up of different severable materials. These insightful moments are too rare and most of Knack is disappointingly routine. Punch. Dodge. Get bigger. Move on.
Cerny says he created Knack to be a family-friendly game and even an entry-level experience for new, young PS4 gamers. There's a co-op mode that lets a second player provide an assist. Given the goal, Knack is surprisingly challenging at normal difficulty. A few sections required me to brute-force my way through to the next checkpoint, relying on amassing yellow crystal energy across multiple attempts and then using Knack's special powers to just smart-bomb through. I was also frustrated by the game's checkpointing, which sometimes knocks the player back to fights that precede areas where you can restore your health in full. Why push the player that far back if you know that they'll restore their health before getting to the part where they failed?
At a PS4 launch event this week, I talked to Cerny about the game's tricky difficulty and, with a smile, he pointed out that older platformers were way more challenging. In the new game, there might only be eight enemies between checkpoints, he said, but in an old game like Crash Bandicoot 2, which he designed, he calculated that there were some 150 challenge points (jumps to be made, enemies to be defeated) between each checkpoint. Yes, Knack is way easier than all that.
The game's difficulty spikes would be more forgivable if Knack's moveset was more interesting. That's the problem with this simpler, old-school approach to gameplay and level design. Keeping a character's move-set svelte, reducing gameplay clutter and adding challenge are all commendable things for a game designer to do. But doing those things leaves the core gameplay nowhere to hide. It must be fun. It must be fun repeatedly. Feel is subjective, and even as I punched and dodged with Knack, I never fell in love with the game's feel. There wasn't the hop of a Mario or the wallop of a Ratchet and Clank gun. There wasn't the effective crowd control of a God of War nor the fluidity of an Arkham game.
Cerny suggested I go back and try to dive toward more enemies. Evasions can feel good in the game, but it still feels like something is missing. Well, funny enough, something was missing. Having reviewed the game offline before the PS4's online network was active, I unfortunately did not get to experience one of the more interesting-sounding systems Cerny put into the game.
I'll tell you about it, though, because it might turn out to make the game more appealing—if you have friends who are also playing the game. It's also one of Knack's fresher, more modern concepts. This online system involves unlocking gadgets that give Knack extra abilities, including a combo meter that I have a hunch would make combat more engaging. Unfortunately, playing the game offline without friends makes the combo meter hard to unlock. To get these added abilities, you have to find treasure chests hidden throughout the game's levels. Open the chest and you get a prize. If you play offline, the game will simply run some math and randomly give you a gadget part or a special crystal. You can combine these with others to make things that either give Knack new abilities or even transform him into new types of Knack (I really wanted to be Vampire Knack!). If you're playing online, the game will still offer you an item, but it will also give you the chance to claim any item that any of your PS4 friends found when they encountered that chest in their copy of the game.
Cerny estimated that an offline playthrough would only give you enough parts to make one or two gadgets out of eight but that an online playthrough should net you more than half. Reader, I wish I'd played this game online. And that you did, too. And that we were friends. Well, PS4 friends, at least.
I can't be mad at a game like Knack. It's pretty. It's mostly traditional. It also could be something much better. It's on a brand-new console and, Super Mario 64 aside, my expectations for games on new systems is sea-bottom low. I like the intent to make something classic and sweet. I wish I had more fun playing it, but I'm happy to have seen so much eye-candy.
Knack is not a game to buy a PS4 for, but it's a game to use on the PS4, one that'll dazzle you with crisp visuals and excite you with its detailed main character. Get it as a showpiece for now if you're getting a PS4. Just don't expect to love it in a year.
To contact the author of this post, write to email@example.com or find him on Twitter @stephentotilo.