PAM_XAUTH
Section: Linux\-PAM Manual (8)Updated: 06/16/2009
Index Return to Main Contents
pam_xauth - PAM module to forward xauth keys between users
Synopsis
- pam_xauth.so [debug] [xauthpath=/path/to/xauth] [systemuser=UID] [targetuser=UID]
DESCRIPTION
Without pam_xauth, when xauth is enabled and a user uses the su(1) command to assume another user's privileges, that user is no longer able to access the original user's X display because the new user does not have the key needed to access the display. pam_xauth solves the problem by forwarding the key from the user running su (the source user) to the user whose identity the source user is assuming (the target user) when the session is created, and destroying the key when the session is torn down.
This means, for example, that when you run su(1) from an xterm session, you will be able to run X programs without explicitly dealing with the xauth(1) xauth command or ~/.Xauthority files.
pam_xauth will only forward keys if xauth can list a key connected to the $DISPLAY environment variable.
Primitive access control is provided by FC~/.xauth/exportF[] in the invoking user's home directory and FC~/.xauth/importF[] in the target user's home directory.
If a user has a FC~/.xauth/importF[] file, the user will only receive cookies from users listed in the file. If there is no FC~/.xauth/importF[] file, the user will accept cookies from any other user.
If a user has a FC.xauth/exportF[] file, the user will only forward cookies to users listed in the file. If there is no FC~/.xauth/exportF[] file, and the invoking user is not root, the user will forward cookies to any other user. If there is no FC~/.xauth/exportF[] file, and the invoking user is root, the user will not forward cookies to other users.
Both the import and export files support wildcards (such as *). Both the import and export files can be empty, signifying that no users are allowed.
OPTIONS
debug
- Print debug information.
xauthpath=/path/to/xauth
- Specify the path the xauth program (it is expected in FC/usr/X11R6/bin/xauthF[], FC/usr/bin/xauthF[], or FC/usr/bin/X11/xauthF[] by default).
systemuser=UID
- Specify the highest UID which will be assumed to belong to a "system" user. pam_xauth will refuse to forward credentials to users with UID less than or equal to this number, except for root and the "targetuser", if specified.
targetuser=UID
- Specify a single target UID which is exempt from the systemuser check.
MODULE TYPES PROVIDED
Only the session type is provided.
RETURN VALUES
PAM_BUF_ERR
- Memory buffer error.
PAM_PERM_DENIED
- Permission denied by import/export file.
PAM_SESSION_ERR
- Cannot determine user name, UID or access users home directory.
PAM_SUCCESS
- Success.
PAM_USER_UNKNOWN
- User not known.
EXAMPLES
Add the following line to FC/etc/pam.d/suF[] to forward xauth keys between users when calling su:
-
session optional pam_xauth.so
IMPLEMENTATION DETAILS
pam_xauth will work only if it is used from a setuid application in which the getuid() call returns the id of the user running the application, and for which PAM can supply the name of the account that the user is attempting to assume. The typical application of this type is su(1). The application must call both pam_open_session() and pam_close_session() with the ruid set to the uid of the calling user and the euid set to root, and must have provided as the PAM_USER item the name of the target user.
pam_xauth calls xauth(1) as the source user to extract the key for $DISPLAY, then calls xauth as the target user to merge the key into the a temporary database and later remove the database.
pam_xauth cannot be told to not remove the keys when the session is closed.
FILES
FC~/.xauth/importF[]
- XXX
FC~/.xauth/exportF[]
- XXX
SEE ALSO
AUTHOR
pam_xauth was written by Nalin Dahyabhai<EMAIL_ADDRESS>based on original version by Michael K. Johnson<EMAIL_ADDRESS>Index
- Synopsis
- DESCRIPTION
- OPTIONS
- MODULE TYPES PROVIDED
- RETURN VALUES
- EXAMPLES
- IMPLEMENTATION DETAILS
- FILES
- SEE ALSO
- AUTHOR
This document was created by man2html, using the manual pages.
Time: 05:34:28 GMT, December 24, 2015


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You will hear this many times, most real estate agents do not make it past the first 2 years. Estimates range as high as 90% failure rate within the first two years.
It is hard to exactly prove how many real estate licensees give up after the first 2 years, but looking at the data published by CA DRE, I can extrapolate some facts by looking at the number of new licenses issued in 2015, and seeing how many of those people who got their licenses in 2015 still have a valid and active licensees in the year 2021.
Why did I pick 2015’s data? That’s because in California, real estate licenses are valid for 4 years, and they are given a grace period of 2 years to renew it. If they were still actively participating in the industry, they would have renewed their licenses by now.
From DRE’s website, they issued 25,210 new salesperson and broker licenses for the entire year of 2015. In February 2021, more than 5 years later, there were only 11,042 people who got their licenses in 2015 with a still valid license and attached to a brokerage (salesperson licensees have to hang their licenses with a brokerage in order to do any business).
That means only 43% of the agents who took up their new license in 2015 remained in business in 2021. In other words, 57% of the people who worked so hard to pass their exam, simply gave up. Of the people remaining, I have yet to find enough data to determine how many of them are actually making a living wage. If you have any ideas where I can find data, let me know!


PERLBS2000
Section: Perl Programmers Reference Guide (1)Updated: 2009-02-12
Index Return to Main Contents
NAME
README.BS2000 - building and installing Perl for BS2000.SYNOPSIS
This document will help you Configure, build, test and install Perl on BS2000 in the POSIX subsystem.DESCRIPTION
This is a ported perl for the POSIX subsystem in BS2000 VERSION OSD V3.1A or later. It may work on other versions, but we started porting and testing it with 3.1A and are currently using Version V4.0A.You may need the following GNU programs in order to install perl:
gzip on BS2000
We used version 1.2.4, which could be installed out of the box with one failure during 'make check'.bison on BS2000
The yacc coming with BS2000 POSIX didn't work for us. So we had to use bison. We had to make a few changes to perl in order to use the pure (reentrant) parser of bison. We used version 1.25, but we had to add a few changes due to EBCDIC. See below for more details concerning yacc.Unpacking Perl Distribution on BS2000
To extract an ASCII tar archive on BS2000 POSIX you need an ASCII filesystem (we used the mountpoint /usr/local/ascii for this). Now you extract the archive in the ASCII filesystem without I/O-conversion:cd /usr/local/ascii export IO_CONVERSION=NO gunzip < /usr/local/src/perl.tar.gz | pax -r
You may ignore the error message for the first element of the archive (this doesn't look like a tar archive / skipping to next file...), it's only the directory which will be created automatically anyway.
After extracting the archive you copy the whole directory tree to your EBCDIC filesystem. This time you use I/O-conversion:
cd /usr/local/src IO_CONVERSION=YES cp -r /usr/local/ascii/perl5.005_02 ./
Compiling Perl on BS2000
There is a ``hints'' file for BS2000 called hints.posix-bc (because posix-bc is the OS name given by `uname`) that specifies the correct values for most things. The major problem is (of course) the EBCDIC character set. We have german EBCDIC version.Because of our problems with the native yacc we used GNU bison to generate a pure (=reentrant) parser for perly.y. So our yacc is really the following script:
-----8<-----/usr/local/bin/yacc-----8<----- #! /usr/bin/sh
# Bison as a reentrant yacc:
# save parameters:
params="``
while [[ $# -gt 1 ]]; do
params=''$params $1"
shift
done
# add flag %pure_parser:
tmpfile=/tmp/bison.$$.y echo %pure_parser > $tmpfile cat $1 >> $tmpfile
# call bison:
echo ``/usr/local/bin/bison --yacc $params $1\t\t\t(Pure Parser)'' /usr/local/bin/bison --yacc $params $tmpfile
# cleanup:
rm -f $tmpfile -----8<----------8<-----
We still use the normal yacc for a2p.y though!!! We made a softlink called byacc to distinguish between the two versions:
ln -s /usr/bin/yacc /usr/local/bin/byacc
We build perl using GNU make. We tried the native make once and it worked too.
Testing Perl on BS2000
We still got a few errors during "make test". Some of them are the result of using bison. Bison prints parser error instead of syntax error, so we may ignore them. The following list shows our errors, your results may differ:op/numconvert.......FAILED tests 1409-1440 op/regexp...........FAILED tests 483, 496 op/regexp_noamp.....FAILED tests 483, 496 pragma/overload.....FAILED tests 152-153, 170-171 pragma/warnings.....FAILED tests 14, 82, 129, 155, 192, 205, 207 lib/bigfloat........FAILED tests 351-352, 355 lib/bigfltpm........FAILED tests 354-355, 358 lib/complex.........FAILED tests 267, 487 lib/dumper..........FAILED tests 43, 45 Failed 11/231 test scripts, 95.24% okay. 57/10595 subtests failed, 99.46% okay.
Installing Perl on BS2000
We have no nroff on BS2000 POSIX (yet), so we ignored any errors while installing the documentation.Using Perl in the Posix-Shell of BS2000
BS2000 POSIX doesn't support the shebang notation ("#!/usr/local/bin/perl"), so you have to use the following lines instead:
: # use perl
eval 'exec /usr/local/bin/perl -S $0 ${1+``$@''}'
if $running_under_some_shell;
Using Perl in native BS2000
We don't have much experience with this yet, but try the following:Copy your Perl executable to a BS2000 LLM using bs2cp:
"bs2cp /usr/local/bin/perl 'bs2:perl(perl,l)'"
Now you can start it with the following (SDF) command:
"/START-PROG FROM-FILE=*MODULE(PERL,PERL),PROG-MODE=*ANY,RUN-MODE=*ADV"
First you get the BS2000 commandline prompt ('*'). Here you may enter your parameters, e.g. "-e 'print "Hello World!\\n";'" (note the double backslash!) or "-w" and the name of your Perl script. Filenames starting with "/" are searched in the Posix filesystem, others are searched in the BS2000 filesystem. You may even use wildcards if you put a "%" in front of your filename (e.g. "-w checkfiles.pl %*.c"). Read your C/C++ manual for additional possibilities of the commandline prompt (look for PARAMETER-PROMPTING).
Floating point anomalies on BS2000
There appears to be a bug in the floating point implementation on BS2000 POSIX systems such that calling int() on the product of a number and a small magnitude number is not the same as calling int() on the quotient of that number and a large magnitude number. For example, in the following Perl code:
my $x = 100000.0; my $y = int($x * 1e-5) * 1e5; # '0' my $z = int($x / 1e+5) * 1e5; # '100000' print "\$y is $y and \$z is $z\n"; # $y is 0 and $z is 100000
Although one would expect the quantities $y and $z to be the same and equal to 100000 they will differ and instead will be 0 and 100000 respectively.
Using PerlIO and different encodings on ASCII and EBCDIC partitions
Since version 5.8 Perl uses the new PerlIO on BS2000. This enables you using different encodings per IO channel. For example you may use
use Encode; open($f, ">:encoding(ascii)", "test.ascii"); print $f "Hello World!\n"; open($f, ">:encoding(posix-bc)", "test.ebcdic"); print $f "Hello World!\n"; open($f, ">:encoding(latin1)", "test.latin1"); print $f "Hello World!\n"; open($f, ">:encoding(utf8)", "test.utf8"); print $f "Hello World!\n";
to get two files containing ``Hello World!\n'' in ASCII, EBCDIC, ISO Latin-1 (in this example identical to ASCII) respective UTF-EBCDIC (in this example identical to normal EBCDIC). See the documentation of Encode::PerlIO for details.
As the PerlIO layer uses raw IO internally, all this totally ignores the type of your filesystem (ASCII or EBCDIC) and the IO_CONVERSION environment variable. If you want to get the old behavior, that the BS2000 IO functions determine conversion depending on the filesystem PerlIO still is your friend. You use IO_CONVERSION as usual and tell Perl, that it should use the native IO layer:
export IO_CONVERSION=YES export PERLIO=stdio
Now your IO would be ASCII on ASCII partitions and EBCDIC on EBCDIC partitions. See the documentation of PerlIO (without "Encode::"!) for further posibilities.
AUTHORS
Thomas DornerSEE ALSO
INSTALL, perlport.Mailing list
If you are interested in the VM/ESA, z/OS (formerly known as OS/390) and POSIX-BC (BS2000) ports of Perl then see the perl-mvs mailing list. To subscribe, send an empty message to<EMAIL_ADDRESS>also:
http://lists.perl.org/showlist.cgi?name=perl-mvs
There are web archives of the mailing list at:
http://www.xray.mpe.mpg.de/mailing-lists/perl-mvs/<EMAIL_ADDRESS>HISTORY
This document was originally written by Thomas Dorner for the 5.005 release of Perl.This document was podified for the 5.6 release of perl 11 July 2000.
Index
- NAME
- SYNOPSIS
- DESCRIPTION
-
- gzip on BS2000
- bison on BS2000
- Unpacking Perl Distribution on BS2000
- Compiling Perl on BS2000
- Testing Perl on BS2000
- Installing Perl on BS2000
- Using Perl in the Posix-Shell of BS2000
- Using Perl in native BS2000
- Floating point anomalies on BS2000
- Using PerlIO and different encodings on ASCII and EBCDIC partitions
- AUTHORS
- SEE ALSO
- HISTORY
This document was created by man2html, using the manual pages.
Time: 05:29:07 GMT, December 24, 2015


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First off I should point out that I'm on 100mg methadone per day (for the last 7 years)for opioid dependence therapy, as well as 54mg methylphenidate (concerta) per day for ADD. I don't consider them as contributers to this trip, but I'm sure their presence affected the quality of the trip to some degree.
All doses were weighed on an accurate scale, and all drugs prepeared for injection were done so using sterile equipment in a sterile fashion.
Sweet mother of Jesus! My first DMT breakthrough was nothing like my 4-Aco-DMT breakthrough! Perhaps it's cause I managed to take the entire 50mg in two montser hits... perhaps it's because my launching pad was primed with 30mg of turbocharged-IM-2CB-goodness, and 30mg ultra-high-octane IM 4-Aco-DMT .... yaaa that could be it lol. Here follows an account of the evening....
Sitting at the computer, browsing the vast stores of knowledge ... drinking a few beers and wondering if perhaps I am ready for my first breakthrough DMT experience? After consulting a few of the greatest minds in the field this world has seen since Albert Hoffman - I decide to begin preparations for this epic voyage into the unknown ... my destination lacking all shape and form, only a vague prescience... a shadow of a thought... (in a low whisper) terra incognita.
Preparations were of primary concern. Perceptual priming is sensitive to the modality and exact format of the stimulus, and thus, priming this finely tuned, soon-to-be-oh-so-spice-saturated machine, was of the uttmost importance. I felt that some well placed modifications to the rocket were in order, with a particular focus on a stream-lined, high altittude launch pad constructed of equal parts Nexus (2CB) and psilacetin (4-Aco-DMT). Anticipating high heat and stresses on various structural components of this vessel during the faster-than-light entry to hyperspace, I took 7.5mg of zopiclone while I drank my three beers, as I've heard that small amounts of benzos can actually enhance visuals without clouding the experience too much, provided you only take a tiny amount.
While finishing my beer, I mixed 30mg of 4-Aco-DMT with 30mg of 2CB, placed the off white powders in a spoon, and added 30 units of distilled water. A slight amount of heat was added, though very little was necessary to make it dissolve. Unfortunately I was out of micron filters, so I filtered the solution three seperate times, by packing a few balls of cotton in the end of a syringe, wetting it and squishing it down with the plunger, and then backloading the solution. When this was completed, I had about 27 units of perfectly clear liquid. I cleaned my shoulder with alcohol and injected half into the muscle in my shoulder, put the rest in a carrying case, and hopped on my bike
It was dusk outside, with a light rain and a bit of fog swirling through the night, patches of stars peeking through gaps in the clouds, and the horizon the deepest shade indigo... I love twilight. Half way to Tim Horton's I got my first alert... another minute and I was no longer just riding a bike... I was flying it. An incredible extension of my body, with limitless energy coursing through my veins... along with something else too ;) I stopped briefly in a clump of sumach and IM'd everything else except 5 units which I IV'd. Within seconds I was up to a strong +++ the beautiful synergy of tryptamines and phnelthylamines... pure body bliss. Euphoria far exceeding MDMA... gorgeous sensory perception and visual colour palette that felt and looked like a new psychedelic as opposed to the mix of two.
Joy. Graced by the touch of God...the unending gratitude and honor of being alive, right here, in this moment of time. A few minutes pass and I'm back on my bike, soaring at near light speed through the fog and mist. Can I go faster? You better believe I can! I can do anything at all at this moment! Anything at all! Save for exercise realistic judgement ... or tie my shoelace Damn it! What do I do about this lace!? Getting caught in the gears... This will require a deceleration, effectively slowing from relativistic speeds... a return to mortality, but only a momentary return. Now, time to exercise all my powers, bending the faculties of my mind, both profound and acute, to that task at hand! hmm.. hmmm... hmmmm... never fear I'm up to the challenge! Now how does that ryhme go?...
 I shall skillfully manipuate my dexterous hands, flex the sheer size of my intellect...... and tuck my laces down the side of my shoe! After taking a moment to pat myself on the back and bathe in the glory of my own ingenuity, I hopped back on my bike, warping right to the door of Tim's, ready for a coffee. I'll comment here that I usually quite enjoy interacting with the public on psychedelics... it does however, present a few unique challenges lol.
As I approach the door of the coffee shop I understand several things inherently... almost instinctually, and feel as a keeper of vital knowledge. I know what I want, (a large double-double), and I have an abstract understanding of how to get it...in my pocket I have metalic objects, devices that humans use to represent their worth or the worth of their abilities. I reflect that the thing of greatest value one can give another, is their time. (aside from respect or love or friendship but these are of a different nature and have no real monetary or quantitative equivalent). It also occurs to me that people exchange their time for these small token representations, and that the people who work in Tim Horton's are considered to have 'low-grade' time. It occures to me that all people's time is not created equal, which is quite strange as time exists for us all in the same way...or at least similar.
I look at the girl standing at the counter. She's gorgeous. How does she feel about getting so few symbolic units in exchange for her work? Her time seems valuable... much more so than our flat money.. paper and metalic representations with no inherent worth. It occurs to me that I'd love it if she'd give me some of her time.... well perhaps if I were single, but I'm in love and only enjoy looking these days lol...
With a little difficulty, I manage to communicate my desires to this gorgeous girl... not all of them luckily ...but the coffee yes. I watch with fascination like an outsider observer as this interaction and exchange takes place. I watch my hand extend, handing her all the money in my pocket ... about $15 and some odd change. She looks at the handfull of money, squints at me strangly and says, 'It's only $1.45'... I puzzle over this unexpected turn of events... hmmm...in the words of a famous psychonaught, I think to myself, 'what now? what comes next???' Luckily she takes matters into her own hands (don't you love a woman with initiative!?), hands me back the coins and the $10 bill and performs the complex set of equations to determine my resulting change.
A wave of relief washes over me as I realize that I have narrowly avoided a very challenging social/mathmatical/and physical operation that would probably have required me to once again (like with the shoelaces) use the full capacity of my mental faculties. A good thing too, as surly the brilliance of my mind working at full capacity would blind everyone within a one mile radius? The combined climax of 2 million years of evolution and millions of synapses firing... The employees and customers of the coffee shop are safe ....for now.
I finish my coffee and head for home, riding into the night and the fog, modified memories flashing through my mind...I think of a Neal Stephenson novel.. I feel like I'm flying a high-powered mode of transportation.. belong to a hallowed suborder of elite warriors. I've got esprit up to here. My clothes are black as activated charcoal, filtering the very light out of the air. A bullet would bounce off the cotten and acrylic microweave like a bird flying into a mirrored window, but excess perspiration wafts through it like a breeze through a freshly napalmed forest.
Man of steel... my body protected in an invisible bubble, clothes as soft as a sherling jacket, feels like smooth soft leather, protects like a stack of phonebooks. Need to get home. Have a job to do. I can shoot lasers from my eyes to smite my enemys. I have never used my laser eyes in fear or anger. But I have used them in Walmart. Got asked to sign a paper promising I'd never try to get a union or have employee/human rights while working there. It also promised to pay every walmart employee as little as humanly possible so long as the profits from illegally exploiting employees is greater than the few $100 million they are fined every year for doing it.
Once again I feel free and alive..light and full of energy and good-will. The visuals have just reached their peak, the initial edgyness of the 2CB's onset has past, and I know that I am now ready. It has been approx. 40-50mins since I first injected. The pipe is at home, brillo packed with 50-60mg of pure white powdered DMT , which has been gently melted so it would stick to the brillo. The launch pad has reached sufficient altitude to facilitate a high probability breakthrough experience... and I'm excited to say the least.
The nature of the visuals I was experiencing at this point were a strange combination of tryptamine and phenylthylamine... the very colourful and crisp geometric neon patters and ideographic characters I get from DMT and 4-Aco, but with a phenythylamine softness and flowing movement that warped the dimentions and proportions of the environment around me. Everything was soft and smoothe and flowing... fractal and geometric shapes shifting and swirling... and I felt highly attuned to the universe and my immediate environment. When I looked at people in the public areas, I would get little glimpses of who they were, like little movies or stories being told in a flash of insight. Real or not, these small glimpses inside peoples souls felt real, and seemed based on the persons karma or simply the energy they projected.
I sat on the bottom stair of my workshop with the door to my appartment closed and the light in my kitchen shinning through the drape in the door window. I took the largest toke I could, rotating the pipe slowly, and holding the flame just from actually touching the Spice. My lungs filled with a very sweet and not at all harsh smoke which I held in long and deep. By the second inhale I was starting to hear the universe being torn in half... the second toke was harsher but still not bad at all. By the time I exhaled I was well on my way to hyperspace.
I can no longer see! The patterns are small and moving quickly and unfolding into an imense alien landscape... and there's someone, or several things here too. They are peaking at me!! lol, they smile mischieviously and keep just out of site. They seem to know what's going on. This is their world. They come prepared. I keep seeing them poking around objects and peeking, peeking at me! Who and what are they!? They seem friendly but not entirely benign either. Pleasure and love and vibrating information being sent into my head but it's too much, I don't understand... punctuated moments of fear, but fear can be a good thing...it can heal and remind and most of all it makes me appreciate my smallness and insignificance, and also my tiny role in this great dimentional symphony. This is overwhelming.
1000 years... no 2 or 3 minutes has past. What I see is somewhat recognizable...the door to my kitchen, but instead of it moving or flowing, it is rapidly changing into completely different doors....it's cycling through them and each one is AMAZINGLY intricate and looks like it could lead to a different universe. The visuals are so strange! Changed so much by the 4-Aco and 2CB! I stand and open the the door. The room on the other size is not mine, but I am welcome... things keep peeking at me from behind objects and furniture lol! I have never seen visuals where I can be looking at an object and it simply becomes another object or moves instantly... amazing!
I see my shoes on the carpet...what odd shoes, and as I look they (and I don't know if I'd believe this could happen if I hadn't seen it myself) literally are bending and dancing to the vibrations. But not like walls breath or patterns swirl on traditional psychedeilcs.... I mean they look like they are physically dancing, and very quickly while the rest of the room stays the same. Then I look at something else and it too changes into different fantastic objects.
Wow! In the wise words of someone I have great respect for, 'Yarbles!
Great bolshy yarblockos to you!!' Oh my god my CAT! It is a cubically geometric, rapidly moving block animal with a knack for changing colours, shapes, and performing physically impossible feats. The room is a new world every few seconds... I have never seen visuals where objects change shape, colour, appearance, and geometry so completely and quickly... this is incredible.....
I find the brilliance of the DMT experience to be too short lived and intense for real reflection or insight. With longer lasting psychedelics I move through the trip, evolving with the experience... DMT just takes me there. There is time for thought or reflection. No time for insight in the way LSD or mushrooms imparts it. With DMT it feels like a vast amount of information is being downloaded into my head all at once... and I find it difficult to decipher and translate that wisdom. The DMT experience feels like an exercise in pure being.
I have no more words to describe this trip.... at least not now, but perhaps I will add to this after I start to integrate the experience. I feel great today, and there is many more insights that I'll be writing about when I have time to reflect on this experience...
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


The Manson Family killed on this plant.
I had first heard about Belladonna in Kurgan, Siberia. There was a local thrash metal band named after the plant, and their motto was 'Many poisoned, few cured!'. A few years later, while crashing at a communal apartment Western, WI with several punks from across the state, one of the couples told me about experimenting with a tea made from the plant while in Texas. The girl was originally from there, and they were apparantly turned on to the drug by her grandmother. The description they gave me led me to believe that it was something like a mix between a near blackout alchohol experience and an intense LSD trip.
I managed to procure some foilage of the plant about a year later while I was living on the other side of the state with my girlfriend and my best friend. We were involved with some fairly sizable amounts of LSD and experimented regularly with a plethora of chemicals from Cocaine to DXM to Dimenhydrinate to Ketamine etc. We considered ourselves experienced psychonauts, and I had a particularly high tollerance to the drugs. This drug in particular was difficult to find information on, so we truly had to 'experiment' with it.
We used a coffee maker to brew the tea. We did not measure out a specific amount of foilage and just decided that we would measure by glasses. My friend and girlfriend only drank one glass of the tea. I drank two for starters. I was ignorant and arrogant, but figured that since I usually needed almost twice as much as anyone else when using other drugs, that the same would be valid with this. I understood that the drug was extremely toxic and potentially fatal, but I had taken dosages of several chemicals that could have in other people proven fatal and felt that my tollerance would somehow come into play with this drug as well.
After a few hours I decided to drink a couple more cups of tea as I was not
feeling anything... this I can only attribute to the fact that my judgment was already impaired by the drug.
Shortly after this, we, for some reason, decided that it would be a good idea to split up. My girlfriend was feeling sleepy, so she layed down for a nap. My friend felt a bit queezy, and decided that it might be a good idea to go stay at his parent's house for the night, where he would have a little more privacy. I went over to another friend's house.
For the next few hours, I simply lay back on my friends floor, trying to shake the discomfort I felt. I could compare it to a slight overdose of caffeine. Eventually my friend went to sleep, and I lay on the floor convulsing all night long. I did not experience anything that I could have considered 'mind-altering' or 'psychedelic'. The next morning, my friend and his wife came and picked me up to spend the day with them.
We went out to eat and I noticed that people were looking at me strange. I could not read the menu, and felt a slightly disconnected. The next time I spoke to my friend and his wife, they explained to me that the whole time I was with them I shook and quaked, almost like I was having a seizure. I was unaware of it, and they told me they didn't tell me, because they figured that I was on something and didn't want to freak me out. They said that my face was sunken in and dark and that I looked very sick. I only felt a slight disconnection that lasted for somewhere near 48 hours after consuming the tea.
During this time I could not focus on printed words, and was near the end of the 48 hours was starting to feel great concern. I thought I might never be able to read again.
I didn't see my friend and roomate until a few days later. What he described to me could best be compared to a three day Dimenhydrinate trip multiplied in intensity by a hundred. His mother ended up finding him in his underwear in the middle of the night talking to people who weren't there. My friend had spent a couple of years of his life institutionalized for schizophrenia, so his mother assumed he was going through an episode and brought him to the psychiatrist the next morning.
He constantly refered and talked to people who weren't there. He did not seem alarmed or scared by what was happening and did not even remember that he had consumed the tea or that he had been expecting a 'trip'. Unfortunatly for him, he also had his first meeting with his new probation officer two days after consuming the tea, while he was still deep within the grip of the drug.  Nobody expected that it was anything other than a psychotic episode for him, and his psychiatrist just raised his prescription.
I saw my girlfriend the evening after we drank the tea. When I got home she was gone. She had went to work. When she came home, the first thing she did was tell me that when she woke up that morning she found our cat, cold, stiff and dead on the couch. She picked it up and held it for a while. When she put the cat down, she said it awoke from the dead and started walking around. At this point she believed what she was saying to be true. She had not even considered the possibility that she was perceiving this because of the drugs we had consumed the day before. I asked her about her 'trip' and she said that after we left, all sorts of people she hadn't seen in a long time showed up at our apartment, and that there was a big party. She actually thought that both my friend and I had come back at some point during the night. She said she had a lot of fun.
We later contacted virtually everyone she saw (some were unreachable as she hadn't been in contact with them for years) and none of them had come over, most of them were not within 200 miles from our apartment at the time. When she was at work that day, she thought that I came to visit her (she worked alone most of the day as a screen printer in a big shop) and that we had talked all day long. She said that her boss came in a few times and asked who she was talking to, and anytime he did, she explained that she couldn't exactly remember. Only shortly after he left did I reappear and she did not at the time (both when it was happening, and again as she was explaining it to me) seem to understand how illogical this was.
Eventually, over the course of the evening she started coming back to her senses. Never once as I talked to her did I get the feeling that she was 'tripping' so much as she was delusional, but she was so calm that unless you listened to what she was saying, you wouldn't have noticed.
Since our experiment, none of us have had any urge to try and repeat it. I myself did not notice any hallucinations or anything particularly strange at all. I feel very sure that I put myself and my friends at great risk of dying, but feel particularly lucky that I am alive to tell the story.
I would recommend that anyone wishing to experiment with this plant excersize great caution. I would recommend doing some serious research into the toxicological effects of the plant and try to find out what is a reasonably safe amount before consuming any. I would also strongly recommend taking a few lower level practice runs before jumping into it, and I would say that it is imparitive that you have a sober sitter around, as it is very likely that if you come into contact with someone who doesn't know or understand what's going on (or possibly even worse if they do) that you will end up in jail or the mental institution.
I would also recommend reading the trial statements (
testimony 1 &
testimony 3)of Charles 'Tex' Watson of the Manson Family, to get another interesting take on this plant.
Experience Reports are the writings and opinions of the individual authors who submit them.
Some of the activities described are dangerous and/or illegal and none are recommended by Erowid.


2020 Nissan Sentra Looks Much Better, Larger Engine Comes Standard
by Mircea PanaitThe sedan may no longer be the hottest body style out there, but Nissan certainly knows how to make a pretty sedan. Taking inspiration from the Maxima and Altima, the all-new Sentra is a sharp-looking model that packs a larger engine than the previous generation.
From 1.8 to 2.0 liters doesn’t sound like that much of an upgrade, but 149 horsepower and 146 pound-feet of torque translates to increases of 20 and 16 percent, respectively. Even the fuel economy is better according to Nissan, and independent rear suspension should work wonders in the twisties and on the long haul. On the handling front, the electric power steering system should help the driver feel more at ease when maneuvering in the parking lot.
"With more than 6 million Sentras sold, we believe the new one will reach new heights offering refinement and quality, technology and performance not seen before,” declared sales and operations vice president David Kershaw. The original was introduced in 1982, and for the eighth generation, Nissan decided on the CMF-C/D vehicle architecture co-developed with alliance partner Renault for compact- and mid-sized applications. The Sylphy sold in China is the nearest equivalent to the Sentra the U.S. will get early next year for 2020.
Stateside production takes place at the Canton facility in Mississippi, and as you can tell from the photo gallery, new underpinnings add approximately two inches in width. The Sentra’s roofline is also lower, adding to the visual drama of the sporty-looking profile. The interior has also been improved by a considerable margin, now featuring NASA-inspired Zero Gravity seats, Intelligent Around View Monitor, and a floating 8.0-inch touchscreen.
Connectivity includes Apple CarPlay and Android Auto, and if you ask nicely, the seats can be upgraded to a leather-appointed quilted motif. Nissan doesn’t mention anything about ProPILOT Assist semi-autonomous driving technologies, and zooming in on the steering wheel doesn’t reveal any blue icon on the right-hand-side cluster of buttons. It’s quite a curious matter, yes, more so if you remember that the Leaf is available with this tech. 🏁
PRESS RELEASE
20 NOVEMBER 2019
On the eve of the 2019 Los Angeles Auto Show, Nissan unveiled its all-new 2020 Nissan Sentra celebrating the reinvention of the company's best-selling U.S. model of all time. The 2020 Sentra, which goes on sale in late January, transforms the storied nameplate into a head-turning compact sedan with class-leading interior refinement, standard Safety Shield 360, seamless connectivity and fun-to-drive performance. Sentra completes Nissan's redesigned sedan lineup– following major updates to Versa, Altima, and Maxima over the past two years.
2020 Nissan Sentra
"Nissan has a vibrant portfolio of new-generation sedans for customers in the U.S. market," said David Kershaw, division vice president, Nissan Sales & Regional Operations, Nissan North America, Inc. "With more than 6 million Sentra vehicles sold, we believe the all-new Sentra will reach new heights offering refinement and quality, technology and performance not seen before. The lower stance and more athletic design cues from the Maxima sports sedan give Sentra a sexy new look."
Originally introduced for the 1982 model year, the eighth-generation Sentra is built on a new platform that provides greatly improved proportions and stance – about two inches lower and two inches wider than the previous generation. The exterior also incorporates Nissan's latest design language found on its other dramatic sedans, including its signature V-motion grille, thin LED headlamps and floating roof. Sentra also features new wheel designs and a slate of new colors, including three new two-tone color combinations.
Inside, the all-new interior of Sentra is more refined and luxurious, creating a high-quality experience for driver and passengers. Extra attention was paid to the smallest of details to improve the perceived and actual quality of the new Sentra. The feel of the steering wheel in the driver's hands, the smooth operation of the dials and switches were carefully crafted to create a premium feel. Available amenities range from quilted, leather-appointed, heated front seats and heated outside mirrors to Nissan's renowned NASA-inspired Zero Gravity seats and Intelligent Around View® Monitor. Infotainment and connectivity features include an available floating 8-inch multi-touch center display and NissanConnect® featuring Apple CarPlay® and Android Auto™.
The 2020 Sentra also features a new, fuel-efficient 2.0-liter, 4-cylinder engine rated at 149 horsepower and 146 lb-ft of torque – increases of 20 percent and 16 percent respectively over the previous generation's 1.8-liter engine. The new engine is also projected to offer improved fuel economy. Dynamic performance has been greatly improved through the use of a new independent rear suspension and a new rack electric power steering system.
Advanced safety and driver assistance technologies, now available across the entire family of Nissan sedans, include standard Nissan Safety Shield 360, a suite of six advanced driver-assist systems that includes Automatic Emergency Braking with Pedestrian Detection, Rear Automatic Braking, and High Beam Assist. The new Sentra also offers standard 10 airbags, Rear Door Alert, Intelligent Forward Collision Warning, and Intelligent Driver Alertness.
"The all-new Sentra delivers the whole package, with features and value that are hard to ignore," said Kershaw. "It's stylish, confident and connected – a true breakthrough in compact sedans."


Meltwater is the world's leading media intelligence firm. Our software combines the power of AI with the most comprehensive source database in existence to bring our clients advanced media monitoring, social listening, social media management, PR Analytics and Influencer Engagement tools.
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The sources for GeoCODES comes mostly from collaboration with the EarthCube Council of Data Facilities (CDF).
CDF members who express their resources via structured data on the web approaches can be indexed.
GeoCODES uses the gleaner program (gleaner.io) to build the index and (GROW) as a server. See the about section for more.
A very rough draft providing an overview on some topics related to GeoCODES on the about page.
Much of the work taking place here by providers is in support of FAIR data principles. We will be expanding this section to better connect the work here with FAIR.
The GeoCODES architecture is exploring leveraging basic web architecture and structured data on the web to scale its services.
Schema.org is a collaborative, community activity with a mission to create, maintain, and promote schemas for structured data on the Internet, on web pages, in email messages, and beyond. Schema.org can be extended with vocabularies such as DCAT, SOSA, etc. This work is taking place at the ESIP Science on Schema.
Such an approach also allows us to leverage the rich ecosystem of tools developers currently leverage for JSON. Additionally a grow suite of tools and guides specifically for geosciences and structured data on the web are under development.


Welcome to the University of Georgia's New Media Institute! The NMI offers an array of benefits and opportunities for students looking to get involved in the new media and technology field. We have intensively designed a certificate program to best equip students for this are of study in order to assist them in every day life and future job endeavours. Our team works to supply job, internship, shadowing, and interview opportunities with businesses looking for motivated, hard-working students.


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Related Documents
Selected use cases using the RIS3 Innovation Mapping tool of the Online-S3 platform:
-
The World Bank Group (2017), Towards an innovative Poland: The entrepreneurial discovery process and business needs analysis, Washington; The World Bank Group,
pp.29-30, 97-101. [Online] Available at: /
Introduction to the Innovation Map Methodology including Case Study: Mapping Innovative Research in the Dolnoslaskie region (PL) based on "Fast Track" applications to the Polish NCBR.
Selected RIS3 strategies including the Innovation Map method in their implementation process:


The goal of trainr is to offer interactive tutorials built on top of the learnr package.
You can install trainr from github with:
# the development version from github
# install.packages("remotes")
remotes::install_github("rsquaredacademy/olsrr")
trainr uses consistent prefix learn_
for easy tab completion.
Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.


| Package | Description |
|---|---|
| uk.nhs.interoperability.client.samples | |
| uk.nhs.interoperability.client.samples.cda | |
| uk.nhs.interoperability.client.samples.notification | |
| uk.nhs.interoperability.client.samples.smsp | |
| uk.nhs.interoperability.consumer |
API pertinent to ITK message consumers.
|
| uk.nhs.interoperability.consumer.appemulator | |
| uk.nhs.interoperability.payload |
Interfaces to support the generic handling of ITK messages by the transport and distribution infrastructure.
|
| uk.nhs.interoperability.source |
Interfaces to represent information/document/message sources responsibilities in support of ITK message exchange patterns.
|
| uk.nhs.interoperability.transport |
Interfaces representing the abstraction of transport elements of the ITK transport and distribution infrastructure.
|
| uk.nhs.interoperability.transport.WS |
HTTP SOAP Web Service transport implementation classes.
|
| uk.nhs.interoperability.util |
General utility classes.
|
| Modifier and Type | Method and Description |
|---|---|
void |
SimpleMessageCallbackHandler.onMessage(ITKMessage request) |
void |
RoutedMessageCallbackHandler.onMessage(ITKMessage request) |
| Modifier and Type | Method and Description |
|---|---|
ITKMessage |
CDARepository.onSyncMessage(ITKMessage request) |
| Modifier and Type | Method and Description |
|---|---|
void |
CDARepository.onMessage(ITKMessage request) |
ITKMessage |
CDARepository.onSyncMessage(ITKMessage request) |
| Modifier and Type | Method and Description |
|---|---|
ITKMessage |
NotificationRepository.onSyncMessage(ITKMessage request)
Routed messages do not support true synchronous responses.
|
| Modifier and Type | Method and Description |
|---|---|
void |
NotificationRepository.onMessage(ITKMessage request) |
ITKMessage |
NotificationRepository.onSyncMessage(ITKMessage request)
Routed messages do not support true synchronous responses.
|
| Constructor and Description |
|---|
GetNHSNumberResponse(ITKMessage response)
Instantiates a new verify nhs number response.
|
GetPatientDetailsByNHSNumberResponse(ITKMessage response)
Instantiates a new gets the patient details by nhs number response.
|
VerifyNHSNumberResponse(ITKMessage response)
Instantiates a new verify nhs number response.
|
| Modifier and Type | Method and Description |
|---|---|
protected ITKMessage |
ITKServlet.addITKWrappers(ITKMessage itkMessage)
Adds the itk wrappers.
|
ITKMessage |
ITKMessageConsumer.onSyncMessage(ITKMessage request)
Call to process a request message where the application response is returned
synchronously (in the same thread)
|
| Modifier and Type | Method and Description |
|---|---|
protected ITKMessage |
ITKServlet.addITKWrappers(ITKMessage itkMessage)
Adds the itk wrappers.
|
void |
ITKMessageConsumer.onMessage(ITKMessage request)
Call to process a request message where no application response is returned
synchronously.
|
ITKMessage |
ITKMessageConsumer.onSyncMessage(ITKMessage request)
Call to process a request message where the application response is returned
synchronously (in the same thread)
|
| Modifier and Type | Method and Description |
|---|---|
ITKMessage |
SimpleApplicationEmulator.onSyncMessage(ITKMessage request) |
ITKMessage |
RoutedApplicationEmulator.onSyncMessage(ITKMessage request) |
ITKMessage |
ConsumerApplicationEmulator.onSyncMessage(ITKMessage request) |
| Modifier and Type | Method and Description |
|---|---|
void |
SimpleApplicationEmulator.onMessage(ITKMessage request) |
void |
RoutedApplicationEmulator.onMessage(ITKMessage request) |
void |
ConsumerApplicationEmulator.onMessage(ITKMessage request) |
ITKMessage |
SimpleApplicationEmulator.onSyncMessage(ITKMessage request) |
ITKMessage |
RoutedApplicationEmulator.onSyncMessage(ITKMessage request) |
ITKMessage |
ConsumerApplicationEmulator.onSyncMessage(ITKMessage request) |
| Modifier and Type | Class and Description |
|---|---|
class |
DEWrappedMessage
The Class DEWrappedMessage.
|
class |
ITKMessageImpl
The Class ITKMessageImpl.
|
class |
ITKSimpleMessageResponse
The Class ITKSimpleMessageResponse.
|
class |
SimpleMessage
The Class SimpleMessage.
|
| Constructor and Description |
|---|
DEWrappedMessage(ITKMessage message)
Instantiates a new dE wrapped message.
|
DEWrappedMessage(ITKService service,
ITKMessage message,
boolean addressed)
Instantiates a new dE wrapped message.
|
| Modifier and Type | Method and Description |
|---|---|
ITKMessage |
ITKMessageSenderImpl.sendSync(ITKMessage request) |
ITKMessage |
ITKMessageSender.sendSync(ITKMessage request)
Operation that allows a business payload to be sent synchronously to the
destination service/system returning the appropriate business response.
|
| Modifier and Type | Method and Description |
|---|---|
void |
ITKCallbackHandler.onMessage(ITKMessage response)
Allows the transport and distribution infrastructure
to pass back an asynchronous response received in
response to an asynchronous request.
The response message may be a generic ITK Business Acknowledgement (for instance as a result of a sendCDA
invocation) or a specific business response associated
with the request message.Note: It is the responsibility of the application to maintain state and do the necessary correlation of this message against the original request to complete the transaction. |
void |
ITKMessageSenderImpl.send(ITKMessage request) |
void |
ITKMessageSender.send(ITKMessage request)
Operation that allows a business payload to be sent to the
destination service/system with no response expected (a.k.a.
|
void |
ITKMessageSenderImpl.sendAsync(ITKMessage request) |
void |
ITKMessageSender.sendAsync(ITKMessage businessPayload)
Operation that allows a business payload to be sent asynchronously to the
destination service/system.
|
ITKMessage |
ITKMessageSenderImpl.sendSync(ITKMessage request) |
ITKMessage |
ITKMessageSender.sendSync(ITKMessage request)
Operation that allows a business payload to be sent synchronously to the
destination service/system returning the appropriate business response.
|
| Modifier and Type | Class and Description |
|---|---|
class |
ITKInfrastructureAck
The Class ITKInfrastructureAck.
|
| Modifier and Type | Method and Description |
|---|---|
ITKMessage |
ITKSender.sendSync(ITKTransportRoute destination,
ITKMessage request)
Operation that allows a business payload and ITK wrappers (e.g.
|
| Modifier and Type | Method and Description |
|---|---|
void |
ITKSender.send(ITKTransportRoute destination,
ITKMessage request)
Operation that allows a business payload and ITK wrappers (e.g.
|
void |
ITKSender.sendAysnc(ITKTransportRoute destination,
ITKMessage request)
Operation that allows a business payload and ITK wrappers (e.g.
|
ITKMessage |
ITKSender.sendSync(ITKTransportRoute destination,
ITKMessage request)
Operation that allows a business payload and ITK wrappers (e.g.
|
| Modifier and Type | Class and Description |
|---|---|
class |
WSSOAPMessageImpl
The Class WSSOAPMessageImpl.
|
| Modifier and Type | Method and Description |
|---|---|
ITKMessage |
ITKSenderWSImpl.sendSync(ITKTransportRoute destination,
ITKMessage request) |
| Modifier and Type | Method and Description |
|---|---|
void |
ITKSenderWSImpl.send(ITKTransportRoute destination,
ITKMessage request) |
void |
ITKSenderWSImpl.sendAysnc(ITKTransportRoute destination,
ITKMessage request) |
ITKMessage |
ITKSenderWSImpl.sendSync(ITKTransportRoute destination,
ITKMessage request) |
| Constructor and Description |
|---|
WSSOAPMessageImpl(ITKMessage itkMessage,
String messageType) |
WSSOAPMessageImpl(ITKTransportRoute destination,
ITKMessage itkMessage,
String messageType)
Instantiates a new wSSOAP message impl.
|
| Modifier and Type | Method and Description |
|---|---|
void |
MessageQueue.queue(ITKMessage request)
Queue.
|
All content is available under the Open Government Licence, except where otherwise stated
All example source code is available under Apache 2.0, except where otherwise stated


...a programmer 😊
I'm Lokesh Rathore,currently studying at VIT university and a future web developer.
⭐Web developer
⭐C++ programmer
⭐soft Python skills
⭐Dance
⭐Music
⭐Teamwork Skills
©2021 Lokesh Rathore.


Poisson Equation Solver¶
Using DFT to find the energy of a system requires the ability to solve poission’s equation.
API Documentation¶
This module contains methods used to solve the poisson equation.
-
pydft.poisson.
charge_dist
(s, R, coeffs, sigmas)[source]¶ Finds the charge distribution for the system represented as a sumattion of gaussians.
Parameters: - s (list of int) – The number of samples points along each basis vector.
- R (numpy.ndarray) – The basis vectors for the unit cell.
- coeffs (list of float) – The coefficient for each gaussian.
- sigmas (list of float) – The sigma values for each gaussian.
Returns: n –
- The value of the charge distribution at each
point in the space.
Return type: numpy.ndarray
Raises: ValueError
– if the number of coefficients doesn’t match the number of sigmas, i.e., len(ceoffs) != len(sigmas).Examples
The following example finds the charge distribution contsructed from two gaussians in a simple cubic unit cell. The distribution is evaluated at such that there are 10 sample points in the R[0] direction, 5 in the R[1] direction, and 15 in th R[2] directon. The distribution is then constructed as: \(n(r) = coeff_{1} \frac{ \exp(\frac{-r^2}{2 \sigma_1^2})}{(2 \pi \sigma_1^2)^{3/2}} + coeff_2 \frac{\exp(\frac{-r^2}{2 \sigma_2^2})}{(2 \pi \sigma_2^2)^{3/2}}\) where r is the distance from each sample point to the center of the cell.
>>> from pydft.poisson import charge_dist >>> import numpy as np >>> s = [10,5,15] >>> R = np.array([[1,0,0],[0,1,0],[0,0,1]) >>> coeffs = [1, -1] >>> sigmas = [0.75, 0.5] >>> n = charge_dist(s,R,coeffs,sigmas)
-
pydft.poisson.
poisson
(s, R, n)[source]¶ Calculates the solution to poisson’s equation.
Parameters: - s (list of int) – The number of samples points along each basis vector.
- R (numpy.ndarray) – The basis vectors for the unit cell.
- n (numpy.ndarray) – The charge distribution evaluated at the sample points.
Returns: phi –
- The value of the function phi at the
sample points.
Return type: numpy.ndaray
Examples
>>> from pydft.poisson import charge_dist, poisson >>> import numpy as np >>> s = [10,5,15] >>> R = np.array([[1,0,0],[0,1,0],[0,0,1]) >>> coeffs = [1, -1] >>> sigmas = [0.75, 0.5] >>> n = charge_dist(s,R,coeffs,sigmas) >>> phi = poisson(s,R,n)


Main
Navigating between landmarks focuses the landmark, so pressing Tab picks up from the current landmark. Navigating between landmarks in turn should pick up from where the focus is.
Nested landmark 1
This is in a nested landmark.
This isn't in a nested landmark.
Nested landmark 2
This is in a nested landmark.
Nested landmark A
This is in a nested landmark.
This isn't in a nested landmark.
A <div>
! :-)
Nested landmark B
This is in a nested landmark.


subject
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---
layout: default
title: HTML and CSS Design and Build Websites Book
---
HTML and CSS Design and Build Websites Book
Practicing examples and exercises in the HTML and CSS: Design and Build Websites Book
Publisher : John Wiley & Sons; 1st edition (November 8, 2011)
Author: Jon Duckett


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There must be an unwritten rule that states you are not allowed to graduate unless you attempt to produce at least one writeup about the Kalman filter. This is my attempt. $ \newcommand{\abs}[1]{| #1 |} \newcommand{\bigabs}[1]{\left| #1 \right|} \newcommand{\R}{\mathbb{R}} \newcommand{\E}{\mathbb{E}} \renewcommand{\Pr}{\mathbb{P}} \newcommand{\calE}{\mathcal{E}} \newcommand{\calF}{\mathcal{F}} \newcommand{\calD}{\mathcal{D}} \newcommand{\calN}{\mathcal{N}} \newcommand{\calL}{\mathcal{L}} \newcommand{\calM}{\mathcal{M}} \newcommand{\calN}{\mathcal{N}} \newcommand{\bbP}{\mathbb{P}} \newcommand{\bbQ}{\mathbb{Q}} \newcommand{\ip}[2]{\langle #1, #2 \rangle} \newcommand{\bigip}[2]{\left\langle #1, #2 \right\rangle} \newcommand{\T}{\mathsf{T}} \newcommand{\Tr}{\mathrm{Tr}} \newcommand{\ind}{\mathbf{1}} \newcommand{\calL}{\mathcal{L}} \newcommand{\norm}[1]{\lVert #1 \rVert} \newcommand{\barx}{\overline{x}} \newcommand{\cvectwo}[2]{\begin{bmatrix} #1 \\ #2 \end{bmatrix}} \newcommand{\bmattwo}[4]{\begin{bmatrix} #1 & #2 \\ #3 & #4 \end{bmatrix}} $
First, let us set up the filtering problem. Consider the following linear dynamical system: $$ \begin{align*} x_{t+1} &= A x_t + B u_t + w_t \:, \\ y_t &= C x_t + v_t \:. \end{align*} $$ Here, we will assume that $x_0 \sim \calN(0, X)$, $w_t \sim \calN(0, W)$, $v_t \sim \calN(0, V)$, and that the $w_t$ and $v_t$'s are independent across time. We will also assume that the inputs $u_t$ are only a function of $y_1, ..., y_t$. The filtering problem is, given a sequence of observations $y_1, ..., y_t$, construct an estimate of the state $x_t$. The Kalman filter is an elegant solution to this problem.
There are many interpretations of the Kalman filter. In this post, I will take the Bayesian interpretation. This interpretation starts with the distribution $x_t | y_{1:t}$ as given (the prior), observes $y_{t+1}$, and then updates $x_{t+1} | y_{1:t+1}$ (the posterior).
To do the derivation, let us first define some notation. We let $$ \barx(t|t) = \E[ x_t | y_{1:t}] \:, \:\: \barx(t+1|t) = \E[ x_{t+1} | y_{1:t} ] \:. $$ We also let $$ \begin{align*} P(t|t) &= \E[ (x_t - \barx(t|t))(x_t - \barx(t|t))^\T | y_{1:t} ] \:, \\ P(t+1|t) &= \E[ (x_{t+1} - \barx(t+1|t))(x_{t+1} - \barx(t+1|t))^\T | y_{1:t} ] \:. \end{align*} $$ We now proceed inductively. Suppose at time $t$, we have that $x_t | y_{1:t} \sim \calN( \barx(t|t) , P(t|t))$. Let us now compute $x_{t+1} | y_{1:t+1}$ given this inductive hypothesis. We do this by first computing the joint distribution of $(x_{t+1}, y_{t+1})$ conditioned on $y_{1:t}$. We know by the linear dynamical system update rule that this joint distibution will also be a Gaussian distribution, so it suffices to compute the mean and covariance. First, we have: $$ \E\left[ \cvectwo{x_{t+1}}{y_{t+1}} \:\bigg|\: y_{1:t} \right] = \cvectwo{I}{C} \barx(t+1|t) \:. $$ Next, we have: $$ \mathrm{Cov}\left( \cvectwo{x_{t+1}}{y_{t+1}} \:\bigg|\: y_{1:t}\right) = \bmattwo{ P(t+1|t) }{ P(t+1|t) C^\T }{ C P(t+1|t) }{ C P(t+1|t) C^\T + V } \:. $$ Therefore: $$ \begin{align} \cvectwo{x_{t+1}}{y_{t+1}} \:\bigg|\: y_{1:t} \stackrel{d}{=} \calN\left( \cvectwo{\barx(t+1|t)}{C \barx(t+1|t)}, \bmattwo{ P(t+1|t) }{ P(t+1|t) C^\T }{ C P(t+1|t) }{ C P(t+1|t) C^\T + V }\right) \:. \label{eq:jointdist} \end{align} $$ Now we need a classic result regarding the conditional distribution of jointly Gaussian random vectors.
Lemma. Suppose that: $$ \cvectwo{u}{v} \stackrel{d}{=} \calN\left( \cvectwo{\mu_1}{\mu_2}, \bmattwo{\Sigma_{11}}{\Sigma_{12}}{\Sigma_{12}^\T}{\Sigma_{22}} \right) \:. $$ Then we have that $$ u | v \stackrel{d}{=} \calN( \mu_1 + \Sigma_{12} \Sigma_{22}^{-1}( v - \mu_2), \Sigma_{11} - \Sigma_{12} \Sigma_{22}^{-1} \Sigma_{12}^\T ) \:. $$
Applying this lemma to $\eqref{eq:jointdist}$, we conclude that: $$ \begin{align*} \barx(t+1|t+1) &= \barx(t+1|t) + P(t+1|t) C^\T (C P(t+1|t) C^\T + V)^{-1} (y_{t+1} - C \barx(t+1|t)) \:, \\ P(t+1|t+1) &= P(t+1|t) - P(t+1|t) C^\T (C P(t+1|t) C^\T + V)^{-1} C P(t+1|t) \:. \end{align*} $$ We can also compute $\barx(t+1|t)$ and $P(t+1|t)$: $$ \begin{align*} \barx(t+1|t) &= A \barx(t|t) + B u_t \:, \\ P(t+1|t) &= A P(t|t) A^\T + W \:. \end{align*} $$ For $\barx(t+1|t)$, we use the assumption that $u_t$ is $y_{1:t}$ measurable. These are the equations that define a Kalman filter. Start with $\barx(0|0) = 0$ and $P(0|0) = X$. Then iteratively update: $$ \begin{align*} \barx(t+1|t) &= A \barx(t|t) + B u_t \:, \\ P(t+1|t) &= A P(t|t) A^\T + W \:, \\ \barx(t+1|t+1) &= \barx(t+1|t) + P(t+1|t) C^\T (C P(t+1|t) C^\T + V)^{-1} (y_{t+1} - C \barx(t+1|t)) \:, \\ P(t+1|t+1) &= P(t+1|t) - P(t+1|t) C^\T (C P(t+1|t) C^\T + V)^{-1} C P(t+1|t) \:. \end{align*} $$ And there we have it.
Miscellaneous
There is a Riccati recursion happening behind the scenes of the Kalman filter updates. To see this, observe: $$ \begin{align*} P(t+1|t) &= A P(t|t) A^\T + W \\ &= A P(t|t-1) A^\T + W - A P(t|t-1) C^\T (C P(t|t-1) C^\T + V)^{-1} C P(t|t-1) A^\T \:. \end{align*} $$ This is the Riccati recursion for the LQR problem with parameters $(A^\T, C^\T, W, V)$ taking the place of $(A, B, Q, R)$.
Also observe that the conditional covariance $P(t+1|t+1)$ are not a function of the inputs $u_t$. This means that no matter what policy $u_t$ is applied, it does not affect the covariance of the estimator. This observation gives rise to what is known as (an instance of) the separation principle in optimal control. Suppose we want to solve the following finite horizon optimal control problem: $$ J = \E\left[ \sum_{t=1}^{T-1} x_t^\T Q x_t + u_t^\T R u_t + x_T Q x_T \right] \:, $$ where our policy $u_t$ is only allowed to depend on $y_1, ..., y_t$ and not $x_t$. This classic setup is known as the Linear Quadratic Gaussian (LQG) control problem. Here the finite horizon is for simplicity: the separation principle generalizes to the infinite horizon setting as well.
We can decompose the stage wise cost for the state $x_t$ as follows: $$ \begin{align*} \E[ x_t^\T Q x_t ] &= \Tr(Q \E[x_tx_t^\T ]) \\ &= \Tr(Q \E[\E[ x_tx_t^\T | y_{1:t}]]) \\ &= \Tr(Q \E[ P(t|t) + \barx(t|t)\barx(t|t)^\T ]) \\ &= \Tr(Q \E[P(t|t)]) + \E[ \barx(t|t)^\T Q \barx(t|t) ] \:. \end{align*} $$ Therefore, $$ J = \Tr\left(Q \E\left[ \sum_{t=1}^{T} P(t|t)\right]\right) + \E\left[ \sum_{t=1}^{T} \barx(t|t)^\T Q \barx(t|t) + u_t^\T R u_t + \barx(T|T) Q \barx(T|T) \right] \:. $$ Because $P(t|t)$ is not a function of the inputs $u_t$, this means that the first term is the same for any policy. On the other hand, $\barx(t|t)$ evolves according to $\barx(t+1|t) = A \barx(t|t) + B u_t$. Therefore, if we want to minimize the cost on the RHS, we simply need to play the controller $u_t = K_t \barx(t|t)$, where $K_t$ is the optimal controller at time $t$ for the LQR problem $(A, B, Q, R)$. This is quite remarkable, as it says we can solve the LQG problem by combining a Kalman filter with the optimal LQR controller. While this is a very natural thing to do, it turns out to be optimal for LQG!


Introducing Oneself
Elementary A Introducing Oneself In this lesson, you will learn about words used to introduce oneself, the use of simple present, and the use of the articles ‘a/an/the’.
Appearance
Elementary A Introducing Oneself In this lesson, you will learn about words used to introduce oneself, the use of simple present, and the use of the articles ‘a/an/the’.
Descriptions
Elementary A Introducing Oneself In this lesson, you will learn about words used to introduce oneself, the use of simple present, and the use of the articles ‘a/an/the’.
Likes and Dislikes
Elementary A Introducing Oneself In this lesson, you will learn about words used to introduce oneself, the use of simple present, and the use of the articles ‘a/an/the’.


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