This appeared in salon.com, The Rumpus, The Nervous Breakdown, Men's Health, and Nylon. She lives in Upstate New York. Please welcome Chloe. Hi everyone. It's her back to follow, you guys are great. Thanks for having me. I have like a lot of different friends here from all different walks of life, so thanks for coming. And I've never been to San Francisco before. I got in last night and if we're being honest, I got really hammered and I'm in like pretty rough shape right now. I'm sorry I was late. We couldn't find the room. But I love San Francisco so far and it's been amazing. I'm going to read from my book. Unfortunately, I don't have any copies with me because I was, I'm all out. I'm reading from this like busted up review copy with a sticker on it. And but if you want to buy a copy, just talk to me and I'll have copies soon and we can figure something out. It is a novella and it's a story of two women, 19 years apart.  She has a girlfriend and the other one doesn't really know what she is. And they start up a torrid love affair that's just up and down. So I'm going to actually read from different parts of it since there's really no spoiler. It's just a totally, it's just doomed from the beginning. So I'm going to skip around. So if you're like wondering, oh, I'm confused. Are they together or not together? It's just totally a roller coaster. I knew I found Finn's aesthetic attractive, but I hadn't yet explored feelings of being attracted to her, in part because I hadn't yet explored my ability to fall for a woman. I figured if I were going to be with a woman, I would have been with one by now. I would know if I was bisexual or gay. Being a writer, I assumed I was at least mildly self-aware. It also had not occurred to me that Finn might be attracted to me. It didn't occur to me she might be interested in me as more than a friend. It didn't occur to me, even though she wrote me an email in which she said she wanted me to read on a bar stool under dim lights for her while she sipped on a beer. Yeah, book it, her email ended. Book it. And I do vaguely remember staring at her brown hands while she spoke. Her knuckle tattoos, thinking they were the most beautiful hands I had ever seen. After the first time I sleep with Finn, I excitedly tell one of my bisexual friends about my weekend. She shakes her head. You guys shouldn't do that.  She raises her voice and says, because you're not a lesbian, because she has a girlfriend. She is hot, though, she adds, and I agree. When morning, my phone interrupts my sleep and it's Finn. She says she wanted to hear my voice. She has left work on her lunch break and she's going to buy a slice of pizza. Sometimes on American Idol, Nicki Minaj says, I'm obsessed with you, she says. I'm obsessed with you right now, I say. I'm so obsessed with you right now. My mother had recently told me that life could be exciting without drugs. After having sex with Finn, I begin to agree with my mother. I've never had a therapist before, but in this city, everyone seems to have both a therapist and an acupuncturist. After a week of avoidant behavior, spend eating my weight in macaroni and cheese while watching the movie Mermaids, I decide, hey, maybe I could use someone to talk to you. I find a woman named Karma, and I call her, but she's $100 per session, and I quickly hang up. I find a woman with long red hair. She's smiling in her online photo, her arm is around her dog. Her voice is meek, but she sounds nurturing like I can trust her. Dr. Kay's office is on the third floor of a large building. The room is spacious with two windows. Through them, there is a large tree I grow accustomed to staring at through each season. The furniture is Ikea style. Dr. Kay wears cardigans and flats. She never takes notes while I talk, but she remembers everything. I love having this woman's full attention. I love the way she looks at me while I talk. I love the way her eyes tear up when mine do. Does your therapist think I'm bad for you? Finn asks. I don't want to be bad for you. Finn gives me a choice. Do I want to wear her flannel shirt or her sweatshirt or her leather jacket? It is a few weeks after the first time we slept together, and it's a weeknight. I choose the flannel because I've already worn the sweatshirt and jacket, and I like to wear as many different pieces of clothing of other peoples as I can. Finn fingers me under the table under my dress, which makes this easier. Come home with me, she says, three times in my ear. She's too drunk to steer her bike home. She thinks she is going to puke. She accuses me of roofing her drink. So I walk her bike, and she stumbles along next to me. This is the first time she has drunk more than I have. We fall asleep holding each other and wake up early. What are these underwear? She asks. What do they look like? I tell her they are gray and lace and cheap.  Like, even if there was a war, they would still stay on. I tell Finn I'm worried her rings are going to come off inside of me. I'm terrified of things getting stuck inside my vagina, though nothing like that has ever happened. Whenever we have sex, Finn throws one of her back ribs out and can feel it for weeks afterward. No one has ever laughed at that before. My right shoulder blade is always bothering me. I'm hyper aware of it sticking out of my back. She calls it my wing. I love asking her, will you fix my wing? When I ask that, she nods, turns me onto my back, and touches my shoulder blade tenderly. She takes my hand, stretches my arm out, and moves it in circles, coaxes it back into place. Tonight, while she is doing this, it is quiet until she says, I don't know, but when you moved here, I felt like you belonged to me. She says, if you fall in love with someone else, will you tell me? I ask her, why? So I can be happy for you. And sad for me, she says. And we both laugh a little. Then she mumbles, I don't want you to fall in love with anyone else. Finn and I both have a birthday in spring. She gives me nothing for my birthday. I give her nothing for hers. On my birthday Eve, Nathan and I hit the bars after work.  And at the end of the night, we find ourselves at a strip club. I keep putting dollar bills into the stripper's underwear and a man on the loudspeaker says, please stop touching the dancers. Nathan drives me home and is patient with my manic chatter while we sit parked outside my apartment. I sing along to dream on by Aerosmith and when I'm finished, I lean over and vomit on the sidewalk. Nathan holds my hair back from my face, rubs my back. When I finish, he looks apologetic and embarrassed. He tells me he's gotten his period and could he come use the bathroom? His testosterone levels are out of whack. I feel terrible that he's been silently struggling all night. While we walk downstairs to my apartment, he gently points out to me that I have pissed myself. My mom's birthday also falls in spring and she flies in to visit me. I meet her at the airport. I do with my mother many of the same things I do with Finn. We lie in my bed and watch girls. My mom sleeps on the side of the bed Finn slept on.  She makes comments on my outfit choices. I have a newfound fascination with my mother. If she has a new bracelet, I want to try it on. If she has a glass of water, I want to sip. If she has boots I haven't seen, I want to borrow them for the day. I want to know her dreams in the morning. It was similar with Finn.  I took her rings off of her fingers and onto my own. I once told her I wanted to dress up in all her clothes. I wanted what was not mine. In Finn's absence I crave the attention of women. It doesn't matter who it is. I jump at the chance to be around females in public and private settings with friends and strangers. I also join an online dating site. Remember when you went dyke shopping? The female Woody Allen asked me over the phone recently. That sounded exhausting and depressing.  I accept all invitations and often I do the inviting. One Saturday I go on three dates in a row with women I meet online. I tell myself these dates are a distraction technique but there is part of me that hopes I will fall in love. I meet a woman who describes herself in her online profile as a dyke who rides bikes. This is perfect and I wonder if she'll be like Finn. I meet her on the patio of a bar and 10 minutes into our conversation I learn. One, she's an alcoholic. Two, Augustine Burroughs is her hero. Three, she checks herself into rehab often. She works delivering sandwiches for a cafe. Her face is all busted up from falling off of her bike the night before drunk. I'm attracted to this kind of mess and we make plans to hang out again a few days later. I meet her outside of her grandmother's house. We sit on the lawn close to one another and she passes me the apple she is eating. I take a bite and pass it back. This feels intimate to me, sharing saliva. Are we girlfriends? I wonder in my head. Or are we just sharing an apple? We walk to the grocery store to buy a six pack and I make a salad at the salad bar. She asks me for $10 to purchase the beer saying she doesn't have any money. She whispers in my ear, just walk out the door with the salad. I am surprised when she says this. Not because it's something I have never done but because it is something I have. We sit outside drinking beers, sharing my stolen salad which is when she tells me she was recently arrested for stealing beer from this very grocery store. She tells me she had done a bag of cocaine beforehand and I begin to wonder about the recklessness of hanging out with a girl like this. I descend forward through the day with her anyway. On some level I know I should feel uncomfortable but I do not and when she says follow me, I do. I follow her through her bedroom window. We lie in her bed, drink Svedka and play with her cat. Another woman sends me an enthusiastic and articulate message about books and writing because in my profile I say I'm a writer. We meet late one night at a bar. Her profile says that one of the first things people notice about her is that she's a drogenous but she's tall and skinny and blonde and very feminine. She tells me she's the gayest person in the world but in my head I think I've seen gayer. She is five years younger than I am, 10 inches taller. She walks me home. We go on a few more dates to the movies, to dinner and drinks and to a show. She pays for everything. She has money in a car. I have nothing. Months later I receive a mass email from her with the subject line, gender exclamation point. Those of us who receive this email are to know she now identifies as genderqueer and we must try to transition away from the pronouns she and her. A friend sets me up with a woman named Angel. Angel is wearing the uniform of women our age in this city, American apparel sweatshirt, under a jean jacket, black jeans and fry boots. They're the motorcycle design. She's sure to tell me she actually used to ride a motorcycle and that's the only reason she has them. We run into a group of her friends and she begins telling them about a girl she met and is falling in love with. She's 30, which is perfect. She turns to me and says no offense but I really need a partner who has already gone through the Saturn return. It's like San Francisco, you guys Latin, some cities nobody knows what the Saturn return is. I meet another girl in a patio of a bar. Her posture is horrendous and her social skills non-existent. I find out she's vegan and ask her related questions until I excuse myself saying I have to go to a friend's house to meet her new dog. Sitting half dressed in my bra and tights on Finn's bed I listen to Katie laying on my phone while she showers. I thought I heard music, she says, entering the room. She grabs my head and kisses me hard. One, two or three, she asks, standing at my back. What? Oh, she's talking about the clasp on my bra. It is undone and she is asking me which clasp she should put it on. One, two or three. I tell her I don't know. Any of them are fine. Maybe two, I'm not sure. No one has ever asked me this before. During my break at the library I opened the book of questions. I opened randomly to a page and the question is would you exclude sex from your life for a year if you knew you would be more peaceful? Finn asked me to marry her once. She was off to get our third round of drinks and she leaned over me where I was sitting. Her arm hung over the booth. She hunched over me. She told me she'd been thinking about it. Would you marry me? She asks. I won't answer, but she won't let me off the hook so finally I say either duh or of course. In the morning I remind her of it.  I see now that she said would you as opposed to will you. This is what happened. I fell in love with someone I shouldn't have fallen in love with is what Finn says, all logical and slowly when she is mad at me one night. She talks to me like I have a learning disability. I wonder if she realizes she just quoted a Buzzcock song but I don't say anything. I let it go. Who cares? She used to be able to see my mind gears turning. What? She'd ask, seeing a certain expression on my face.  Put your heart on my heart. So I'd sigh and straddle her and lay my heart down and she'd say, this is gonna be a good one. Any discipline that ever existed flies fast out the window. Drained of mania, I become soft, gain weight. I am lethargic and the heat makes it worse. Poor me. There's nothing so sweet as wallowing in it, is there?  Jeanette Winterson writes and written on the body. I get drunk and high like in high school. I smoke weed out of a can. I drink wine out of a box. I used to be more hardcore in myself destruction but I'm back to the basics now. I develop a nap habit for the first time in my life. I'm a proper hedonist. I do most things I can without getting out of bed. I buy one dollar pizza from 7-Eleven where the guy tells me it is $2 for two slices. I hide the pizza in my purse while I walk home because no one wants to be friends with someone who eats 7-Eleven pizza. I'll stop there, thank you so much.


This is stock number 9124, a 2015 Jeep Wrangler Unlimited Rubicon. This vehicle has the 3.6 liter V6 Pentastar motor. From this video, you'll be able to tell that this Jeep is extremely clean all the way around. If you have HD capabilities on your computer or a smart device, turn them on now because we shoot all our videos in HD. This one has Nitto Trail Grappler MT 35x12.5 R20 LT tires and they are on 20 inch XD series painted alloy rims that are in excellent condition. These tires look like they have probably about 80-90% of the tread left. You can see the frame and underbody on this vehicle is very, very clean. I didn't see any dents or dings on the hood. The front grille is in excellent shape. It has a very nice heavy-duty metal front bumper. Nice tow hooks on it. The passenger side rim is in really nice condition as well. And as you go down this side of the vehicle, you can see just how clean the body is, how reflective the paint is. That's why we do these videos. We want to make sure that our out-of-state customers or the people that just can't make it down and take a look at it in person can experience it like they are right here right now. That's why we do it in HD. So you can get a really good idea of the overall condition and make sure that you're making a smart buying decision even if you're not here. Heavy-duty rock rails with step bars on them. Back rim is in excellent condition. The back tires have just as much tread as the front tires. And you can see the frame and underbody on this vehicle. Very, very clean, like new underneath. All the lower rockers look really good as well. It has the black hardtop. Rear bumper is in excellent condition. This one does have a towing package with the receiver hitch and wiring. And that's what a brand new tire looks like with the tread. So you can compare that to the tread that's on the tires right now. Very, very new tires on there. Back rims in pretty nice condition as well. Back storage area, very clean. Has the factory in-floor subwoofer. You have the mat back here, the Jeep mat. Now with that subwoofer you do lose a little bit of storage space. But you do still have your holes for your door hinges and roof bolts. Underneath there is where the jack is. And you can see that subwoofer takes up that old storage area that they used to have. But it frees up all the space right there instead of the subwoofer taking up, you know, that much of the storage area. These hardtops are pretty easy to come off. Three bolts on each side and then one on the top on each side. So four bolts. And she lifts right off. Gonna want to have two people to take that off though. The door shuts nice and solidly. You got the nice gas door cover on there and down this side of the vehicle just as clean as a passenger side. Hardtops in nice shape on this side, no major scratches or scuffs. And the body on this side of the Jeep is very, very clean as well. See just how glass-like that paint is. Inside you get the black leather seats. Both of these seats are heated. Driver seat height adjust. You got the Rubicon stitched into the backrest. There's no rips or tears or major wear on the seats. You have factory all-weather floor mats throughout. Of course on the Rubicon you get the sway bar and axle lock buttons right there. Power windows, power locks. You can see that this Jeep has 17,895 miles. You get Bluetooth audio controls on the leather-wrapped steering wheel. Cruise controls on this side. You have a compass temperature and mileage display. The 430N radio with the factory navigation system in it. You can also do 28 gigs of hard drive data on here. So you just go there and you can download your CDs and everything. Heated seat buttons, power mirrors. Automatic five-speed transmission with the 4x4 shifter on the floor. You also have stability control, downhill assist control. The passenger seat is very clean as well. This vehicle has never been smoked in. It's absolutely perfect on the inside. It has 115 volt, 150 watt plug-in. The all-weather floor mat on that side as well. Take a quick look at the back seats and then check under the hood. No rips or tears back here. You do get the latch child safety system down there. And then these seats do fold down. Four extra storage. Both sides go down like that and they go completely flat. So if you put something over here you can easily make yourself a lot of extra room. And of course we have the all-weather floor mat back here as well. Very nice Jeep, very well set up. Drives like a dream. I just drove it over here. Probably one of the nicest used Wranglers we have on the lot right now. And we got quite a few used Wranglers. So check them all out at our website, summitauto.com. See the engine bay is very clean, runs very smooth. 3.6 liter Pentastar V6 motor. Been on towards the top 10 engine list four different times. This one has been fully safety inspected by our service shop and Chrysler certified technicians as a fresh oil and filter change. All the fluids have been checked off, checked and topped off. And the vehicle has been gone through mechanically 100% and this vehicle is 100% ready to go. And to see more pictures of this Jeep or one of our other 400 new and used cars, SUVs, minivans, especially Wranglers, we are an AEV certified dealer. Check us out.  Videos of every single used vehicle that we have all at summitauto.com. Thank you so much. If you want to check out more videos, you can go to our YouTube channel which is youtube.com slash summitauto. Like, subscribe and share.  Ask for one of our sales associates to help make this Jeep yours today. Once again, that number is<PHONE_NUMBER>. Thanks again. And in a second, you'll notice actually a link to subscribe to our YouTube channel on the left. A link to more Wrangler videos like this one on your right. And if you're not on our website, on the bottom, there's a link right to this vehicle on our website. Click all those. Check them out. Like, subscribe and share. I'm Ford Alpany with the Super Clean 2015 Jeep Wrangler Rubicon Unlimited. Thanks again.


Luckily there's a lot of great herbs that can help you thwart these nasty brain crunching problems. You can take them as pills, powders or essential oils but if you're a tea lover or just looking for another option these are the top 10 herbs that can help stop those headaches and more specifically migraines. Number 10 green tea yep good old green tea because it contains oodles of egcg that thing and other great antioxidants green tea is thought to help with headaches by improving overall health and improving mental acuity this is backed up by the national center for complementary and integrative medicine this respected organization recognizes green tea's ability to help with headaches and mental alertness the downside of green tea is that it does have caffeine which for certain migraine and headache sufferers is a big trigger but luckily it also just depends on who you're talking about as a 2001 study found that caffeine was effective at reducing pain as much as ibuprofen in 58 percent of participants when combined with ibuprofen that number bumped up to 71 percent as such green tea might just be the headache helping tea you need number nine clove tea cloves have been well documented as a pain fighter throughout history however that historical and anecdotal evidence is really the bulk of what we have regarding cloves and headaches that said researchers firmly believe that cloves and clove tea can help with migraines because of its ability to reduce inflammation and improve blood flow now cloves have been known not to mesh with certain blood thinner medications so if you're on something like that it's best to check with your doctor before you try clove tea number eight lavender tea no doubt some of you saw this one coming as lavender is one of the top teas for relaxing both your body and your mind there have been various studies on lavender oil and aromatherapy for headaches unfortunately there aren't any specific ones on lavender tea why do i even try well luckily the studies that are out there show a significant reduction in headache and migraine severity so hopefully they'll do a more specific tea study soon researchers get on it number seven turmeric tea this one again is lower on the list because there aren't that many direct studies on the benefits of turmeric as a tea but there are lots of studies on turmeric and it's active agent curcumin that document turmeric as a massive pain reliever watch the top 10 herbs and spices for pain to find out more turmeric's ability as an anti-inflammatory and its neuroprotective effects really backs up turmeric tea as a big fighter of migraines and headaches now for some people you know just some long-term use of turmeric has been known to cause indigestion so if you get this side effect you know you're just gonna need to ease up on your use a little bit number six capsaicin or chili pepper tea what chili pepper for headaches well i guess if anything i'll make you forget about pain that well actually in a way capsaicin works just like that capsaicin depletes a compound called substance p sounds like code for the virus that starts the zombie apocalypse well substance p conveys the pain sensation from the peripheral to the central nervous system and so being able to dull these direct pathways goes a long way from stopping those migraines and headaches from occurring now the easiest way to make cayenne tea just grab a pinch of cayenne pepper drop it right on into your tea or even put a dab of hot sauce in the same way now i've got quite a big cayenne in here number five peppermint tea peppermint tea is another well-known fighter of pain inflammation and upset stomach its ability to not only fight the headache itself but also many of its side effects is what gets peppermint so high on this list now typically for most people according to studies typically applying a peppermint oil solution to your forehead or temples is said to get rid of your migraines and headaches faster but if this kind of application doesn't work for you then just stick with the peppermint tea number four willow bark tea willow bark for those in the know is the grandparent of aspirin and many people actually call willow bark nature's aspirin and it's no wonder is this herbs been used for pain and inflammation for many centuries now a study in phyto therapy research looked at the various studies on willow barks ability to stop headaches and confirmed yes willow bark can do the trick for headaches and even things like back pain and osteoarthritis the one thing to be careful of is like aspirin you'll want to avoid it if you're on blood thinners or even possibly if you're on certain blood sugar disorder medications experts also say that even though willow bark is aspirin's granddaddy mixing the two at the same time isn't really advisable number three chamomile tea the colossus known as chamomile tea has lots of research when it comes to its ability to help you relax and either evade or relieve those nasty headaches one study found that chamomile not only helped headache pain but also nausea vomiting as well as light and sound sensitivity and when it comes to migraines there might not be another tea that can equal it as chamomile tea has the best research showing how it can thwart migraine headaches without aura or warning signs another study documented how it's awesome at working as a non-steroidal anti-inflammatory drug to stop inflammation and migraines number two feverfew tea now when it comes to various types of headaches feverfew might very well be the number one herb on this list no other tea is listed at being able to fight such a wide variety of headaches including things like menstrual or cluster headaches now the trick with feverfew tea is it works amazingly well for some and others not at all and because of this the american headache society only lists it as probably effective but the studies that are out there are very compelling a review of dozens of studies on feverfew found that it not only helps with the severity and frequency of headaches but it also lessens the side effects feverfew tea works by inhibiting the release of compounds that trigger headaches like serotonin now in some people feverfew can cause oral irritation in large amounts if you know one of those all right feverfew up honorable mentions i'm starting off this section with butter burr because while it's really effective at helping with migraines according to some studies there is also lots of evidence that shows that it can cause liver damage and as such it's actually been banned by numerous countries so it has that big knock against it as well now there are lots of other herbal buddies that might be good for your headaches but really there isn't much research or discernible evidence for most of them yet so i gotta put them here they include rhodiola chrysanthemum rosemary nettle or stinging nettle tea skullcap moringa linden otherwise known as basswood or lime tree tea coriander citron otherwise known as yuzu tea basil shishwan loveage aniseed dried cherry stems and cost merry and now the number one overspice for headaches ginger tea now i kid you not i actually tried pretty darn hard trying to disprove this as the number one tea on this list because i couldn't believe just how many people were saying oh yeah it's the best usually it's because of lots of promotion and companies trying to pump it up when they see stuff like that turns out though according to current research it really does earn the title in addition to helping with headaches ginger tea is renowned for helping with side effects like upset stomach cramps and nausea a study of 100 people who suffer from acute migraines found that ginger was just as effective as the migraine drug suma triptan and had less side effects to boot yeah go ginger take down those nasty drugs that's what i'm talking about oh i gotta strain something so how do you drink tea for headaches whatever your herbal tea of choice there's two main ways to use tea when stopping headaches one is to try and head them off at the pass and have one or two cups of tea early in the day to stop the onset of headaches the other is that as soon as you feel that headache coming on start that water boiling and get that cup ready oh my gosh that's strong now while some people notice the effects immediately others find that it's just a little bit more gradual either way hopefully one of these herbs or spices can help you get rid of those headaches and stay pain-free and happy please be kind take care of each other and watch out for that noggin with a little bit of tea oh my god there's so much cayenne in there


Look what we have to be able to have a meal dude linen moldy bread and a shack over our heads that even capital would be this great we have a lot of my dear freedom freedom. Look at that bird sitting on that also out there I think it's a way to know yes on the side of his life of black and ugly but it's free of the space that the heavens belong to him he can fly under the sun but I'll bet he can't write poetry we can't but you can his wings given flight but your poetry gives you flight that's a lot beyond the life of all that silly old bird yes perhaps beyond your life that you should live and beyond his life there will be nothing your life our lives they shall be forever more and his life shall be never more never more close to Raven never more Virginia excuse me I'm going to my room to my room in Virginia don't disturb me the Raven is going to quote never more and Edgar Allan Poe in that one word I promise you shall live forever more inspiration as you went to his room sat at his desk and pondered head in hands just how we should plan this point he did it all rationally with sober reason not in abandoned drunken madness as it has been said this was a frenzy which all poets know the poetic frenzy of inspiration drove him on and held his thoughts to their purpose but it was that he planned first the length and the impression and tone of appointment planned the refrain and finally he wrote the last part first so that he would have some definite entity taught which to build in this way Edgar Allan Poe worked in that poor cheap little house and so grew those 108 clients of mournful and never ending remembrance the raven upon the midnight jury while I pondered weak and weary over many a quaint and furious volume of forgotten lore while he nodded nearly napping suddenly there came is some visitor tapping at my chamber door only this nothing more it was in the bleak December and each separate dying ember wrought its ghost upon the floor vainly he had sought to borrow from his books a cease of sorrow sorrow for the lost Lenore of the rare and radiant maiden whom the angels name Lenore but presently his soul grew stronger and hesitating then no longer he opened wide the door nothing more and the only word there spoken was the whispered word then you are this he whispered and an echo murmured back the word nearly this and nothing more back into the chamber turning all his soul within him burning soon again he heard it tapping somewhat louder than before open here he flung the shutter when with many a flirt and flutter in their step to stately raven of the saintly days of yore and perched upon the chamber door perched and fat and nothing more so like crests be shorn and shaven our sure no craving gas like grim and ancient raven from the nightly shore then quote the raven much he marveled this ungainly foul to hear this course so plainly though its answer little meaning little relevancy bore but the raven sitting lonely upon the door spoke only that one word profit raven tell this soul with sorrow laden if within the distant aid and it shall cross the fainted maiden whom the angel named the north quote the raven but that word our sign of parting get the back into the tempest and the night's plutonium shore take thy beat from out my heart and take thy form from off my door then quote the raven and the raven never flitting still is sitting just above the chamber door and his eyes have all the meaning of a demon that is dreaming and the lamp light or him streaming throws his shadow on the floor and the soul from out that shadow shall be lifted they bought it same unfortunate my dear no more moly bread and cheese that even a microcuse all Virginia my dearest we're reaching it what's the matter darling what is it? didn't they buy it after all? yes Virginia they bought it for all rights privileges publications and copies for your poem The Raven please find enclosed check in the amount in the amount of ten dollars Virginia we are rich indeed never more the beautiful Annabelle Lee the sweet chime of music that was to Edgar Allen pro the very essence of life died out upon the morning air and there by the wild sea pounding and in the presence of Heaven's angels he buried her then his footsteps turned the predestined track let him on to a new and strange experience in the ancient scroll it is written the angel Israel gives to his chosen only once in ten thousand years the power of vision into the future Edgar Allen po the chosen of this angel had caught that prophetic crystal and the realms above had held it guarded it in his heart and now he stands without the portals of the strange and foreboding house of Roderick Usher in his own words ear him tell in the flash of genius the most sparkling narrative that mortal ear has ever caught as I approached the ancient domain of usher I hence the peculiar atmosphere one which had no affinity to the air of heaven but which reached up from the decayed trees in the gray walls and the silent town the pestilence and mystic vapor dull sluggish faintly discernible and led me and I became aware of a great factor or crack which extending from the roof of the building in front made its way down the wall in a zigzag direction until it became lost in the sullen waters of the town I crossed the heavy bridge of the moat and went filled with a common feeling for the ancient portal of the house of Roderick Usher I wish shelter and warmth tell your master that an old friend has come to call that his name is Edgar Allen po very well you may come in you will wait here in the hall while I inform Mr. Usher of your life as the devils serve and disappeared into the gloom of the long vaulted corridor by gaze wandered to the tomb like structure of my surroundings I say to like only to describe the decaying furnishings and architecture in which I felt strangely confined and such reports hung loosely and dull within cracked pub web frame greening mass of armor peered out from the shadows a great circular staircase wound and coil like some black ugly serpents into the reaches of the room Oh Edgar Allen po Roderick upon my life I've never been so surprised let me look at you it is you isn't it it is Edgar Allen po not some specter come to these halls of us it is truly I rub it and I think it is only within his hunger and cold which lend me this I hope I haven't included intruded my good man let me say that no visitor to this house has ever been more welcome than yourself over come we'll not stand here in the draft of the hall we repair to the warmth and comfort of my studio will you allow me to lead the way my friend Edgar Allen po now now if you will comfort yourself with a fire the great chair we'll talk and I think we have much to say haven't you have much and I have little but tell me Roderick how's it been have you been well since you've asked I can only tell you the truth Edgar I trust it shan't frighten you or disturb your visit I fear that I am falling air to the same sickness which has held my sister in bondage are you speaking of Madeline do you mean to tell me this is ill oh yes but I can't conceive of illness striking such duty of both body and soul that is Madeline the Madeline that I knew life is a strange thing Edgar were you excuse me yes come in well silly what is it I beg your forgiveness for this intrusion yes yes I have just returned from the room of the lady Madeline sir she she's worse she wants me to come to her no sir I beg to inform you sir that the lady Madeline is dead for the servant of us are pronounced the red words the lady Madeline is dead slowly the great ancestral clock the powering the minutes and hours the past in morbid reverie the bells of the tower still swayed in a half-crazed dance and I found myself standing with Roderick Usher within the subterranean copperline bolt that was now the tomb of his lovely sister the lady Madeline Roderick Roderick will you not leave her side now the gaze upon death too long my friend is destructive to the soul of the living but Edgar like I can't believe it somehow my mind refuses to accept the truth this is my sister Roderick this was your sister look at me Roderick and listen life is the end death is the start and only through death may life begin the survival constructive value of this life is the only medium to which man civilization empires they achieve the ultimate of perfection in the fulfillment of the two cardinal laws of God birth and death do we only see beauty in its most perfect form all things must end Robert before they can begin and not his consolation not his condolence do I say to you that death is the life of everlasting peace and triumph that before the dawn of that perfect era of creation shall break before we stupid infinitesimal minutiae a commonplace episode shall find the perfect karma of achievement peace without war metamorphosis of death must decay this flesh of a lot and germinate the cell of new life that shall be forever without the power of death but Edgar surely these things I know Roderick how I know why but I do know them as surely as I know that man shall die so shall civilization but as the selfish forms of social organization shall fall so also shall fall the house of usher and then we'll come the miracle of birth and the phenomenon of everlasting life Roderick usher last of the symbolic line that reaches far back into the history of civilization sinks deeper into his morbid shell only his music the strange half mad innuendo of sound that seems to emanate from the depths of his soul continues on to the murky nights and lyric days to console him then knowing that human companionship alone can hope to break this introverted mania Edgar Alan Paul works in the point of solitary usher and diverts him from his vigil of lone sorrow Roderick Roderick you must put an end to that means of self-portrait Roderick don't go mad and I shall go mad Bobby and soul can't Edgar Edgar my sister is dead and your sister's brother shall also become dead if you don't see this vigil of ones and self-attacement have you ever heard the voices of silence have you ever listened to the words of condemnation echoing from the shadowed corners from rooms from hallways no don't get away to this is no hysteria I'm not mad not insane the voices I have heard were not the mumblings of imagination I tell you Edgar Paul they were real repeating the same words over and over word he is not dead he's buried alive in the name of God Roderick look as I am looking please I am seeing if your eyes do not see his mind and I am truly the rest of reason mad insane the door because I fell with a mad shuddering upon the now lifeless coughs of the serum and in full existence from that chamber and from that mansion I fled to gas and suddenly they're shocked along the path a wild light and while I gave that crack in the castle rapidly widened my brain reeled and I saw the mighty world rushing asunder and they came then through the brilliant that can come only from capacity a strange and perfecting sight of things to come you have been listening to obsession


We might not exist in the world yet, but this place did. Even before, this was a town on earth. This place did indeed exist, yet it wasn't talked about. It existed but was lost for those who would die before their actual lives began. Though some locations of this town are still residing on earth and are now being lived by others, here's what we know. Basically in 1998, there was a place called Elmore. Elmore is a place that exists. The people are nice, but there's sometimes trouble. A lot of the people in Elmore are regular human beings, though there's one family in particular that's more special than the rest of the town of Elmore. This is the Watterson family. There's five residents who reside in the family. Out of the other residents of the family, Anais, the younger sister, Nicole, the mother, Richard, the father, and Darwin, the adopted brother, are normal people, but there's one child in particular named Gumball. He has that name because his family gave it to him. Though he prefers to be named Zac at times. He's a troublemaker, but he's a good boy, though he was diagnosed with ADHD, a common brain disorder, and is a student at the school of Elmore, commonly known as Elmore Junior High. Usually he tries to fit in with the other children, but he's usually left out due to his disorder. He's usually described by other students as annoying.  He even has a girlfriend named Penny, and she adores him so much. Because of his attitude and complaints about him, his parents got a call about his behavior, and they sent him to the school counselor. This counselor is known as Steve Small, or Mr. Small. After Gumball seeing the counselor after a few days, he was starting to act a little normal, and he started being likable around the school. Though after a few days, he suddenly started getting depressed for unknown reasons, it's due to him realizing that the other kids hated him before. That's when his family started noticing their child's depression. As it turns out, he got diagnosed with depression. The doctor prescribed Gumball, a medication made to help his depression. He was supposed to take it for a couple of days. He did what he was told, and he was happier and normal, oddly normal. Lucky for Gumball, it was the weekend, so he could rest. But when it came to Sunday, Gumball told his parents that he wanted a computer. Richard and Nicole hesitated but realized that Gumball was pretty bored, so he got his computer, but his parents told him to be good to get the computer. He did exactly what his parents asked him, and he got the computer he wanted. He immediately started using it, but there's a thing he wanted to try out the most, which is animating. His idea was to draw a cartoon character that looked like a blue cat and had the same clothing as him. But judging by the fact that the Wattersons barely had a budget, he had no choice but to download any free software that would allow him to animate. He called this cartoon character, Gumball. The same name as him. What he animated was of Gumball walking on a loop in a white background. He wasn't going to publish this anywhere, but he wanted to only show it to himself. He thought about the potential for a future show of his, but he didn't want to make it yet. That's how proud he was. It was Thursday, and Gumball went to school, but before he went to school, he took some pills to stay calm. Before he walked to school, he noticed a man standing near the school, somewhere where he couldn't be seen, selling what looked like drugs. Judging by the fact that he was just a child and didn't know better, he asked the man for some, and he got drugs. Gumball gave the man some money, which he earned from the allowance for the drugs. He took them and went to school as normal. It turns out there was a test, and Gumball asked to go to the bathroom. The teacher, Lucy Simeon, allowed him, but before allowing him, Lucy scolded him for a minute for asking during class, and she allowed him afterwards. This was Gumball's opportunity to take the drugs, and he did exactly that. He went back to the classroom, and so far, he was normal. Some students in the hallway reported that his behavior was getting odd. However, before Gumball got close to the classroom, he started vibrating, and he began to vomit a little fluid, and he fell to the ground. When teachers walked by and noticed this scene, Gumball had to leave early and get some help. He began to recover afterward. Gumball's eyes were slightly red, and he couldn't walk properly, almost getting ready to faint at times. He walked into his room and opened the window. Apparently in his head, we thought Gumball thought life was a cartoon, and he couldn't die, so he wanted to test that theory by jumping out of the window. Nicole tried to catch him, but she wasn't fast enough, and Gumball was lying on the ground, possibly dead. Richard and Nicole, along with Garwin and Eunice, were shocked and began to cry until they noticed drugs coming out of Gumball's pocket. Their grumpy neighbor, Mr. Robinson, was wondering what on earth was going on until he noticed Gumball's motionless body on the ground. He called the ambulance, and they drove to the house.  Gumball was picked up, and he was being taken into one of the vehicles to be transported to the Elmore Hospital. They got to the hospital, one of the doctors put a bandage over Gumball's head, and they laid him on the bed.  Gumball was alive, but he wasn't acting right. It was almost like he was possessed. He took a stance as if he were about to attack, but Garwin shoved him back on the bed, and a doctor injected him with something to knock him out. A nurse came into the room and went over to the young and ill Watterson, and the nurse comforted him to make sure he was okay. But if it wasn't already, the odd thing happened. Gumball started groaning as a response. Suddenly, people over at Cartoon Network and numerous scientists went into the room, and apparently, they found out about Gumball's intelligence in animation, but they really wanted to figure out what's truly in his mind.  The doctor did so, and then a scientist was connecting wires and cables to Gumball's body, and one of the Cartoon Network employees started connecting the cables to a TV near the bed. They thought about the potential in Gumball's mind of being the next big show. As they were connecting the wires and cables to the television, it was of Gumball, the cat, the cat version of him behind bars. This represents the fact that he's trapped and he's in a coma. His body can't function at all. The scientists thought this was interesting, so they wrote it on the clipboard, and one of them showed it to a seatan employee. The television eventually changed from static to jumbles to colors, and it started to form the following words. The Amazing World of Gumball Following that was a title card, which read, The Mind. It was played almost like an episode. Gumball's family was also looking at the screen, finding it interesting and odd. A couple of scientists were writing on the clipboard, as they were also interested in this intelligence. It started with Gumball, but there were newer characters that looked like Gumball's family. The fat pink rabbit was Richard, the father. He acted like a slog in the show. Apparently, the female blue cat was like Gumball's already existing cartoon design. This was indeed Nicole, the mother. Gumball's siblings were also included. The smaller pink bunny was Anias. Intelligent as the brother and another being an orange goldfish, this was Darwin. They were just sitting on the couch in their home, exactly as it was in the real world. During this odd and shocking moment, Gumball's girlfriend Penny walked into the hospital room, and she noticed Gumball's lifeless body lying in the hospital bed and looked directly at the television. Gumball was indeed in a coma though. Something caught Penny's attention. She noticed the wires and cables coming out of Gumball's body toward the television. She asked what was going on, and she was informed that they found out about the intelligence of the little boy, and they were displaying his thoughts on television, not realistic but cartoony. On the television screen, it showed Gumball's school, still the same, but it showed cartoon versions of everyone in the school.  Carrie, originally an emo girl, is now a ghostly emo girl, and everyone else was just inanimate objects and animals, but what caught Penny's attention was who she looked like. Penny was a yellow fairy, but in a shell, yet Gumball still realized how beautiful she was, so his mind captured her like this. Gumball did exactly what he did in real life at school, but didn't pass out or anything. All he did was start trouble in the school and get chased in the halls, though he also dragged his adopted brother into the chase. Though this imaginary show was odd, it will certainly be a hit like other shows like Ed Ed In A, SpongeBob SquarePants, Phineas and Ferg, and many others. Though this show was coming to an end, a lot of the other characters were introduced and written down by the scientists. There was nothing else to write down, so cartoon network employees picked up what the scientists wrote down and sent them to a man named Ben Botlett. As Ben was receiving what he got, the family, doctors and Penny noticed Gumball's body vibrating and twitching, and then it stopped. Gumball passed away.


Is there something that we could focus on lifestyle wise for four weeks and say, let's see if you're better? You know, that's such a good question. And I write about this in my new book, Eat to Beat Your Diet, where I talk about metabolism, I talk about the foods that can help your metabolism. And then I present kind of an approach, a strategy that anybody can put into their lives. And it involves taking a look at the things that are not so good for you and auditing that and actually trying to cut down or cut those out. The six grams of dietary fiber, which are present in an average size pair, has been shown by MD Anderson research to improve your gut microbiome and actually make the difference of whether you're going to survive melanoma, getting an immunotherapy or not. Or the bacteria acrymansia, which can be grown by drinking pomegranate juice or concrete grape juice or cranberry juice that seems to be present in every patient who's a positive responder. They benefit. The tumor is wiped out by your immune system. And people who get checkpoint inhibitors for their cancer, because we don't know who responds and who doesn't respond, will be getting to find out that what you eat and how it happens to change the ecosystem of your gut bacteria, looks like you can actually make a big difference. And that big difference could be life and death.


With some examples about how to use 3d for the for the Arctic valve and SNR is where we actually do Tavis, which I think it's It's actually a good way to actually get introduced as I mentioned before I don't have any disclosures here And again, I think at that point we have actually been Really really involved in how to orient ourselves. So for this specific clinical cases, I think To get the right the right casp is very important to orient or self Again, you have the models you can use the web page as we mentioned you before But I think this is what I have in my brain every single time that I'm doing Transes of agile echo. Okay, so in the short axis view of the Arctic valve again We are going to have the non-coronane casp, which is always the reference between the inter-artial septum Okay, the left and the right and that's how we are actually going to orient ourselves compared to those structures here, okay? so If we go to the long axis What we are going to be able to see and that's what I always tell everyone so we have This cap here that everyone know what it is now at that point The right what about this one It's difficult know and that's when the things come in no between the known and the left what I can't tell you is you increase your Angle up to a hundred and forty you have higher chance to actually pick the left if you decrease a little bit your angle to 110 so you most likely will actually get the known so 110 So we are like that and then we are increasing to 120 So a little bit decrease non-coronane and a little bit increase the left That's another way to actually try to get the view. Okay? So that's the first example, and I wanted to point that out We we consistently talk about that you need to add something that will help you So what I will normally do is I will take a bigger box sample To orient myself put it when I like it and the presentation that I like it And then I will crop it and then mark the structures even on the 3d that I said So you can actually when you go back in because you can see the internal septum here But you need to know that you are there Okay, so for that you need to be able to actually see the rest of the Structures and that's the 2d picture. This is an example of abicast Casp with a raffi in between the left and the and the right, okay? So we have it actually over there. So the same thing with with 3d Okay, so another thing that I would like to point is the fact of the LBOT diameter Okay, we always assess our tecestanosis when we are in the or we are under anesthesia conditions Can actually be very variable So one of the things that you can definitely do and based on the findings that the LBOT is actually not circular Is actually elliptic you can really take a 3d picture of the of the LBOT track and As an example here the LBOT diameter by 2d again, it's difficult sometimes the article is very Classified so it's 2.3 and we got an article by area of 1.3.  Okay, so you go there and you can actually measure two things You can get Your diameter which in this case it can be seen very well here That's is 2.02, which is a little bit of a difference or you can even get the area and it's your cross-sectional area Calculation you can actually use it and it's going to be actually more accurate even but the diameter is going to change too So if you use those calculations with 3d your area is really pointing Okay, so it is another point That is actually important when we are using that technology. Okay So our taking sufficiency so I Normally go to the long axis. I try to optimize my image. I have say that before in the hands-on I always try to go to for example if we are using phillips HBR Okay, the high volume rate you try to mobilize when you're happy with the image that you are getting You stop the vent you try to get as much as you can to get the best resolution for your image After that you can actually crop it and then to show the image that you want with that. What can we do? So this is an example for example We were able to calculate by pizza the effective requisite an orifice So one thing that we can do with 3d is you can go there Go to multi-plane reconstruction freeze the freeze the image and get This window here, so long axis of the article short axis as you can see I'm narrowing the sector to get the maximum frame rate and then here which is actually seen from From from above so you can actually have your effective regurgitan orifice area and you can You can multiply that by your BTI on your a matter of which it and yet and get an estimation on how much is your regurgitan volume Okay, and then you can compare one on the other which is another thing that you can definitely use that technology for okay so I Wanted to put an example of hypertrophic obstructive calloderma your body, so This is a an image of there the other thing It's how to measure for example the interventicular septum So you know exactly where you are cutting the septum and then I think it's actually good too because sometimes you can see When you have this LBOT acceleration flow how so that's the image that we are getting So that's not the way that we are supposed to actually looking at no So we change it and then that's the view from the surgeon So the surgeon as max mentioned is going to pull from the vicarinic gas It's going to go down it's going to do the the septum myectomy over there And that's the view that he's actually going to have the opposite that we were actually having there no so One of the other things that we can do is before the myectomy You can actually estimate your smaller like the minimal area the minimal area of the LBOT Diameter you can do it by 3d choose trace you get the measurement You know pre myectomy and after myectomy you measure from the annulus up to the minimal area What was the distance you apply the same distance here and then you measure it again And you can tell the surgeon your barbaria went from 2.5 to 3.05 Which is another way of absolutely telling him let the myectomy is good It's opening there is no laminar flow But you can give him an objective measurement on the LBOT area the minimum LBOT area is actually increased But at least 0.5 centimeters, okay, which is pretty good on top of doing the gradient So I apologize for that, but that's happening since I did the system too So the first case for Tavar. I think I always will recommend To go with the X plane because it gives you a lot of information in both planes So I just wanted to put an example here of an aortic An aortic stenosis that was actually going with a Tavar with a little finding in the TECO that was Actually pretty interesting so this case What the cardiologist saw we give a little annular plane and again You can do it into D or you can go to 3d know exactly where you are and give a full area and you give them What's the full area? Okay, you go to X plane and you can actually see both structures in both planes Which I think it's really really important for us when we are doing that and then What happened here is? They before deploying the the Tavar they actually normally do like a little Balboulo plastic and after the Balboulo plastic what we were able to see is that flap here Which I saw there so again if you want to know there what's involved You really don't know so you go to your X plane you cut there And you can certainly see that there was a little dissection of their non-coronautic cast with the balloon Dilatation okay, so what they did is they decided to go ahead and deploy the sapiens valve And after the sapien was was actually deployed they were able to actually fix that just with the with the valve and there was no received one Which I think is another Good example on how to assess those those things so This is another case so this one was like a very long day and extremely long day in the or so We have a patient that has a previous So that they came to actually get a Tavar for an aortic stenosis So they try to actually deploy a core valve and as you can see the shape of the core valve It's completely different from the sapiens those are the main valves that we actually use here sapiens 3 and the core valve and the core valve the head should be situated in between the annulus and this should actually go up So we don't occlude the coronaries The only difference basically with the sapiens and with this one this one tends to embolize a little bit more and The other one tends to actually occlude a little bit more the coronaries when we actually deploy them Okay, so in this situation on the problem that we have is this after the deployment What do you think is happening here? So the the the valve might greater a little bit higher than it's supposed to be as you can see in the image this part here should This part here should be actually at this level and then the crown should actually start here and not over there So really with that we can't really do anything. So what they decide to do is go with the sapiens deploy the valve in the annulus and try to actually fish the core back the core valve down and We try for several several hours The problem that we got is that Okay, when we were trying to fish in and out in and out in and out so at the end on the Descending out we get like a little flap we get like a distal dissection Was not a happy day We were not never able to actually fish the ball and we end up requiring to do a turaco to me for rescue that Balvin, but again this explain for these Cases I think it's one of the the best things to have because you can at the same time that things are happening You cannot end yourself in two planes and you are giving real information in real time to the to the surgeons Okay any question


Welcome to this lecture on digital communication using GNU radio. My name is Kumar Appaya and in this lecture we are going to continue our look at demodulation in the context of symbol error rates and bit error rates. If you recall in our previous lectures, we have been looking at symbol error rate rather closely and we have seen how we can compute the symbol error rate for a host of constellation types. In particular, we checked it for BPSK, for PAM4, for QPSK, QAM16 and we remarked about the similarities and differences among these. One aspect that we touched upon was that for complicated constellations, you may need to use something like a union bound to have an approximation. But one thing that was left unanswered was this is about symbol error rates. What this course is about transmission of bits. So what is the difference between symbol error rates and bit error rates and how are bit error rates computed for a given constellation. That is the topic that we will concern ourselves with today. So the first thing that you must observe is that bit error rates are different from symbol error rates. The intuition is that in MRE signaling, it is not always the case that when you have one symbol error, all your bits are wrong. For example, in the case of let us say QPSK, in the case of QPSK, you have four symbols. Each symbol corresponds to two bits. So if you send the symbol that corresponds to the bit pair 00, it could be that the symbol gets flipped to 01, meaning it gets switched to the symbol that corresponds to 01 because of the noise. In this case, the 00 is going to be detected as 01. This corresponds to of course, a symbol error as you have seen in the previous lectures. But out of these two bits, only one of the bits is incorrect. Therefore, this particular symbol error resulted in only one bit error. So in the same way extending this, one symbol error does not mean that all bits are erroneous. Therefore, we need to extend our computation of the symbol error rates to actually account for this and therefore, bit error rates also called bit error ratios are different from symbol error rates. Now, this leads to an interesting question which I have already hinted to. You have M symbols and you want to assign bits to these symbols. How do we assign these bits appropriately? For example, let's say that you have a QPSK, which symbol becomes 00, which symbol should become 11, which one should be 01, which one should be 10, does my arrangement of these actually affect the performance? This is something that we will see. For the moment, we will concern ourselves with those constellations where M is the power of 2 so that we can easily assign the bits. For example, if we have a number like 16, that easily means that each symbol corresponds to 4 bits. So does the actual bit allocation to symbols matter? The answer is that in many constellations it does. So you have to carefully allot the bits to the symbols in order to minimize the bit errors in case a symbol error occurs. So that is, you have to make sure that the mapping between the bits and the symbols is made in such a way that for most symbol error events, the number of bit errors is not really high. That is something that we will see momentarily. We will take the example of QPSK. In the case of QPSK, you have let's say 01, 00, 10 and 11, this particular allotment. Let's actually just do this more carefully. So we have 01, 00, 11 and I think you have 10. If you remember our discussion on symbol error rates, then let's say that you look at 01. When you send 01, the most likely events in terms of nearest neighbors as well you can say are the so say QPSK and this and this are the most likely error events. Why is that the case? That is, it is more likely that the real part goes above D by 2 or the imaginary part goes above D by 2, the probability that both go above D by 2 is smaller. If you don't remember this, you can go back to the previous lecture and confirm the probability of these events was actually Q of D upon 2 sigma times 1 minus Q of D upon 2 sigma. While the probability of this particular thing happening was square. That is the probability of both real part and imaginary part going into the incorrect region. This is smaller. So we can essentially say that 01 becoming 11 is less likely. But that's actually not what we want because in this case 01 going to 10 is a problem because this particular event you have 01 becoming 10 corresponds to 2 bit errors. This is a very bad thing because a very likely event is causing 2 bit errors when you have a single symbol error. Similarly for 00 also, if you go here this corresponds to 2 bit errors. Therefore this is a bad allocation of symbols to bits, bad allocation because this particular allocation of bits or mapping of the pair of bits to the 4 QPSK symbols results in likely symbol error events corresponding to a large amount of bit error. This is something that we want to avoid and this is something that we should try to avoid if at all possible. So in this particular manner one symbol error rather the most likely symbol error results in 2 bit errors and that is something which that we want to strictly avoid. So how do you do this? So in this case we now choose a different approach. We say 0 1 0 0 1 0 1 1 that is let me just 0 1 0 0 let's see. I am going to call this gray coded it's in the name of the scientist okay. Gray coding is where you ensure that all the likely events, likely symbol error events result in the minimum number of bit flips. So let me just check what I chose here so I am consistent 0 1 1 1 0 0 1 0. Now let us look at our likely events our let's look at it for this one. Our likely events are this one or likely events are this one. These correspond to only 1 bit error okay therefore the most likely transition of the symbols which is from this particular location to here and this particular location to here these are the more likely ones these correspond to only 1 bit error as opposed to the less likely one which corresponds to 2 bit errors which is okay I mean the sense you cannot avoid it if that happens it is fine but in terms of how less likely it is if this is D and this is D this is D this is T root 2 therefore this is actually much less probable because this appears in the exponential if you look at the approximation for the Q it appears in the exponential and this is going to be less likely. Therefore by performing gray coding you have ensured in this particular constellation that the less likely error events are going to result in exactly 1 bit error for the symbol error and for the you know sorry the more likely symbol error events you are ensuring that there is only going to be 1 bit error for 1 symbol error for the least likely symbol error event you will have 2 bit errors but that's fine but this is much much better than the previous situation if you really want to calculate the bit error probability for this you can go ahead but I am actually going to calculate the bit error probability for this particular gray coded constellation. Let's start with a clean slate okay so I am going to say this is 0 1 this is okay this is 0 1 0 0 1 0 1 1 and if you don't if you recall this particular constellation point was root ES upon 2 comma root ES upon 2 this choice was made primarily because we wanted the average energy to be ES so we choose all of these at a distance of ES root ES from the origin you will end up getting an average energy of this constellation to be ES which is what we wanted now the distance between these two constellation points is D is I mean between the nearest neighbors is it's 2 times root ES upon 2 root ES this is something which you remember now we want to find the bit error rate so let us focus on let's say only one of them let's focus only on the MSB that is we'll focus on this MSB now there are a couple of approaches which you can use but there is a nice trick which you can play the trick which you can play is to observe that the MSB is 0 whenever the received point is above the y axis sorry the above the x axis MSB is 1 whenever the received point is below the x axis that is whenever you are here the MSB is 0 whenever you are here MSB is 1 irrespective of the real point at which you are in on the x axis above x axis first bit is 0 below x axis first bit is 1 so this is a really neat observation meaning you can make decisions about bits optimally without having to for one of the bits optimally without having to care about the other bit but this is something which I remarked about in the previous lecture very briefly although that this is something which is to be expected why the reason is because what we actually have is we have a BPSK sitting on the x axis and a BPSK sitting on the y axis and you're essentially combining them you're combining these to get this particular constellation therefore if you now start looking at QPSK as a pair of BPSK's it will become really easy for you to understand and appreciate the similarity between these and you can also easily compute the bit error rate or symbol error rate so I'm just going to say this is a so combination of BPSK's fine okay let's actually now just compute the bit error rate for qualms bit error rate for QAM4 or QPSK now before we go ahead there is an important point that I have to mention which is about the bit energy so in this case in the case of QPSK the constellation point has energy ES and this ES corresponds to two bits and therefore what is the energy per bit since ES corresponds to one constellation point and one constellation point has two bits we will define a new quantity called EB which is equal to ES upon bits per symbol which in this particular constellation is ES upon 2 so ES upon 2 is our EB now let us actually find out this particular you know bit error rate for this but even before that let's actually do it for BPSK for BPSK it's very easy you have this you have this and this is 0 and this is minus root ES plus root ES ES corresponds to one bit therefore EB is equal to ES therefore the bit error rate is actually the symbol error rate why one bit is one symbol so we can write this as Q of root of 2 EB upon n naught why because in the case of BPSK one symbol error corresponds to one bit error okay and that's the only event which is possible so the symbol error rate and bit error rate are the same Q of root of 2 ES upon n naught which is the same as Q of root of 2 EB upon n naught but for QPSK it's a little complicated and tricky but there are a couple of ways to do this first if you observe the fact that our only the imaginary value is going to determine your MSB then the only thing you need to concern yourself yourself with is the value of the imaginary axis of the received point therefore you just have to decide on the y-axis projection what the value is and as you recall you had Gaussian noise therefore for for QPSK let's say you had this this is the distance and remember D is the distance and our recipe was always Q of D upon 2 sigma okay Q of D upon 2 sigma in this case however our D is going to be root 2 ES so this is going to be let me just write it in a more neat way okay so now Q of D by 2 sigma which is equal to and remember that our D is actually 2 root ES but 2 root ES is 2 times you know 2 times ES but EB is actually ES upon 2 so our D is actually going to be 2 times so what I am trying to point out is that ES is 2 EB so this is equal to Q of root of 4 EB okay divided by 2 times root of N0 by 2 why did I do this because it is D upon 2 sigma and remember N0 by 2 is the amount of noise per dimension so we get this to be Q of root of and this 4 and 2 cancel 2 EB by N0 okay this is what we get now here there is some element of confusion or you know worry because you I said for BPSK it's Q of root of 2 EB by N0 while for QPSK also it is Q of root of 2 EB by N0 what gives well it turns out that the formula for both is the same but since the constellations are different the amount of power that you spend which is ES in both the cases is different that is in the case of QPSK your ES is actually 2 EB when in the case of BPSK the ES is actually EB and because of that the amount of noise that actually affects you in the case of BPSK is only the real noise in the case of QPSK there is real noise and imaginary noise affecting each part so now this Q of root of 2 EB by N0 is the bit error rate probability for the MSB and I don't think you will be surprised by symmetry for the LSB also it is the same so this way we can actually compute the bit error probability for QPSK as well now let's actually go back to our discussions so for the case of QPSK we have root Q of root of 2 EB by N0 okay this is actually incorrect this is actually ES by N0 okay this is the key take away from this that you can look at it as 2 BPSK and use the same approach and the formula turns out to be the same form but note the difference in the case of QPSK BPSK has ES equal to EB QPSK has ES equal to EB that is the key difference now in the case of PAM4 let's actually just try to brainstorm a little and try to see what happens in the case of PAM4 actually let me just let me make another remark before I go to PAM4 if you remember we had a complicated formula for the similar rate for QPSK right let's actually just get that so 0 0 0 1 1 1 1 0 and remember Q of root of 2 EB by N0 which is equal to Q of root of ES by N0 is the probability of making a bit error now if you want the simple error probability you can actually compute it very easily now the simple error probability is equal to and just go back in our slides you can get the expression yeah it was Q you know 2 Q of ES minus square and all those you can actually get this from the you can actually get this from this particular bit error rate expression a simple error occurs when at least one bit error has occurred at least one bit error has occurred when there's actually the 1 minus no bits have occurred so it's actually you can do it in multiple ways what at least one bit error has occurred so what is one bit error occurring mean one bit error can occur because of this so that leads to this you know Q of root of 2 EB by N0 is a probability that the MSB gets flipped plus Q of root of 2 EB by N0 sorry let me just change it up and I wanted to write this as ES so that you know your consistent okay so this is ES here also we write ES minus of course so this is basically one has occurred another has occurred minus both this is the event with that corresponds to both the bits getting flipped that is double countered so we'll do minus you can use the bit error rate formula to compute the symbol area it as well you just have to look at the probability of making at least one bit error okay the other approach is to just say the probability of getting at least one bit error one minus no bit error has occurred and no bit error you can always just use the Q formula and figure it out so if you want to do that you'll essentially have to do one minus one minus Q the whole square and you'll get the same result now let us just move to Pam 4 I'm going to write 1 2 3 4 and you can write the normalized forms I have no you know I'm not going to do that right now but you have to now assign 4 that means you have to assign a pair of bits to each you can do 0 0 0 1 1 0 1 and 1 0 and 1 1 so this evidently is not a good idea because if you look at these two these are nearest neighbors and a single bit error results in sorry single symbol error results in two bit errors this is a very likely event because these are very close and a single bit error results in single symbol error results in two bit errors so you should not do this so this is not the right way so I'm going to just undo what I did here and I'm going to write 1 1 1 0 now if you look at this these two are close one symbol error results in one bit error these two are close 0 1 and 1 1 1 similar error only one bit is flipped these two are close one symbol error only one bit error that's it so in this particular scenario the bit error rate is minimized because of your the fact that you have done gray coding wherein you have ensured that a flip of one bit flip of a symbol results in only one bit flip in the most likely symbol flip event of course you can still say what if I go from here to here okay it is true you will get two bits what if we go from here to here of course you'll get two bits in incorrect but still it is better than the old one because these two are much further in fact twice as far the probability of those events is much less likely therefore for pan 4 you should use gray coding and like I did 0 0 0 1 1 1 1 0 the most likely event lead to only one bit error the BR can be found much like VPSK except there is a slight issue the issue is you have to do it separately for this one and this one and separately for these pair as well because in this particular case for 0 0 to 0 1 it's very easy you just have to find see for example 0 0 going to 0 1 right you just have to find the probability of this particular symbol landing in this region because that is the region where that's the reason way that's the region where the least significant bit essentially flips in fact over here it doesn't flip so you have to essentially evaluate the error probability by integrating evaluate the error probability by integrating this particular intake this particular Gaussian from this point all the way till this point now similarly for these two you have slightly more complicated scenario because there can be two different error events going to the left and right so over here this 0 over here if you go to the left this one becomes 0 to the right this one remains one but goes further to the right and becomes 0 so you have to be very careful about the exact regions of integration but again if you really want to you can just perform a simulation and try to get the bit error rate as well one thing to remember is that the PAM4 essentially serves as an ingredient for your quam 16 as well now in the case of quam 16 we have to ensure that we do a bit allocation that results in one bit error as far as possible for the least like for the most likely error set symbol error events in this particular gray coding situation we have actually done that what have we done we have said 1 0 1 0 1 0 1 1 so let's look at what we have done here in fact let's search for 0 0 I started here 0 0 0 0 there are two nearest neighbors this one and this one for each of them we want exactly one error was one bit error whenever one symbol error happens so we I chose to flip the third bit from the right here and the first bit over here so I got 0 0 0 0 1 0 0 this is great next let's look at it for this one to the left we've already checked when you go above 0 1 0 0 goes to 0 1 0 1 that corresponds exactly to 1 bit flip 0 1 0 0 to 1 1 0 0 corresponds only the most significant bit flip 1 bit flipped the rest for example these are not significant events because they are much further than the nearest neighbors next if you look at this particular symbol 0 1 0 1 we checked below it's only one bit we check to the left it's only one bit we check to the right 0 1 0 1 1 0 only one bit we check above 0 1 1 1 to 0 1 0 only one bit so if you want to just pause and check this particular configuration ensures that you will have the nearest neighbors all four nearest neighbors for these and all two for these all three for these have only one bit flip this is just an extension of the pamphor or if you want another way I'll give you another way to look at it the MSB the most significant bit is 0 to the left and 1 to the right ok this is a way by which you can get the constellation it's 1 to 0 to the left and 1 to the right next if you look at the least significant bit it actually it 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 ok and if you look at the other bits as well there is a pattern I want to remark that this particular allocation of bits to symbols is not unique and you can come up with your own gray coded version of you know the constellations that is as good as any other as good as this so you'll actually have no problems in coming up with another allocation which will still be gray coded but it will have the same performance and it is equivalent in every other way it's just a question of your choice of mapping now again in this case computing bit errors you can do for example like I told you if you decipher a pattern for the MSB right 0 is on the left 1 is on the right therefore you can just use your BPSK like approach to compute the bit error rate for the MSB but for the others you have to look carefully for example for the let's say third one it's 1 1 here 0 0 here and you have to decipher it more carefully in general it is cumbersome but it is something which you can do again if you don't want to do it or if in a scenario where you don't need to do it you can just perform a simulation in your scenario and get the bit error rate for the SNR that you desire one more remark I wanted to make is that in this case remember 4 EB is yes something that you should keep in mind so let's summarize remember that the ratio of the signal energy and noise energy decides the symbol and bit error rates and we can compute the similar rates you know using accurate approaches or you can approximate them using probability based approaches like the union bound or using the nearest neighbors and approximating it and when it comes to bitter rates the same things apply except that you also have to ensure that you have to first look at the allocation of bits to symbols and only when you allocate bits to symbols then you can compute the bitter rate and when you do the allocation of bits to symbols make sure that you do it in such a way that the number of bit errors for the for the most likely symbol errors is minimized gray coding is a perfect recipe for that basically the most likely symbol errors will result in only one bit error and that is the key to ensuring that you minimize the bit error rate now so far we have looked at the impact of noise on symbols and similar rates and bit error rates but we have still have an idealized communication system where there is no other impairments other than noise in the next lecture series onwards we are going to look at how we can relax the assumptions on ideality of our transmit receiver system they're pairing and so on and see how we can get towards a more realistic communication system model thank you