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Paralyzed and progressing towards solo sky diving -info on what were doing

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teamshred  (D 422)

Feb 4, 2009, 11:21 AM
Post #76 of 133 (1623 views)
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 Re: [gimpboogie] Paralyzed and progressing towards solo sky diving -info on what were doing [In reply to] Can't Post
Well checkout this online disabled Skydiving manual: http://www.jagworksdesign.com/html/Para%20Manul%20opening%20page.htm
Rod Mack D-422

mdrejhon  (C 3268)

Feb 4, 2009, 3:19 PM
Post #77 of 133 (1610 views)
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Clicky:
Disabled Skydiving Manual

gimpboogie

Mar 2, 2009, 7:32 AM
Post #78 of 133 (1569 views)
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 Re:WINTER SKYDING & update on modifications [In reply to] Can't Post
WINTER SKYDIVING UPDATE & MODIFICATIONS
[from experiences to myself-this MAY be helpful to anyone preparing to dive in the winter,
as the previous posts on this topic shows]

Last months Canpara had an article, somewhat prompted by this discussion,
on nWINTER SKYDIVING.

There are thousands [nit sure of #'s-guessing]of skydivers around the world
who dive in the winters.

Having said that, same here in CANADA-MORE 'POPULAR' in some locations and DZ's then others.
Although many shut down for the winters-financially perhaps best to do so [:?]
but some, like the PARACHUTE SCHOOL OF TORONTO stays open, and Adam flies his plane for a handful of us
perhaps for free at times, to help us 'skydiving addicts' to come out and put ourselves through
experiences which I've seen left people puking, and crying in the cold of their fingers-to people who
admit 'it's damn cold UP THERE, I'M MANIFESTING AGAIN! [as soon as their fingers warm up :)]

I'm one of those paraplegics who would be up in every available load if my health permitted it.
Yet, I got up there a bit this winter-and if some miracle happens, perhaps again before the winter is over/
(perhaps my last, and first winter skydives, who knows-or cares-its TODAY WHAT COUNTS, for its ALL WE TRULY HAVE.

So here are some of the MODIFICATIONS FOR ME, FROM MY 1ST PLAN.

1) MY PANTS, I knew I needed them larger-to fit more layers of warmth under me-for those potential OFF DZ LANDINGS [ODZL from now on]
I'm NOT talking of ANYTHING under there, SPEND THE $ON QUALITY EXPEDITION QUALITY underwear. IT'S$ OF A JUMP TICKETx2, BUT WORTH YOUR LIFE potentially. I haven't heard of anyone dying from OFF Dz landings
due to hypothermia, but im not ba about to be the 1st on that-if i can help it. with paralysis there is
GREATER RISK of frost bite for we feel not areas which easily get back n drop off-toes or fingers :( .
[that's life 'suck it up princess' is what my diving friend says to me- and i love him dearly for it]

I Went with TEMPORARY for now,PAINT BALL PLAYERS PANTS.
REASON" TOUGH MATERIALS, PADDING, WATER RESISTANCE, TOUGH 'WEAR N TEAR' POSSIBILITY-
THEY TAKE A BEATING-better then that pink bunny with the batteries.
BETTER THEN SKI PANTS, SNOWBOARDING PANTS ETC.
due to the above measures, and CHEAPER.

BUT, I MUST MODIFY MY LEG STRAP SYSTEM-FOR ALL MY PANTS [summer or winter], BECAUSE THE CURRENT METHOD IS
STILL A SNAG POTENTIAL I DO NOT WANT TO CONTINUE WITH.
If I have a high speed mal. for some reason-its possible off static line-i saw a guy hanging from his feet'
off the risers spinning pretty fast off a static line-bad exit-but IF I FALL OUT, as I almost felt like
i would once, but my JM REASSURED ME HE HAS ME HELD [and if he can fireman carry me up several
flights, i trust he can hang on to me from my harness as i position myself with all this bulk against a
wind which feels SO MUCH STRONGER-I do not know why, but it does-i'm not imaging,
i felt it each winter jump-it was harder to position to exit and each exit was not as good as
my summer exits were-strap modification for ALL PANTS IS A MUST.

PANTS MUST have MORE PADDING-obvious reason-landings on potentially
rock hard frozen earth-in my case preferably then deep snow-
obvious reason being the difficulty in getting myself out of there
-if i truly had to- i can pack my gear in plastic bags n roll to roadway to
wheelchair, but LUCKILY I HAVE THE PST SPARTANS coming to grab my
gear, bring my chair n drag me back to the warmth [my DZO even passed me
2nd pair of hot packs once when was shivering lots.-skydivers are such
beautiful people in their hearts, why is there such a 'out of control addicted to adrenalin, risks their life for it perspective out therein the
public who do not dive?
I do not understand it,
had no thoughts what so ever of skydivers, as a group, before became one.

anyways, tangent-sorry for my hit in the head problem popping up-say too much, in more ways then one.

PANTS MUST ACCOMODATE MORE CLOTHING underneath, due to the layers required to keep yourself warm
for those 'just incase it goes to hell' landings that we all dread-but are inconveniences of a 10 min.
car ride for the walkers-but could be so dangerous for a para-i may be 'too safety concious' in
the eys of some, but its better then saying, yah go out there, have fun, wear your nicest/coolest/what ever the hell
your 'thing' is clothes and do the highest FF YOU THINK you can handle and just while your added
get used to new clothing, new methods for flying the openings, new eerything right down tothe flare-
so safety-as much as i can think of-others help me think of more-thank to such as Farmer-for his \true
watchfulness of my flying, and landings-talking like a debreif to me-he is respected by all at out our
DZ and him tlking like this to me-when its time giving me shit he does that too-i love
folks like farmer.

okso to m,y situation, an update
& GENERAL INFO FOR WINTER DIVING CONSIDERATIONS FOR SKYDIVERS WITH PARALYSIS:

-pants, as discused.
my jacket is a hunters orange jacket with 'gimpgear' written all over it with the hopes that it wont disappear. [whjo wants one of those lol].

the safety gear which i discussed previously, incase of ODZL needed to be put inmy pants pocket instead of the jacket.
in the jacket it was too bulky just below the handles for cut away and reserve so i did not want to risk them to a factor in not finding my handles in a highspeed mal situation, which is possible even of static line.

My intention is to change the leg lifting straopping sytem -we still do not like the snag potential with them the way they are] so i did not put any such permanent modifications on my winter diving pants-which are paintm\ball pants.

The method I tried to use initially was to have ready made loops in each pocket of the pants and under a functional canopy, after which i would tape out these ready made loops out of the pockets and lift each leg up with my hands placing the loop above my knee and clipping it onto my chest strap.

this became evidently too difficult to do while flying in such cold temps.
windchill would have made my hands a danger to me had i taken off myh gloves to do this-not to mention god forbid i drop a glove-then i would definitely have trouble flaring with totally useless hands.

THUS I HAD TO LAND WITH MY F\LEGS DANGLING DOWNWARDS.
I HAVE SLIGHT CONTRACTURES ON MY KNEES WHICH HELPED to keep my legs in a semi-bent position.
this means a totally new klearning curve to flare.
ineeded to flare like a walking person, and gently aplfa myself onto the ground.

this was fine, but i also had to make sure i landed on the runway.

first time i had the dificulty that i needed to bled off altitudfe due to the cold temps and needing to get down faster.
by the time i was reaching my landing approach at 1000f i was slightly off to the east of our intended landing area-the DZ lol

this means i needed to get back home and use what i got out of my hands for a flare.
i was unable to put my hands completely into the toggles needing to use very new landing technique, with slightly limited grip became a challenge.

I got back home, and landing on the runway is the only optiion for me to land in the safest place.
its always smootest, and clear of snow hyet makes my landings more critical due to bneing totally no cushion from snow, and hard frozen ground.

modifications were:
-pants
-landing pattern and
-landing itself the flare had to be relearned in harness and soimulatuion on our DZ simulator online game. very realistic since it is put on top of our DZ map exactly as you see it.
-must keep orange jacket for visibility but must put safety gear in pant pockets to l\keep jhandles visible.

i will try to post some photos after i resize them for posting.

(This post was edited by gimpboogie on Mar 2, 2009, 8:40 AM)

gimpboogie

Mar 2, 2009, 8:45 AM
Post #79 of 133 (1561 views)
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gimpboogie

Mar 3, 2009, 6:14 PM
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gimpboogie

Apr 20, 2009, 6:54 AM
Post #81 of 133 (1471 views)
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 Re: [gimpboogie] flying Peters gear 1st time myself [In reply to] Can't Post
lots has changed since last posting here. had another systemic infection (ALS seems to be determined to get me -but I'm more determined to get away each time i feel death dripping on the walls-laying there with a central line in my neck wasnt pretty-in SCU it was a visit from Lonnie that reminded me there is much living left to do! -thanks Lonnie for stopping by-that was a VERY long trip for you and your visit mean a HUGE deal to me)

OK PETER the video will go up in a day or so on youtube-of me flying your gear.
i will try to get some photos up here once I re size them.

initial assessment=

* this canopy is sweet to fly!
I LOVE IT!

line twists from risers to slider- and 3 more above the slider-but they just started to untwist on their own.! nothing to do but watch her doing her job.
She responds to minimal input, very easy to use rear risers-again responds well and actually doesn't take as much effort as the reg. student gear I've been flying (solo 270's mostly or navigators)
-I would choose this xp285 over either of them.
Also the container fits beautifully...like it was made for me.

leg snaps are easy for me to put the gear on but for safety's sake my JM wanted quick ties closing the snaps (he felt there was potential for them to come apart-and for me to fall out=this was OK for me-having the quick ties, just makes it so i need to carry cutters to take them off on landing...)

any feedback from anyone on this?

flare is beautiful-smooth.

what a treat to fly this canopy.
As you said, this canopy does penetrate the air well and has more speed then expected-then i ever had from the other two canopies used (or that big boy rig-manta yuck!)

KermieCorleone  (C 39300)

Apr 21, 2009, 4:58 PM
Post #82 of 133 (1443 views)
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 Re: [gimpboogie] flying Peters gear 1st time myself [In reply to] Can't Post

gimpboogie

Apr 23, 2009, 8:34 PM
Post #83 of 133 (1425 views)
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 Re: [gimpboogie] the video is up now [In reply to] Can't Post
Here's the video.

As you may notice, I'm not speaking any more like I was last summers videos....
ALS is starting to show itself a little more....
( I had to turn up the volume on the video quite a bit to hear myself clearly enough-although at the end of the dive I was screaming [my screaming -so no it's not my Bogart imitation)
BUT who can complain, March 28th I left the SCU after battling sepsis
(a central line in my jugular pumping dopamine and kick-ass antibiotics kept my heart rate and blood pressure high enough that after 6 days doc was going to send me to a 'step down' unit- to which I replied that it must mean HOME!... reluctantly he said 'ok, when do you want to go?' NOW! I replied [at 8PM]-his thoughts were more like in a few days-but I got my way and was home just before midnight )

and 22 days later-there I am flying like it never happened...

except my voice-well who needs to hear me anyways, I've been told more then once that I'm the most verbose person these folks had ever met...

but now I have a new 'voice' that I'm learning to use:
DYNAVOX "communication device", which is just a seriously expensive ($8,000! god you can get some NICE gear for that!) hard drive (and only 60 gigs at that ) WITH a touch screen... but it can do some pretty cool stuff-like detect my retina movements, so if I decide to hang around long enough to be a statue in an electric chair-I can just use my eye movements to drive this new beast they gave me-yah I got the electric chair-they insisted saying that 'it wont be long now.... blah, blah,"... yah it wont be long now till I jump off a bridge and live to tell about it. IT'S a matter of mind over matter, as long as I keep believing... I will keep on living.... I BELIEVE SO ANYWAYS and you cant convince me otherwise till I'm gone gimpboogie Jun 3, 2009, 6:10 PM Post #84 of 133 (1372 views) Shortcut  going to the 'dark side' [In reply to] Can't Post ROD MACK (D422) made this web page: Adaptive Skydiving Manual http://www.jagworksdesign.com/html/Para%20skydive%20manual.htm with input from Peter Chapman and Angus Smith. (my former coach Angus and my rigger Peter Chapman) I MUST ADD.... Peter (South Africa-AFF instructor Tonto) did at least 30 AFF jumps the first 10 of which he said he was like in a washing machine... before passing the AFF portion. Dale (New Zealand) who followed after me and Peter-is now on his 11th or 12th AFF and they let him go in FF on his 6th (he tossed with his head down-but didnt complain of the opening upon landing-he's pretty happy!-youtube search Dale Elliott).... The thing is, that if a student with lower limb disabilities ends up on static line then that's how you turn them into B.A.S.E. jumpers! TOSSING gimps on static line-were never going to get through the TTO's the exit is not 'gimp friendly' on static line to begin with-add the TTO's and we go buy B.A.S.E. gear! want to keep them in the skies? GO THROUGH THE AFF WITH TWO INSTRUCTORS and analyze each video seriously and with scrutiny. After the AFF came to an end-I found from scrutinizing the videos two critical issues that went completely unrecognized when it was happening-as there was not sufficient debriefing of these videos. to try to analyze frame by frame what went wrong. (i.e. the 1st AFF its simple to see-'let go of the pilot chute!' the 2nd AFF shouldn't have ever been attempted with one instructor-too early to understand the dynamics that were taken away with the 2nd instructor gone-DO NOT ELIMINATE THE 2ND INSTRUCTOR TOO EARLY!) IF there is difficulty in reaching the pilot chute-FIGURE OUT WHY! frame by frame- you may find out! and possibly correct it.... static line the gimps too soon and they will always be stuck there and start looking for ways to jump without that plane-heck no one ever lets us out low enough as it is! so the "skydive" becomes B.A.S.E. training-packing for it, training for quick toggle grabs- on heading openings- and doing 'what ever' with your canopy skills above 2,000f to practice for..... "what ever", until you enter that dreadfully high 1000f final pattern, which would be interesting if it began at 400f-BUT we have CSPA(or USPA ETC.), and FAA, and DZO's, and other skydivers who frown upon BSR violations for this is skydiving after all- ALL the rules apply... the cliffs start to look good-which is where i;m headed-the antenna's were great \9even with the broken ankles with an off heading opening bringing me to the rock clifs rather then the frozen ice i had hoped to go t0-but what the heck-i too the casts off and went skydiving anyways-being a gimp whose gonna care of know if they are broken) so now ALL my skydiving training is for BASE situations-sure my DZO has yelled at me with a "were you trying to make me sh*t my pants' -NO-just trying to practive for the ONLY world I can jump in- AND HAVE SOMETHING MEANINGFUL-TILL i go in... I KNOW this is not a B.A.S.E. forum (which IS where I 'lurk' now all the time), BUT I THINK tHAT THE EXERIENCES of both DALE AND PETER show that we=the individuals with "lower limb" disabilities MUST have the chance to do MORE AFF jumps then 'typical' because IF NOT we may very well be driven out of skydiving, and turn to the 'dark side'. enough siad-take it seriously.\IF YOU PLAN ON TAKING ON A PROJECT LIKE THIS-GIVE IT TIME, GIVE THE STUDENT AS MANY 'INSTRUCTOR DEPLOY' JUMps AS NEEDED, AND have video for ALL jumps and dont just look at them casually,\serioulsy deconstruct them frame by frame.\\I think what DALES instructors are doing is EXCELLENT! i.e. the webbed glove-the chest mount altimeter I CAN SEE makes a difference- and many other 'little' things \9i.e. after my wind tunnel experience-i never jumped with the leg braces-it was decided that they were not necessary-well a wind tunnel turned down to 80mph is very different then the actual experience of true freefall-it gave inappropriate feedback-and thus ended up in having too soon the 2nd instructor taken away (on the 2nd jump onward I had only one instructor-had \i been able to be in the tunnel with proper wind speed simulation some of these 'issues' would have revealed themselves-not to mention going through the 'practive deploy' situation, \i'm sure that at 120 mph i would have flipped upside down in the tunnel-and we would have had to try to understand WHY.... and hopefully would have figured it out...\ MAYBE i would have become a 'skydiver' but as it stands now-I am a B.A.S.E. JUMPER who uses skydiving skills to hone in on BASEa skills-which I THINK the skydiving world in general would not have wanted to end up being the end resullt for any skydiving student.\ enough said. \ UNLESS something new and interesting happens in the skydiving world-this MAY be the last post here in regards to skydiving-and since this is not a B.A.S.E forum-whatr business do i really have here...|?.... (This post was edited by gimpboogie on Jun 3, 2009, 7:11 PM) grannyinthesky (D 30311) Jun 3, 2009, 6:17 PM Post #85 of 133 (1369 views) Shortcut  Re: [gimpboogie] the video is up now [In reply to] Can't Post Hi Minna, I am always so delighted to see you posting and I am constantly amazed by your exploits. Ever consider coming to Idaho and doing a B.A.S.E. jump of the Perrine Bridge in Twin Falls? I would sure love to meet you sometime. Pat gimpboogie Jun 3, 2009, 7:34 PM Post #86 of 133 (1363 views) Shortcut  Re: [grannyinthesky] the video is up now [In reply to] Can't Post HEY Granny in the skies=nice to hear from you HOW is YOUR jumping going (WE STARTED CLOSE TO EACH OTHER a few yrs ago) yes actually, as soon as our 'super grand caravan' we got an engine upgrade=900hp=cruising speed 190 knots=at top floor 13,500f in 10 min! is gone from here (nov 1st) I got plans to go B.A.S.E. in FL with a new friend-who has 'permission' for an antenna I want to go for-and then I guess I will live like a 'hobo' going from one B.A.S.E site as I can-although IF I end up in CA I may try LODI-apparently as long as your breathing, you can jump there- it seems like an interesting enough challenge-multi lane freeway on one side and vineyards on the rest of the sides-i would hate to land in corn but the vineyard construction is way to sketchy-don't want to have to try it.... wierd isnt it? IN Skydiving I do not wish toi take 'ever incvreasing' risks-sucvh as Lodi would be BUT I WILL jump off anything 240f or higher with a BJ IN A PERIGREEII pro, or quite honestly a FLIK even-but NEVER those 'transition gear'=B.A.S.E GEAR WITH A belly mount reserve-thats playing paintball instead of going to war...\it has nothing to do with each other,....a .b.a.s.e. canopy with a reserve? EITHER GO ALL THE WAY,with both feet,or dont bother.... yah i might get a whole lot of flames-but i dont care- i'm SO FED UP with skydiving in general-its a leisurely roimp in the park compared to what makes my heart pump n beat a little noticveably. yah Idoho was one of the plans.... but it also is one of those things, that in my income bracket )-20,000/yr) travelling is done by hitchiking-lets see if thst briger id sn optyion before the homeland securioty tosses me back avross the border... plesase tell me how your doing...? remember your date of starting-sometime sround 2007=lotd tpo dhsre ;0 (This post was edited by gimpboogie on Jun 3, 2009, 7:51 PM) grannyinthesky (D 30311) Jun 3, 2009, 7:58 PM Post #87 of 133 (1359 views) Shortcut  Re: [gimpboogie] the video is up now [In reply to] Can't Post Yes, you remember right. We did start about the same time. 2007. I just did my 300th jump last weekend and got a nice face full of pie. I didn't do anything spectacular for that jump, but chose to do a solo on a load in our little C-182 with one of my former math students doing her first tandem. That was a different kind of special. (Oh, and she like it so well, she's talking about doing AFF) If you make it to Lodi, I'd sure try to make it there to meet you. I jumped there in March and it is a bit of a different place. The vineyards are pretty intimidating and they are all over the place. On my first jump there, I opened and that was about all I could see below me. I didn't know I could go that far, but I did land in the dz landing area, unlike some unlucky other jumpers. The landing are is nice and big by the way and the freeway isn't really a problem. If you can make it to this part of the country, I'll be glad to do what I can to get you to the bridge or other jumpable areas around here. Although I haven't tried it myself yet, I do know some local BASE jumpers. Keep in touch. gimpboogie Jun 7, 2009, 12:53 AM Post #88 of 133 (1329 views) Shortcut  Re: [grannyinthesky] the video is up now [In reply to] Can't Post thanks granny in the skies, would love to jump with you sometime... wow you really stacking up those jump numbers...holy I just pick a number i like and stick to it when some ask if i skydive, i say nah, i just fall out of the plane... what the heck-its all wonderful everyone of them-they are memorable. today i did a canopy control course with peter chapman-and it sure was worth every second of the 8 or so hrs he put into it. jumping i didnt do-today-too tired n worn out-sometimes life just does that.... oohh well thats ok i can always jump another day-the caravan is only a few minutes away from my bed now... so i just moved to the dropzone-its great to have this grand caravan with 900 ponies in my front yard.. not too bad at all here's a link http://www.youtube.com/...feature=channel_page to show you my new 'ride'... it actually was a video to ahow someone that the prop CAn KILL YOU, and interfering with such things will not only knock your head off, n then you just wont even need your gear anymore-but messing with this lil girl in the air could take her and everyone in it down... -it was a video of some guy walking the wing close to the prop -youtube video-and i sort got into a disucssion with folks who said that even idling the prop is not going fast enough to do much of anything... telling me to go stand near it next time... so made the video to show the size, the slicing power and the astounding thrust this lil girl puts out.... with the hopes that folks can see-yah she can kill yah in a split second if your not watching.... i saw the difference from her-yesterday when a student landed about 100f behind and to the left of her as she was idling and started to roll off for her take off-this student was tossed around quite nicely by simply the turbulance from her thrust-while last yr with her 595 hp she took up 3/4 of the runway to get up, now she takes 1/3 or less... and a few photos of my first jump of this season out of her-yesterday... she's a beauty to exit from compared to that 206 we got.. but this weekend we did our 200,000th load-that was a treat... the media showed up to celebrate our 'special day' and the place was buzzing with folks-now i lay here listening to the rain-which we are whorecast to get for the next 3 days... what the heck-gives me more time to work around the DZ and help out my DZO whose generosity and kindness is beyond explenation... i think im in early retirement now-and can sit right back and wake up to this beautiful caravan sitting in my front yeard-the best elevator to altitude ive ever had... close to home-just grab my gear n go out the door n JUMP (that last photo is my 'Tonto' wave off... I still think of him on the way to altitude-and have begun to internalize my arch-as my way to try to respect him and ALL HE HAS DONE for us para-s to fly the skies-heck I'm flying the gear he taught Peter to fly with, and the pants Tonto developed the cocept for-its almost like recognition for him has become engrained in my exit count-and this is what is making me realize more and more-that it is for the HONOUR of individuals such as him-its my RESPONSIBILITY to fly the skies as safe as I know how-for I'd hate like hell to have him fly by and shake his head and whisper in my ear-you stupid gimp-why the f**K you do that for?' and FOR THE HONOUR OF FUZZYDAVE and ANGUS for helping me get to this place-for taking up this project-and brining me to this place-where I now know my soul is free-even while still wearing this human form-like clothes which eventually get worn n tattered enough that its time to move on... until then-this is why my soul is free... (This post was edited by gimpboogie on Jun 7, 2009, 1:21 AM) Attachments: _MG_5882.JPG (75.4 KB) _MG_5883.JPG (71.5 KB) _MG_5884.JPG (97.8 KB) humanflite (D 99999) Jun 11, 2009, 1:59 PM Post #89 of 133 (1298 views) Shortcut  Re: [gimpboogie] the video is up now [In reply to] Can't Post Sweet pictures and write up Minna Great work. Glad your happy in your new home. Also, your static line exit looks a lot better than some non paralysed students Ive seen!!! kudos gimpboogie Jul 1, 2009, 5:35 PM Post #90 of 133 (1258 views) Shortcut  newest plans-leg braces this time [In reply to] Can't Post well seems we will try FF again. having done a ton of static lines,\ tossed TTO's etc. now the idea is that I WILL WEAR LEG BRACES. last attempts last yr. we had no stiff leg braces-those were soft braces typically used for sprains etc.. with a bit of pool noodle type pipe insulation to keep some stiffness going. this time-we will dig out those stiff locking knee braces-and use them to give my legs stability. next plan is to change the pants, to use the leg straps in an enclosed system,\a BOC type pocket on pants to put straps in for FF, stability issues might be a little different this time-who knows.\the leg braces seem like a good move forward.\ my coach still feels i do not need a system to keep my legs up at the back-so they don't hang down at the hips-like we seen happen with para's and quads. my friend, who broke both his ankles on landing also almost broke his nose during the opening because his legs launched forward with such momentum they hit him in the face. i personally disagree-on the leg straps for the back..\ that is Dale's idea/invention-the leg straps at the back. yes, it's said i have 'MORE hip flexors' but that is an assessment based on last year. this year the hip flexors are not near as functional, but i listen to my coach-to the point that i trust him enough if he thinks its ok without the leg braces like last yr-i will go with just that-no braces-as i did last yr.\ this yr. i feel pretty certain i need the strap at the back of my pants i feel my legs will send me quite an amount of momentum forward during deployment-f not affecting my FF... but we will see. so hard/stiff braces this time is the addition. i hope we don't stop the AFF before we try the back leg straps but will just have to see how it goes. been ill-too ill to do my chores at the DZ or to fly for the last two weeks-that's the longest i've gone without a dive since moving to the DZ. I hope to have my leg strap holder/pockets i will be aable to sew up this week-before the weekend so i can try them out from down low-and see how long, how different it is to fasten the leg straps from having them hidden inside these 'pockets' on my thighs. i've been reluctant to try to FF without the leg straps being fully contained-better then they are with duct tape-as they have been now.\ As well as the leg braces-it's just not worth it-to try it without the stiff/hard leg braces, and would be nice to put the strap on the back of the pants-but who am i to argue what is to go on the ppants-so i will go with these modifications for now. the stiff leg braces certainly is great news for me- now i do not feel like most of my concentration isn't 3/43 focussed on trying to keep my legs 'still' ... AND registered for bridge day, got my new base container in the mail this week- it all seems to feel good despite the illness and infections i have again...\ on a bright side-more so- i got a BED to sleep on now|! yah, a friend whom i fly gliders with stopped by here and took me for a drive for the weekend-we went to the glider club and stopped at a store so I CAN GET A BED- woohoo! sleeping on the floor or in my wheelchair since April is over! now to focus on camping gear for Bridge day and then perhaps a trip to FL (OR come back, and fly with the Caravan pilot to Texas or to Pennsylvania-depending on which he is flying to-on Nov 1st)-then from there the base trips will go on for a few months-hopefully. that's the new developments in skydiving for this gimp, FF with stiff leg braces, is the key-if he tosses me out there without anything but a reserve i would be happy enough with it-that i wont worry much about the leg strap i think i need- my idea had been to incorporate a RSL attachment at the butt area for that last leg strap (to keep my legs from falling downward- taking away my arch-which they do now on their own-the hip flexor muscles certainly have demninished a lot-but heck-if all goes sh*t for sideways i got new base gear-so life will always be well JohnDeere (D License) Jul 7, 2009, 9:03 PM Post #91 of 133 (1178 views) Shortcut  Re: [gimpboogie] newest plans-leg braces this time [In reply to] Can't Post Good luck with the leg braces! Since your talking about Texas and caravan, i guess your talking about the going down to Skydive 35? If you make it down here let me know i would love to meet you. gimpboogie Jul 18, 2009, 10:19 PM Post #92 of 133 (1139 views) Shortcut  Re: [JohnDeere] newest plans-leg braces this time [In reply to] Can't Post Hey, well the Caravan got its new engine in Texas-which is where it MAY go back to (unless it goes to it's 'REAL' home ). sO it wasn't really any other reason I would of ended up in Texas in Nov. That is just a plan, because if I did go with the Caravan, I'd have to come back to Canada after Bridge Day *(I'm in jumper group 20 = jump between 9:30AM-9:40AM). My preference is to live by the edge of my pants as of Bridge Day onward-until then I'll stick to being an altitude whore, (the invitation to Florida idea seems more and more appealing besides-i have no more break cord ...). Now back to skydiving-since were in the skydiving forum I did that 13,500 jump with Angus today, had a bit of an interesting day all day long before that j"interesting"jump. The interesting part came when it became apparent on opening that the left rear riser was routed backwards through the slider-but now I know the trick on how to frix that-just keep letting her fly in that spinner-its a large canopy, take off your show-untile the laces till there is only enough to keep the lace on the show and throw the show over the riser-to drag it down-learn something new everyday! (maybe that was the best advice I got today :) ) The day Started off with switching my Raven modified for BASE canopy into my container with the Vertigo reversed risers & WLO toggles... (I will try to post a photo of that jump-nothing spectacular to see-just a nice 'scenery-beautiful clouds today all day). I have UPT risers but I wanted to leave them in and jump with those WLO toggles. BAD MOVE to leave the Vertigo reverse risers in because I forgot about the rsl connection -oops-got none-after that jump the rig is grounded until i change the UPT risers in-should do it on Tuesday, I'm tired, need to give some energy to cleaning the DZ on Sunday, Monday rest, and back to some rigging Tuesday -(heck I need a few days just to think of what stupidity I can think of for the windy and sh*tty days-maybe some paintball duels off the property, go get drunk and rob corner stores-gosh did I JUST SAY THAT! LOL ok I guess I better not do that now... :P Was hoping to use the WLO toggles on the UPT risers-no go. one set is velcro (vertigo) and the other is a pin release for the toggles (UPT) -no match. SO, decision time came. DO I jump with the student gear I had so much trouble with, OR do I wait it out, rig up my gear to the UPT risers and accept the WLO toggles cant be used. Went with the student gear. I just knew I could do it. Angus said it was my call-I went for it. last load of the day-no tandems just friends and folks I knew well enough to be feeling real good with their energy in the plane. Jason's "LITTLE GIRL" (that freaken 900hp engine is now the little girl on steroids-no time to visualize your dive you hop n pop.) got us to '13,500f' or so faster then Ive ever gone. the dive was with the leg braces-which certainly helped hugely. Angus said my legs stayed in proper position-no more heels smacking my butt and backsliding was gone totally. Once I had finished excersizes-I've been a low altitude jumper for so long that I had a few sec's of reminding myself NOT to try to turn towards the DZ till deployment time. So I just waited from 7 grand to 5.5 and deployed. During that time Angus did debrief me on the fact that there was slight potato chipping-because all the axis are controlled by my arms so I was trying slight movements between arms farther back, or further forward. further forward-i started a slight head down orientation, arms further back-fixed it. Deployment was a totally different beast this time then ever before. deployment sent my chest strap grab my chin, shove my head as far back as it would go and to the right within a few secs. after clearing my head (mentally-let the stars disappear-heck there's plenty of time to do it-from such a high deployment) I realized my chest strap help my head so far back and looking up that in order to see where i was going, -or the altimeter even-i needed to push my head backwards just a bit more so i can see from under the chest strap. Around 3 grand I had to take my goggles off-because the chest strap had sort of 'distorted' my glasses with the pressure it was putting on my head... (strangely this student container was set with the main lift web within 1/2 inch as tight as it will go-as well as the leg straps-so the thinking is -for now-initially-that perhaps the position in which i fly -sort of like sitting in a recliner-may have something to do with this happened-because clearly it was not a problem with Angus checking my gear-I trust him with this all) Regardless, the jump was great, neck is sort of whiplashed but the adrenalin of just having those leg braces keep my legs in place so i wasn't going for freefall moves while Angus chases me across the skies seemed to have been enough that I don't give a darn what the neck feels like-im here ready to jump once i fix up the rigging. over n out, -gimp Sandro29 (B 5425) Jul 22, 2009, 1:59 PM Post #93 of 133 (1118 views) Shortcut  Re: [gimpboogie] newest plans-leg braces this time [In reply to] Can't Post Mina, Haven't seen any more of your postings since last month...what up girl! Keep them comming. I haven't been to PST much this season, but hopefully this weekend or next I'll head up there and we can go for wings with Daniel...now that we know how to take appart your chair. Blue ones "FEZ" gimpboogie Jul 23, 2009, 6:07 PM Post #94 of 133 (1103 views) Shortcut  Re: [Sandro29] newest plans-leg braces this time [In reply to] Can't Post In reply to: Mina, Haven't seen any more of your postings since last month...what up girl! Keep them comming. I haven't been to PST much this season, but hopefully this weekend or next I'll head up there and we can go for wings with Daniel...now that we know how to take appart your chair. Blue ones "FEZ" Fez, Sure, to the wingding with Dan we go-dismantling the chair is simple :) staying in it-not so. I just been rigging -supervised by a rigger-project-swwitching risers-again-and sewing toggles to become more stiff and easier to grab-easy grab toggles out of my skydiving gear-so I can fly with confidence. Been tired, n ill-and not gotten much work done-today was supposed to have another coach jump-rained all day-nice sunset though-don't count out Friday :) Come on down Fez gimpboogie Jul 25, 2009, 3:08 PM Post #95 of 133 (1086 views) Shortcut  Re: [gimpboogie] next steps-leg braces-seem to work [In reply to] Can't Post Another FF jump with Angus, turns this time. two things stood out -(asides from my 1st off DZ landing-yES the beer is here allready-waiting for the 'green light' on it). 1) mental state/mind set-importance of it. and 2) the ability to quickly change plans-decipher what is the most important parts of the dive to keep=and what to discard -if that's how its going to be. a trip to 'top floor' @ 13,500f turned into a trip 'as high as we can go'-which we will never know until the pilot turns on the door lights-leaving the 'planning' a 'as you go' process-it seemed at first. the 'fog' up top became evident as patches-and begam to form fairly sobstantially at 9,000f, so 10,000f was the best we'd hope for. not enough FF time for all what we had planned for the dive-and the 'new plan' obviously had to be thinking that at the top of the dive-exit-arch-altitude check on downward= to the very end of the FF were both the 'most important' parts (end being the deployment-on time). everything else in between will be 'altered'/eliminated as the time goes on-and this mindset is what helped me to turn a 'I'm nervous' situation to being on top of the game again. planning on the spot-for sudden changes, was the skill that I realized I had acquired during these yrs of skydiving.... nothing that I wasn't 'taught' about in the beginning-but somehow it had finally stuck in my brain sufficiently that I could utilize it-turning into a potential 'unplanned' mindset into one where I felt the comfort of being on top of the game and knowing what I was doing- -no-- not my 1st time 'being there', but certainly something that is diffirent from this time in FF, to the last time i was there. on point number 1) mental state of mind, interestingly last yr at the time i was working with Angus, my life was filled with some serious consequential issues which were 'unstable', 'evolving', and i had a great deal of responsibility in making things happen-in this 'private world' of mine. -tons on the plate-as some might say. not always a good state of mind to be learning something like skydiving, IF your an intense person like myself. those issues in life-despite them not being in the forefront of my mind, weighed it down sufficiently enough that when i 'thought' i was concentrating on it-i was 'burdening' myself with these other issues-in between jumps-or generally throughout the day-Angus understands this-and i trust him on it-and see that it can be a deciding factor on what subconsciously overwhelms-and spills into the conscious world. At the time I didn't think of it that way, only noticed that in another high risk sport in my life-i had an accident in august last yr-while i had tons on my plate so to say.... now-despite there being as many 'issues' in my life-i have learned a skill-critical-we think.... a skill that allows me to accept those issues i cannot influence in any manner, at this point-and thinking of them-and how they will or will not turn out-even throughout the day i dive on-have no place in this world=and yes-some say it's a selfish existence=to hyper focus so much on something-well-in this sport-and any that i truly love-this intensity of focus on that sport alone-and dismissal of other issues in life-is critical-essential-to make it 'work'. yes-the leg braces have been instrumental in making it possible to remain in FF, and without them, I am not sure what type of individuals, would be able to skydive with lower limb disabilities=or substancial weakness beyond the ability to walk. yes=the 'special pants', with the crotch panel, are also essential-in that such any skydiver with the above detailed differences in their lower limb control-a-bility within the FF environment is hindered, or changed from the typical skydiving expectations of lower limb input, would benefit substantially-if not them being essential. Such things as having the arms as much as possible streamlined-spandex type 'tight fitting' arms-to give most efficient control but also to help eliminate the slight bit of oscillation ('potato chipping') that happens-if the arms and all upper torso is covered in substancially 'floppy' and unstable material. This-we believe also affects this 'potato chipping' I experience-although very minimal at this stage-but to try to eliminate the rest of it-we consider the upper body becoming more streamlined-easier to control, influence the outcome through less input, and being important to consider. Next dive-hopefully tomorrow-coached with Angus-wii focus on stability in FF, working on the differences with arm positioning, and trying to see if the oscillation will be easier to control with tight fitting arms, (clothing modification-and consieration thus that it was substantially important enough-to make it a 'necessary' part of my skydiving gear=to have my upper body clothing material tight fitting-[I think i will use Canoe/Kayak Canada's world championship racing top-those are streamlined and tight fitting-and sort of send out a message-personally]. Other then that-all is the same, trying to get more jumps in certainly has worked-despite the fact that I didn't think I was jumping as much as i wanted to be-it turns out that I seem to average 10 jumps a month more then i was not living here-and this is during times I'm trying to also focus on finishing off my move here-set up medical services-dealing with a severely infected tooth-getting ready to go judge at the Nationals-and it being my 1st time-I'm watching older videos from Nationals for reference on practicing-thus trying to get much done-while working around the DZ to help my DZ jumping be affordable -that's something I truly appreciate Adam for-he understands people-cares about what is important-which is not a fat bank account-but rather having people reach dreams, achieve goals.... if it wasnt for my ability to help around the DZ, I'd be jumping 10%of what I do now. that's it-really nothing else.... worked on the risers-switched them over-sewed an old set of riser material cut into appropriate size=to create a pocket for stiff 'wire {cut away handle cord}, to go on my toggles. Got it done-sewing with proper threat strength, one needle left after breaking the rest-with equally sized, positioned and tensioned stiching, was the biggest challenge. but now I have easy grab toggles-that actually work and are easy enough to pack it doesnt change the process, or the end result-I'm happy with the toggles. They were easier to use-for sure then regular toggles. NO DO NOT MODIFY YOUR GEAR in any manner-without the consultation with a rigger-and the DZO where you jump=i just needed to say that-because even simple things such as toggles=if i mess it up i can't use them-and without something else to put in there-i'm grounded-so important-DO NOT MODIFY GEAR on your own-this project with the toggles was consulted on to two riggers-and DZO gave 'permission' to use them-as they were done-once only then. that's it-nothing else new. gimpboogie Jul 27, 2009, 9:23 PM Post #96 of 133 (1065 views) Shortcut  Re: [gimpboogie] next steps-leg braces-seem to work [In reply to] Can't Post tonight's FF jump with Angus, was exceptionally 'educational'. Well the story really begins last Thurs night-was supposed to be the 'next jump'-but I havent seen a sunny day enough to put up a tent and waterproof it, since last monday-and Thursday we sat around for 6 hrs to get on that sunset load to get one load up-this is like summer in some areas of Europe (for those who did-I chose not to-I could jump with Angus and work on FF, or jump alone and work on canopy issues-which I've developed some 'bad habits' -of which another post-when I'm not so tired from a day of work in the hot sun at the DZ-....). Sat. we got a jump in-which was great-today the winds were hovering at the edge of=will I make it home or not-'student wind hold' levels-shifting between them. Had a chance to get out there.... still oscillating in FF, 3rd attempt at what were doing-and its progressing-well I suppose really 1st attempt at this dive-never made it this far in FF with Angus yet! yah! Angus is more confident this yr with my skill in focussing my mind.... He is correct. The strap which I was sure I would require-has not been an issue-although we have not had video on these jumps at all-no$ for it! since moving to the I've become a real altitude whore-and all I spend \$ on is calculated in jump tickets....
maybe the video is a good idea in a bit-if this issue doesnt sort itself out.

I start oscillativing-potato chipping, around 8,000f out of a 13,500f exit and by 5,500f i'm timing my pull to match the oscillation-with the hopes of pitching which im head up instead of head down....
today was slight head down orientation-was a simple slide to get that pilot chute out,....

the dep;oyment wans good-solid-sound and not hard in any manner-despite the slight head down orientation...

the canopy flight....was interesting...

Since the last jump turned into a case of beer for landing on the horse farm-the 1st off DZ landing
since starting this sport...

this time I flew backwards with the DZ behind my back,
just to make it back.

The landing-well lets sayy it cost me a repack on reserve.

We've had SO much rain-for a week-that the 'little ditch' at the edge of the runway was a 'river' running by about -hhmm...-chest level....
there I saat, trying to keep my canopy from landing directly in it-no luck in she goes.
then trying to get UP OUT of the muddy ditch with water up to my nipples-well-it took till the DZO dragged me out-too slippery.
yup cost a reserve repack-main is hanging a few feet behind me in the East wing-where I type to you all-
and the container -well hopefully the fan will take care of it by morning-luckily I got a rigger hanging at my house-livin in the motorhome in the parkinglot-and he's going to repack so I hopefully wont miss a load.

livin the dream.....

grannyinthesky  (D 30311)

Jul 28, 2009, 6:27 AM
Post #97 of 133 (1063 views)
Shortcut
 Re: [gimpboogie] next steps-leg braces-seem to work [In reply to] Can't Post
I'm always glad to see a post from you and hear about your latest adventures. Sounds like you had quite a time. Where are you jumping?

gimpboogie

Jul 28, 2009, 2:08 PM
Post #98 of 133 (1055 views)
Shortcut
 Re: [grannyinthesky] next steps-leg braces-seem to work [In reply to] Can't Post
I'm always glad to see a post from you and hear about your latest adventures. Sounds like you had quite a time. Where are you jumping?

granny-We started jumping together-sort of, me here n you there.

well the adventures take me where the winds seem to blow -

for now-settled as a perennial for a while here at the DZ what the heck- I just moved house-literally packed up and moved to share a house with a skydiver on the DZ-there's a few who are 'locals' here at the DZ-living here-some work here some elsewhere....
it all seems to become a community of sorts- - - -

certainly a different life-sitting around on 'off days' when we don't fly-with some kind of work always to do.... today seems to complete the digging of our new swoop pond which also ends up sort of doubling our landong area-because the alternate landing area-which used to be cut off from the rest of us by that 'ditch' on the side of the runway- - - ...
but now they've got a culvert in there-and it's getting filled in, giving us one huge landing area and a swoop pond instead of two small areas and a long ditch...

if it's not a DZ project -it may be a dz project.... the folks living around me are in the midts of building something-like when I got here for a while it was building the ramp to my house.

jumping every chance I get, and to do a bit of judging, since I took the course in Feb. it's time start giving back to this sport....

heck there's so many folks dedicating tons of time to coach, teach, JM, help skydivers all over to learn new skills, and enjoy this sport- my thoughts started to evolve around what I could do to support the sport-and it seems that when my health fails enough that I can't jump in any manner-I know I will want to be around skydivers-and watch them flying, and their videos from FF...
It will be a time when life will be so different from anything I can imagine-when my mind won't get any satisfaction from the existence of the body which functions so minimally. If life still breathes within -then- judging will be the only thing i can do-in this sport for all of the rest who will be left behind to continue....

so this summer -i will go beging that journey
-eerily it feels like 'retirement planning', and perhaps it may be-but to me it's practical thinking for the future.
This body will leave me and without it my existence as well.

Then I jump where I wish, when I can, with whom I can, until that all begins to unveil itself more then this... now, I certainly have slowed down on what I can do -breathing has been affected the most I think- occasionally need O2, and in many small ways ALS is showing her strength this year-but I realize there is nothing to do but embrace life and try to get as many adrenalin filled moments as there is imagination for.

so this week's life at the DZ will bring reserve repack for me-hopefully in time to catch the next Caravan load to top floor, and watch Canada's largest collection of vintage parachutes flying our skies this week, with the skydivers reunion around the horizon now, next week judging at the Nationals.
-which will unfortunately mean a week of no skydiving, but I think I will survive that -by virtue of watching others express their skills and surely it will be enjoyable.

gimpboogie

Aug 23, 2009, 8:24 PM
Post #99 of 133 (1026 views)
Shortcut
 next steps-lon hold/health [In reply to] Can't Post
aspiration pneumonia early Aug. kept me home recovering instead of judging at the Nationals.
sucks -yah, but also was a good time to recover, get my 2nd wind, what ever...
because I need to progress this Free Fall progression with Angus, yah I don't have trouble pulling, and the biggest issue this time around is the potato chipping but if it's a problem 'able bodied' skydivers also have-then I know I can figure out ways to work with this.

infact read about it in the forums one day-'melt like choccolate or butter on a hot day' into the wind-let it cradle me.

Unfortunately the rain hasn't stopped-well enough to get Angus (he is so busy with tandem).

In the meantime I have rigging to do-my Astra battery was soaked in that ditch landing...
have one canopy that needs work with, another one on the way and should be here before Oct. so I will have a chance to give it a try before I want to use it in Oct.

Have the provincials coming up in a couple of weeks,
where I will be judging-and it WILL be a busy one-judging 'room' will be set up in my house, and between the fundraising efforts and organizing other aspects-it's a job I look forward to.

It's bizarre how fast the summer has gone.
Did tons of jumps in May to July, but Aug. has been slow-between being ill and now the weather or the intensity of customers coming through the DZ.

It is totally amazing how many folks are drawn here by that fast Caravan-I mean it's honestly the case. I've spoken with many tandem's who show up and they actually say they have 'heard' that PST has the fastest Caravan tossing folks out the door.....

off I go to start another work week at the DZ now that I've recovered from the pnumonia

gimpboogie

Sep 27, 2009, 6:20 PM
Post #100 of 133 (946 views)
Shortcut
 the final PFF [In reply to] Can't Post
It's been a bizarre journey since the last time I offered some details from the gimps in free fall project.

Wanting Angus to be there, along with my most recent PFF instructor Gareth we decided to a modifed jump.
Sure the unstable exit was there, and the typical necessities, but tracking to dock with both instructors along with turning 180's between the instructors (having both there for the 1st time in so long-and doing something with them other then the typical AFF tasks-was different)

I finished my final-7th PFF the other day, with an unstable exit (sort of a back lay over barrel roll combo- on exit-held heading till Gareth showed up ahead of me (later Angus tells me he had tugged at my foot to try to get my attention-later realizing i wasnt feeling any of it ),
and I began my turns-between him and Angus who had planted himself behind me.
This all went well, and the docking was fine (I realize how it affects my body position when the person lets go-the grip didnt move me but letting go i wobbled like stepping into a canoe in the water till stability is established)...

the clouds went up to 6 grand and down to 4 grand.\
I cannot deploy in clouds -against my safety rules.
I typically deploy at 4.5 -wave off at 5.5
this needed to change.
wave off was set at 4.5 giving me a canopy under the clouds.

I sunk out on my friend Baxter on video -seriously and he had to tuck into a ball to get close (as both my instructors wore weights to keep up)....
we decided on reducing all drag-and i was to jump with skin tight spandex top and my usual 'gimp freefly pants'... this helped with the potato chipping, and gave me a wicked fall rate-although it was fast to begin with.

that AFF was my last one... having to jump out with a coach.

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text:
## Occupation Times Within a Block

### Occupation Times Within a Block¶

Suppose the chain starts at $i$. Then it is intuitively plausible that once it returns to $i$, it "starts all over again" as though it were starting at $i$ at time 0. This hand-wavy statement can be turned into mathematics, but in this course we'll just accept it without doing the math.

Start the chain at $i$, that is, with the initial distribution $P(X_0 = i) = 1$. Define an $i$-block to be the chain till the step before it returns to $i$:

• Under the initial condition that $X_0 = i$, an $i$-block is $X_0, X_1, X_2, \ldots, X_{W_i - 1}$.

Here $W_i$ is the hitting time of $i$ as defined in the previous section:

$$W_i = \inf \{n \ge 1: X_n = i \}$$

Notice that in an $i$-block, the chain is only at $i$ once, at time 0.

Notice also that the length of the $i$-block is $W_i$. You can see this by counting indices in the definition of the $i$-block. But the $i$-block doesn't end at time $W_i$; it ends one step earlier. Its length is $W_i$ because it includes time 0, whereas $W_i$ starts counting time at 1. Informally, the $i$-block includes the $i$ at the start of the block but not the $i$ directly following the block, whereas $W_i$ doesn't include time 0 but does include the moment when $i$ appears at the end of the block.

This will become clear when you look at the graph below, in which $i = 3$. The blue dots are the $i$-block. There are 8 dots in it, corresponding to times 0 through 7. The red dot immediately after the $i$-block shows the return to $i$. It's at time 8.

We have been careful not to include $X_{W_i}$ in the $i$-block. At time $W_i$ the chain returns to $i$, and we will think of that as the start of the next $i$-block. Because the chain "starts over" at $i$, we can imagine the entire chain as identically distributed $i$-blocks strung together one after another. Therefore there are close relations between long run properties of the chain and short run properties on an $i$-block. Let's look at one of these relations.

Let $X_0 = i$ and let $N(j)$ be the number of times the chain is at $j$ in the $i$-block. We will call $N(j)$ the number of visits to $j$ in an $i$-block.

As we have already observed, $N(i) = 1$ with probability 1. By partitioning the $i$-block according to visits to the different states, the length of the $i$-block can be written as a sum:

$$\text{length of } i\text{-block} = W_i = 1 + \sum_{j \ne i} N(j)$$

You can check this in the graph above where $i=3$. The graph shows a path for which $N(3) = 1$, $N(4) = 3 = N(5)$, $N(6) = 1$, and $N(j) = 0$ for all other states $j$. The sum of all these occupation times is 8, which is also the value of $W_i$.

So $$\frac{1}{\pi(i)} = E(W_i \mid X_0 = i) = 1 + \sum_{j \ne i} E(N(j) \mid X_0 = i)$$

### Expected Occupation Times in an $i$-Block¶

Fix a state $j$. The expected number of visits to $j$ in an $i$-block is

$$E(N(j) \mid X_0 = i) = \frac{\pi(j)}{\pi(i)}$$

A formal proof requires a little care; we won't go through it. Rather, we will show why the formula is consistent with our previous calculations and with intuition.

• The formula is correct for $j = i$, because $N(i) = 1$ with probability 1.
• The terms add up to $\frac{1}{\pi(i)}$ as we have shown they must.
$$1 + \sum_{j \ne i} \frac{\pi(j)}{\pi(i)} ~ = ~ \frac{\pi(i)}{\pi(i)} + \sum_{j \ne i} \frac{\pi(j)}{\pi(i)} ~ = ~ \frac{1}{\pi(i)} \big{(} \sum_{\text{all }j} \pi(j) \big{)} ~ = ~ \frac{1}{\pi(i)}$$

because $\pi$ is a probability distribution and hence sums to 1.

• Think of the chain as a string of $i$-blocks. You know that overall, the expected proportion of times that the chain spends at $j$ is $\pi(j)$. Since the $i$-blocks are identically distributed copies of each other, it makes sense that the chain is expected to spend the same proportion $\pi(j)$ of time in $j$ in each $i$-block. Since the length of an $i$-block is expected to be $1/\pi(i)$, the expected number of times the chain is at $j$ in an $i$-block is $\pi(j)/\pi(i)$.

### Example: Ehrenfest Model¶

In the example of the Ehrenfest model we worked with in the previous section, the stationary distribution is binomial $(N, 1/2)$. Suppose the chain starts at $X_n = 0$, that is, with Container 1 empty. Then for every $k$, the expected number of times Container 1 has $k$ particles before it is once again empty is

$$\frac{\binom{N}{k}(1/2)^N}{\binom{N}{0}(1/2)^N} = \binom{N}{k}$$

### Example: Uniform Stationary Distribution¶

Consider any chain that has a stationary distribution that is uniform. You have seen in exercises that chains with doubly stochastic transition matrices fall into this category. Suppose such a chain starts at state $i$. Then for any other state $j$, the expected number of times the chain visits $j$ before returning to $i$ is 1.

format: plain


text:
Numerical smoothing and differentiation

Numerical smoothing and differentiation

An experimental datum value can be conceptually described as the sum of a signal and some noise, but in practice the two contributions cannot be separated. The purpose of smoothing is to increase the Signal-to-noise ratio without greatly distorting the signal (i.e. to get rid of the noise). One way to achieve this is by fitting successive sets of m data points to a polynomial of degree less than m by the method of linear least squares. Once the coefficients of the smoothing polynomial have been calculated they can be used to give estimates of the signal or its derivatives.

Convolution coefficients

When the data points are equally spaced a relatively simple analytical solution to the least-squares equations can be found. This solution forms the basis of the convolution method of numerical smoothing and differentiation.

Suppose that the data consists of a set of n {xi, yi} points (i = 1...n), where x is an independent variable and yi is an observed value. A polynomial will be fitted to a set of m (an odd number) adjacent data points, each separated by an interval h. Firstly, a change of variable is made

$z = {{x - \bar x} \over h}$

where ${\bar x}$ is the value of the central point. z takes the values (1-m)/2 .. 0 .. (m-1)/2 (e.g. m = 5 → z = [-2,-1,0,1,2]). The polynomial, of degree k is defined as

$Y = a_0 + a_1 z + a_2 z^2 \cdots + a_k z^k.$

The coefficients a0, a1 etc. are obtained by solving the normal equations

${\mathbf{a}} = \left( {{\mathbf{J}}^{\mathbf{T}} {\mathbf{J}}} \right)^{ - {\mathbf{1}}} {\mathbf{J}}^{\mathbf{T}} {\mathbf{y}}$

where the ith row of the Jacobian matrix J has the values {1 zi zi2zik}. For example, for a quadratic polynomial fitted to 5 points

${\mathbf{J^T}} = \begin{pmatrix} 1 & 1 & 1 & 1 & 1 \\ { - 2} & { - 1} & 0 & 1 & 2 \\ 4 & 1 & 0 & 1 & 4 \\ \end{pmatrix}$
$\begin{pmatrix} {a_0 } \\ {a_1 } \\ {a_2 } \\\end{pmatrix}= \begin{pmatrix}5 & 0 & 10\\ 0 & 10 & 0 \\ 10 & 0 & 34 \\ \end{pmatrix}^{-1} \begin{pmatrix} 1 & 1 & 1 & 1 & 1 \\ { - 2} & { - 1} & 0 & 1 & 2 \\ 4 & 1 & 0 & 1 & 4 \\ \end{pmatrix} \begin{pmatrix}{y_1 }\\{y_2 }\\{y_3 }\\{y_4 }\\{y_5 }\\\end{pmatrix}$
$\begin{pmatrix} {a_0 } \\ {a_1 } \\ {a_2 } \\\end{pmatrix}= \begin{pmatrix} { - 3/35} & {12/35} & {17/35} & {12/35} & { - 3/35} \\ { - 2/10} & { - 1/10} & 0 & {1/10} & {2/10} \\ {2/14} & { - 1/14} & { - 2/14} & { - 1/14} & {2/14} \\ \end{pmatrix} \begin{pmatrix}{y_1 } \\ {y_2 } \\ {y_3 } \\ {y_4 } \\ {y_5 } \\\end{pmatrix}.$

In this example, a0 = ( − 3y1 + 12y2 + 17y3 + 12y4 − 3y5) / 35. This is the smoothed value for the central point (z = 0) of the five data points used in the calculation. The coefficients (-3 12 17 12 -3)/35 are known as convolution coefficients as they are applied in succession to sets of m points at a time.

$Y_j=\sum{C_{-i}y_{j-i} ...+ C_{0}y_j ... +C_iy_{j+i}}{; i=(m-1)/2}$

Tables of convolution coefficients were published by Savitzky and Golay in 1964, though the procedure for calculating them was known in the 19th century (See E. T. Whittaker and G. Robinson, The Calculus of Observations)

The numerical derivatives are obtained by differentiating Y. For a cubic polynomial

$\frac{{dY}} {{dx}} = \frac{1} {h}\left( {a_1 + 2a_2 z + 3a_3 z^2 } \right) = \frac{1} {h}a_1 {\text{ at }}z = {\text{0}}$
$\frac{{d^2 Y}} {{dx^2 }} = \frac{1} {{h^2 }}\left( {2a_2 + 6a_3 z} \right) = \frac{2} {h^2}a_2 {\text{ at }}z = {\text{0 }}$
$\frac{{d^3 Y}} {{dx^3 }} = \frac{6} {{h^3 }}a_3 {\text{ }}.$

It is not necessary always to use the Savitzky-Golay tables as algebraic formulae can be derived for the convolution coefficients. For a cubic polynomial the expressions are

$C_{0j} = \frac{ {\left( {3m^2 - 7 - 20j^2 } \right)/4}} {{m\left( {m^2 - 4} \right)/3}}$
$C_{1j} = \frac{ {5\left( {3m^4 - 18m^2 + 31} \right)j - 28\left( {3m^2 - 7} \right)j^3 }} {{m\left( {m^2 - 1} \right)\left( {3m^4 - 39m^2 + 108} \right)/15}}$
$C_{2j} = \frac{{12mj^2 - m\left( {m^2 - 1} \right)}} {{m^2\left({m^2 - 1} \right) \left( {m^2 - 4} \right)/15}}$
$C_{3j} = \frac{{ - \left( {3m^2 - 7} \right)j + 20j^3 }} {{m\left( {m^2 - 1} \right)\left( {3m^4 - 39m^2 + 108} \right)/420}}.$

Signal distortion and noise reduction

It is inevitable that the signal will be distorted in the convolution process. Both the extent of the distortion and signal-to-noise improvement:

• decrease as the degree of the polynomial increases
• increase as the width, m of the convolution function increases

For example, If the noise in all data points has a constant Standard deviation, σ, when smoothing by a m-point linear polynomial the standard deviation on the noise will be decreased to $\sqrt{1\over{m}} \sigma$, but with a quadratic polynomial it reduces to approximately $\sqrt{9\over{4m}} \sigma$. So, for a 9-point quadratic smooth only half the noise is removed.

Frequency characteristics of convolution filters

Convolution maps to multiplication in the Fourier co-domain (see pseudocode below). The (finite) Fourier transform of a convolution filter shows that it is most efficient for high-frequency noise and can therefore be described as a low-pass filter. The noise that is not removed is primarily low-frequency noise.

### Smooth the vector x[1,...,nx] with an exponentially damped kernel.  The
###  result is a vector "smooth" with indeterminate values at the edges, and
###  smoothed values in between
cutoff = 0.05   ### weights to zero below this value
alpha = 1.8  ### Decay of weight with distance from center
logacutoff = log(cutoff)/log(alpha)   ### log base alpha of cutoff
span = floor(-logacutoff )  ### width to left and right
weights = alpha^(-abs(sequence(left=-span, right=span, step=1)))  ### Overloaded "^"
kernel = weights / sum(weights)  ### Overloaded "/"
nx = length(x)
nk = 2*span+1   ### length(kernel)
assert( nx>nk )
x1 = concatenate( sequence(0,length=ny-1),  x )
k1 = concatenate( kernel, sequence(0,length=nx-1) )
s1 = inverse_fft( fft(x1) * fft(k1) )  ### Overloaded "*"
smooth = sequence(NaN, length=nx)
smooth[1+span:nx-span] = s1[ ny+nk-1 : nx+nk-1 ]  ### using 1 offset notation

Applications

• Smoothing by convolution is performed primarily for aesthetic reasons. Fitting statistical models to smoothed data is generally a mistake, since the smoothing process alters the distribution of noise.
• Location of maxima and minima in experimental data curves. The first derivative of a function is zero at a maximum or minimum.
• Location of an end-point in a titration curve. An end-point is an inflection point where the second derivative of the function is zero.
• Resolution enhancement in spectroscopy. Bands in the second derivative of a spectroscopic curve are narrower than the bands in the spectrum: they have reduced Half-width. This allows partially overlapping bands to be "resolved" into separate peaks.

References

• P. Gans, Data fitting in the chemical sciences, Wiley, 1992.

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Look at other dictionaries:

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text:
# Algorithm for solving incremental max flow problem

I am working on a project where I need to be able to compute the maximum flow between two nodes in a graph after one of the edge weights has been incremented or decremented by 1. The graph is directed and edge weights are all integers. I can find the maximum flow the first time, by Ford-Fulkerson's algorithm or some variant, but at each step thereafter it would be great if I could use a different (faster) algorithm to find the max flow. At each step, only one of the edge weights is changed, and it is only changed by a value of +1 or -1. What sort of algorithm could do this incremental update for me? It needs to be faster than recomputing the max flow from scratch. It could also be two separate algorithms (but similar I would hope): one for the incrementing case and one for the decrementing case. Thanks in advance for the help!

• – D.W. Jan 23 '18 at 21:31

You can do it in $\small \mathcal{O}(m + n)$ time where $\small m$ and $\small n$ are the # of edges and vertices respectively. Let the edge to be updated be $\small e = (u, v)$.
• If you increment the capacity of $\small e$ by $\small 1$, the maximum flow increments by at most $\small 1$. Hence, starting with the current max flow $\small f$, you only need to find an augmenting path in the residual graph one more time, which costs $\small \mathcal{O}(m + n)$ time. Recall that each augmentation increments the flow value by at least $\small 1$. Therefore, it is guaranteed after the augmentation (if any), the flow attained is maximum.
• If you decrement the capacity of $\small e$ by $\small 1$, the maximum flow decrements by at most $\small 1$. If the new capacity (after decreased by $\small 1$) $\small c(e) \geq f(e)$, where $\small f(e)$ is the current flow value of $\small e$, then nothing need to be conducted. Otherwise, we have to decrease the flow value of $\small e$. Let $\small s \rightarrow u$ be a simple path from $\small s$ to $\small u$, in which all edges have positive flow values and similarly define $\small v \rightarrow t$. We then decrease the flow values by $\small 1$ for all edges in the path $\small s \rightarrow u \rightarrow v \rightarrow t$. Finally, we again search for an augmenting path in the resultant residual graph.
• Can this be done in $O(|E|)$? – Addem Apr 9 at 19:53


text:
1. ## (fog)(x)

(fog)(x) =x2 + x. If g(2) = 4 and g’(2) = 5 , find f ‘ (4). Thank you.

2. ## Re: (fog)(x)

$f[g(x)]=x^2+x$

derivative of a composite function requires use of the chain rule ...

$f’[g(x)] \cdot g’(x) = 2x+1$

$f’[g(2)] \cdot g’(2) = 2(2)+1$

$f’(4) \cdot 5 = 5 \implies f’(4)=1$

3. ## Re: (fog)(x)

Thanks a lot.


text:
# Is there a better way of showing multiple NSDictionaries?

I have a method that contains a bunch of NSDictionaries (in fact, the only reason I have that method is to create those NSDictionaries). While I don't believe there are enough NSDictionaries initialized to visibly slow the code down as of yet, that is a good possibility in the future. I am currently just creating all the NSDictionaries separately, but is there a better way to do it while keeping its readability?

- (void)items {

NSDictionary *item1 = @{
@"label"     : @"item1",
@"icon"      : [UIImage imageNamed:@"item1-Icon"],
@"identifier": @"item1"};

NSDictionary *item2 = @{
@"label"     : @"item2",
@"icon"      : [UIImage imageNamed:@"item2-Icon"],
@"identifier": @"item2"};

NSDictionary *item3 = @{
@"label"     : @"item3",
@"icon"      : [UIImage imageNamed:@"item3-Icon"],
@"identifier": @"item3"};

NSDictionary *item4 = @{
@"label"     : @"item4",
@"icon"      : [UIImage imageNamed:@"item4-Icon"],
@"identifier": @"item4"};

items = [ @[item1, item2, item3, item4] mutableCopy];

}

• Maybe this is sort of artificial (as perhaps you've simplified the code to show it here), but you have an ivar named items and a method named items. I would normally consider that a getter. Here, though, you're setting the items ivar, but not returning it (this method is void). If you want lazy initialization, then I'd make it -(NSMutableArray*) items;, and if the content is not dynamic, then check whether the ivar items is initialized yet, and if so, don't do it again. – Nate Apr 20 '13 at 22:55

«Two or more, use a for»
— Edsger W. Dijkstra

Okay, I am not using a for-loop, but an enumeration

NSArray *itemArray = @[
@[@"item1",@"item1-Icon",@"item1"],
@[@"item2",@"item2-Icon",@"item2"],
@[@"item3",@"item3-Icon",@"item3"],
@[@"item4",@"item4-Icon",@"item4"]
];

NSMutableArray *items = [NSMutableArray array];
[itemArray enumerateObjectsUsingBlock:^(NSArray *itemProperties, NSUInteger idx, BOOL *stop) {
@"icon":  [UIImage imageNamed:itemProperties[1]],
@"identifier":  itemProperties[2]
}];
}];

• This declaration of itemArray is still prone to cut and paste errors, especially as the list grows. Better to use a loop as in the other answer. – Nate Apr 20 '13 at 22:46
• in the end we dont know where the names come from. if they are as regular as in the example, they can be created as in the other answer. it they must be read for some source it wont work. – vikingosegundo Apr 20 '13 at 23:53
• You can only review the code you're given, and the code provided used a repeating pattern. If you're going to recommend a solution that's more brittle, requires more code to grow the array (relative to the other answer, that just involves changing the loop's end index), and is more verbose, in order to accomodate a different use case, that's not presented in the question, then you should document that in your answer. Otherwise, the answer is encouraging code cut-n-pasting. – Nate Apr 21 '13 at 1:26

To avoid code redundancy, its better to put this within a loop like the one below:

for (int i = 0; i < 4; i++) {
NSDictionary *item = @{
@"label"     : [NSString stringWithFormat:@"item%d",i+1],
@"icon"      : [UIImage imageNamed:[NSString stringWithFormat:@"item%d-Icon",i+1]],
@"identifier": [NSString stringWithFormat:@"item%d",i+1]};

• +1 for the loop, but in general, I'd advise against naming loop variables i when something more meaningful is available. itemIdx or index seems better to me. More important, though, is if the index is looping from 1 to 4, then loop from 1 to 4. Don't loop from 0 to 3, and then have to add 1 to the index every time you use it. – Nate Apr 20 '13 at 22:48


text:
## Bảng chú giải

Chọn một trong những từ khóa bên trái

# Multivariable CalculusCustom integration

Thời gian đọc: ~10 min

If we want to integrate over a region which doesn't split nicely along lines parallel to the coordinate axes, we can split the region up along other lines or curves.

For example, consider integrating over the region bounded by the hyperbolas and and the lines and . This region naturally splits along hyperbolas of the form where ranges from 1 to 3 and lines of the form where ranges from to 2. One convenient way of describing this family of curves and lines we're using to slice up the region is to write the region as the image of the rectangle under the inverse of the transformation .

To integrate over the region in the -plane using this subdivision, we need to find the area of each small piece. Since the areas of the rectangles in the -plane are easier to deal with, we find the areas of the piece in the -plane by the area of the corresponding rectangle by the area distortion factor of the transformation . This local area distortion factor, or Jacobian determinant is the absolute value of the determinant of the Jacobian matrix . This is because the area distortion factor of a linear transformation is the absolute value of its determinant, and a differentiable function is essentially linear when zoomed far enough in. Thus we arrive at the formula

where is notation for the absolute value of the determinant of the transformation .

Since the area distortion factor of is the of the area distortion factor of , we can work out that , which implies

Let's apply the Jacobian transformation idea to a familiar problem: the area enclosed by a circle.

Exercise
Use the map from the rectangle to the unit disk, and calculate the Jacobian for this transformation. Use your result to integrate 1 over the unit disk and confirm that the result is equal to the area of the unit disk.

Solution. The Jacobian of the given transformation is

So the area of the disk is equal to

Congratulations! You have finished the Data Gymnasia multivariable calculus course.

Bruno


text:
# Tree-based algorithms and ordinal features

For tree-based methods (e.g., DT, Random Forest, Gradient boosting, etc.), does the conversion interval of an ordinal feature to continuous matter matters? (I can see why it matters for linear model, but I am not clear for tree-based methods)

For example: Is there a difference between converting an ordinal feature from [‘Low’,’Medium’,’High’] to [1,2,3] compared to converting it to [1,99, 876]

• Tree based models are scale invariant. So the scale should not matter. However, tree based models cannot recognise interactions very well, so it could make sense to include manual interactions with other variables if this could be relevant. Oct 15 '20 at 20:15

Edit: I misread your post: the answer is no it shouldn't matter which interval is used. So long as the order is not changed the splits your tree finds on this data will effectively be the same.

See my original answer if you want more context:

In scikit-learn specifically (I cannot speak for other implementations of tree-based models) it does not accept categorical data as input. Meaning the user must convert this to real numbers using hot encoding, numerical encoding etc...

When fitting on any given tree - when it's iterating through possible splits it is splitting your column using an inequality (ie is this column's value bigger or smaller than this threshold value). Due to this methodology it does matter in which order your data is encoded.

If you hot-encode your data - each column will be looked at independently (a likely split would be "is this bigger or less than 0.5 as thats effectively the only split to be made when the options are either 0 or 1).

If you numerically encode your data it will just pick the best threshold that maximizes your split criterion function (usually gini inequality). The bias you add to your system by manually determining the order or the numerical encoding can affect how well the tree is able to split on this column. If you do some logical encoding whereby the target increases in value as the value of your feature increases, your tree will be able to split on this column more effectively & you will likely see better results.

For this reason I recommend numerically encoding with a TargetEncoder (https://contrib.scikit-learn.org/category_encoders/targetencoder.html). This way the order of your numerical encoder will make sense for the decision tree.


text:
# Differentiation continuous iff domain is finite dimensional

Let $A\subset C([0,1])$ a closed linear subspace with respect to the usual supremum norm satisfying $A\subset C^1([0,1])$. Is $D\colon A\rightarrow C([0,1]), \ f\rightarrow f'$ continuous iff $A$ is finite dimensional?

If $A$ is finite dimensional $D$ is continuous of course. But is the other implication true at all? Wouldn't something like $A:=\overline{\text{span}\{\sin{\left(t+\frac{1}{n}\right)} \ | \ n\in\mathbb{N}\}}$ be a counterexample?

• So you need some counterexample of infinite dimensional $A$, or you want to prove that every such infinite dimensional $A$ gives discontinuous $D$? – Norbert Jul 31 '12 at 7:02
• Did you write out in detail what continuity of $D$ means? Do you know the Arzelà-Ascoli theorem? What does that tell you about the unit ball of $A$ in the sup-norm if $D$ is continuous? – t.b. Jul 31 '12 at 7:05
• Yes sure! Continuity is equivalent to boundedness, i.e. $\lVert D f\lVert\leq M \lVert f\lVert$. Arzela-Ascoli states that a set is relative compact iff it's uniformly bounded and equicontinuos. How can I apply this here? In the set $A$ above I tried to define something infinite dimensional, uniformly bounded and equicontinuous. – Julian Jul 31 '12 at 7:09
• Well, the condition on continuity you write tells you that the derivatives of functions in the closed unit ball of $A$ are uniformly bounded, right? The mean value theorem then tells you that ... Finally, what do you know about spaces whose unit ball is compact? – t.b. Jul 31 '12 at 7:13
• Yes boundedness is clear. I don't see how to prove equicontinuity. the unit ball is compact iff the space is finite dimensional – Julian Jul 31 '12 at 7:19

From the dicussion above it follows that it is enough to show equicontinuiuty of $\mathrm{Ball}_A(0,1)$ provided $D$ is continuous.
Fix $\varepsilon>0$ and take $\delta=(2\Vert D\Vert)^{-1}\varepsilon$. From mean value theorem it follows that for all $x_1,x_2\in [0,1]$ such that $|x_2-x_1|\leq\delta$ and all $f\in\mathrm{Ball}_A(0,1)$ we have $$|f(x_2)-f(x_1)|=|f'(\xi)(x_2-x_1)|=|f'(\xi)||x_2-x_1|\leq\Vert f'\Vert_\infty\delta\leq$$ $$\Vert D\Vert\Vert f\Vert_\infty\delta\leq\Vert D\Vert\cdot 1\cdot \frac{\varepsilon}{2\Vert D\Vert}<\varepsilon$$ This means that $\mathrm{Ball}_A(0,1)$ is equicontinuous.
• The reason why the intended counterexample (the closed span of shifted sines) doesn't work is that it is not contained in $C^1$. It's a good exercise to find out why. – t.b. Jul 31 '12 at 7:43


text:
Syntax
ok = multi_atomic_takedown(square_root)

Purpose
This routine gathers up the results for each thread and frees memory that was allocated by multi_atomic_setup .

It is assumed that this function is called by thread zero and all the other threads are blocked (waiting).

square_root
This argument has prototype       vector<double>& square_root  The input value of square_root does not matter. Upon return, it has the same size and is the element by element square root of y_squared .

ok
This return value has prototype       bool ok  If it is false, multi_atomic_takedown detected an error.

Source

namespace {
bool multi_atomic_takedown(vector<double>& square_root)
{     bool ok            = true;
//
// extract square roots in original order
square_root.resize(0);
{     // results for this thread
for(size_t i = 0; i < n; i++)
}
//
// go down so that free memory for other threads before memory for master
{     // check that this tread was ok with the work it did
//
// run destructor on vector object for this thread
//
// run destructor on function object for this thread
//
// delete problem specific information
void* v_ptr = static_cast<void*>( work_all_[thread_num] );
//
// check that there is no longer any memory inuse by this thread
}


text:
# Calculating Definate Integrals

1. Jul 10, 2012

### clm222

I made a pdf so that the equation would be more clear

#### Attached Files:

• ###### physics question PF.pdf
File size:
158.9 KB
Views:
120
2. Jul 10, 2012

### Muphrid

Calculating the antiderivative and evaluating it on the bounds is almost always how definite integrals are done. The fundamental theorem of calculus gives an exact result in this way. Are you sure you didn't make some mistake either in finding the antiderivative or the Riemann sum?

Also, did you use LaTeX for that? If so, you can use inline and display math between itex or tex tags. Quote this post to see an example:

$$\int_a^b f(x) \; dx = F(b) - F(a)$$

Edit: though I should say there's an entire field concerning numerical integration--using Riemann sums or improvements on those techniques--to deal with functions whose antidervatives can't be found analytically.

Last edited: Jul 10, 2012
3. Jul 10, 2012

### HallsofIvy

The only purposes of Riemann sums are to give a basic definition of the Riemann integral and, sometimes, to reason out how to set up an integral. You never use Riemann sums to actually do an integral. Find an anti-derivative, evaluate it at the upper and lower bounds, and subtract.

4. Jul 10, 2012

### arildno

Eeh, Riemann sums give the rationale for many numerical integration schemes..

5. Jul 10, 2012

### mathwonk

There are two ways to compute an integral "exactly". Either take the actual limit of the Riemann sums, which is usually quite hard, or do as Halls emphasizes is much more usual, namely find an antiderivative. (His "always" means 99.9% of the time.)

If the antiderivative is elusive or totally unavailable, but usually not otherwise, one may use actual explicit Riemann sums to approximate the integral, as arildno says.

I.e. in almost all textbook problems, like integrating x^18, or cos^4(x) and so on, do as Halls said to get an "exact" answer. In the odd case where the integrand is 1/sqrt(x^5-x+1), or cos(x^2), do as arildno says to get an approximate answer.

I believe Halls thought you meant to get an exact answer, so his answer was chosen accordingly.

6. Jul 10, 2012

### HallsofIvy

Yes, thank you. I didn't think of that. However, I would be inclined to say that most methods, such as Simpson's rule, can be interpreted as approximating the function, over sections of the interval rather than Riemann sums.

7. Jul 10, 2012

### lurflurf

^The initially surprising thing is that approximating a function over an interval by an interpolating polynomial is equal to a Riemann sum.

8. Jul 10, 2012

### clm222

correct me if I'm wrong (I've just started definite integration a few days ago): given an integral

$\int_a^b$ f(x) dx = F(b) - F(a)

Also, what If im trying to find the area under a curve, when the curve is completly random, and is based on no function.

Lastly: do i have to do anything special when some where from point a to point b, there is a negative area.

Thanks

Last edited: Jul 10, 2012
9. Jul 10, 2012

### Muphrid

You don't have to do anything special about the function taking on negative values. This is accounted for by the antiderivative.

"based on no function" makes no sense. If you mean you can't write the function in terms of known elementary functions, that's one thing, but I assume that this curve is still well-behaved--continuous, for instance. Just because you can't write it in terms of polynomials, sines, cosines, or anything like that doesn't make it not a function.

10. Jul 10, 2012

### clm222

can you give me an example please?

11. Jul 10, 2012

### clm222

wait a second, using

$\int_a^b f(x) dx = F(b)-F(a)$

I don't even need to know the function, just the values at point a and point b, am i correct?

One more question: given a function, say: f(x)=x2
to find the area under a curve (a to b) would I need to differentiate:

$\int_a^b$ 2x dx

or would I simply plug in the function?

$\int_a^b$ x2 dx

Last edited: Jul 10, 2012
12. Jul 11, 2012

### arildno

True enough.
The calculative efficiency of the "strict" Riemann sum is low, relative to more advanced schemes that incorporate function approximation over the intervals as well.
(Of course, Riemann sums ALSO "approximate" functions over intervals, but usually only well when the intervals are extremely tiny)

The force of Riemann sums, as I see it, is the ease by which proofs in full generality may be given by means of them.

They are a bit like Cramer's Rule, dreadful as a computational tool, but optimal for some basic theoretical problems of how to prove something.

13. Jul 11, 2012

### micromass

No, Riemann sums are a horrible thing to use in proofs. Many proofs turn out to be very technical and ugly. Proving things like Fubini's theorem is (in my opinion) dreadful. Furthermore, Riemann sums are very restrictive things. Many nice results don't hold for them.

The good thing about Riemann sums is that the definition is easy and intuitive, but that's basically it.

14. Jul 11, 2012

### clm222

1: if I want to calculate the definite integral of say

f(x)=x2

would i need to differentiate before i find the integral or would i just plug in my function into the integral?

$\int_a^b$ x2 dx

or

$\int_a^b$ 2x dx

2: when I use certain rules such as the trapazoid rule:

$\int_a^b$ f(x) dx = (b-a) $\frac{f(a)+f(b)}{2}$

does f(x) equal the derivative of F(x) (given that F'(x)=F(x)), or the function value?

15. Jul 12, 2012

### HallsofIvy

What you are doing is integrating not differentiating.

After integrating, you would not still use the integral sign- that's been done. What you are doing is evaluating $x^2$.
$\int_a^b 2x dx= \left[x^2\right]_a^b= b^2- a^2$

16. Jul 12, 2012

### clm222

Ok, and that is the area of the function?

17. Jul 12, 2012

### HallsofIvy

A "function" is not a geometric object and so does not have an "area". Do you mean the area below a graph of a function?

18. Jul 12, 2012

### clm222

Yes, I thought that was one of the main points of definite integration?

19. Jul 12, 2012

### Muphrid

Careful, I think you confused HallsOfIvy. I'm pretty sure you want to integrate $x^2$, do you not? There's no differentiation involved. You just do $\int_a^b x^2 \; dx$.

You can find the area beneath a graph using a definite integral, but that is not the definition of a definite integral. This is a frequent point of confusion when people try to integrate, say, functions in polar coordinates, where instead of approximating an area as a series of rectangles, one has to use triangles instead. The integral is a tool, but the form that integral takes depends on the geometry of the problem.

20. Jul 12, 2012

### clm222

I'm not sure if this is right but, lets say I wanted to find the total acceleration from t1 to t2.

I could integrate the velocity from t1 to t2? v(t2)-v(t1)

but if i wanted to find the total work done finding the area under the graph of force from t1 to t2, would give the total work, woulnt it?

because using F(b)-F(a) would give me Δx(?)

and finding the area under a graph would give me the average value multiplied by time(?)


text:
Only this week, get the SQL Complete Track of 9 courses in a special prize of $330$89!
Introduction
Concatenation
Simple text functions
How to modify strings
Revision
18. Summary

## Instruction

Good, that's it! Let's revise the text functions we've learned in this part:

• || is the concatenation operator; it merges multiple texts into one (in SQL Server use +, in MySQL use concat()),
• length(x) returns the length of text x (in SQL Server use len()),
• lower(x), upper(x), initcap(x) will all write x in the appropriate case,
• substring(x, y, z) will return the part of x starting from position y and with z characters in length (in Oracle use substr()),
• replace(x,y,z) will search x for y, and if it finds any y, it will replace if with z.

Fine, let's do some practice now.

## Exercise

Press to begin practice.


text:
# How do you convert 0.320 atm to mm Hg?

Jul 23, 2016

$P = 243.2$ $m m$ $H g$

#### Explanation:

Remember that $1$ $a t m$ $= 760$ $m m$ $H g$, from there you have 3 methods you could use:

1) Use the "rule of three"

I'm not quite sure how you call that in English, but the concept is simple

$1$ $a t m \to 760$ $m m$ $H g$
$0.320$ $a t m \to x$ $m m$ $H g$

From there, multiply in a "cross fashion", i.e.:

$1$ $a t m$ $\cdot$ $x$ $m m$ $H g$ $= 760$ $m m$ $H g$ $\cdot 0.320$ $a t m$
$x$ $m m$ $H g$ $= 243.2$ $m m$ $H g$
$x = 243.2$

2) Use a conversion factor

Since $1$ $a t m$ $= 760$ $m m$ $H g$ is an equality, it means that $\frac{1 a t m}{760 m m H g}$ and $\frac{760 m m H g}{1 a t m}$ equals 1, and as such, we can just multiply it by our valor and without changing it.

$0.320 a t m \cdot \frac{760 m m H g}{1 a t m} = 243.2 \frac{m m H g \cdot a t m}{a t m} = 243.2 m m H g$

3) Use the conversion formula of linear scales

The conversion formula of all linear scales say "the ratio of the distance between your value and a set value and the distance between two set points is always the same regardless of scale", or, in simpler terms,

$\frac{{P}_{a} - {P}_{a t m}}{{P}_{a t m} - {P}_{v a c}} = \frac{{P}_{H} - {P}_{H g a t m}}{{P}_{H g a t m} - {P}_{H g v a c}}$

Where ${P}_{a}$ is the pressure is $a t m$ and ${P}_{H}$ is the pressure in $m m H g$, throwing all values into the formula we have

$\frac{0.320 - 1}{1 - 0} = \frac{{P}_{H} - 760}{760 - 0}$
$- 0.680 \cdot 760 = {P}_{H} - 760$
$- 516.8 = {P}_{H} - 760$
${P}_{H} = 243.2$