21 signs you might actually be an ambivalent. If you don't feel like an extrovert or an introvert, this might be why. 1. When you're out in the world, you're probably not going to be studying conversations with strangers. 2. Generally, you're always happy to meet new people, but you'll probably feel uncomfortable if you have to do it without any of your existing friends with you. 3. When a topic of interest comes up in conversation, you're more than happy to talk in great detail about it. 4. But as soon as that's done, you'll happily sit listening to the conversation without saying another word. 5. Spending too much time with other people can be exhausting. 6. Your calm, controlled professional self feels like a very different person to the one your friends see. 7. Asserting yourself is tricky in many situations. 8. You can often go out and have hours of fun being the life of the party, but suddenly find that your energy has dropped and all you really want to do is go home. 9. When you see things written about being an introvert, you start to relate, but then discover that you relate to the extrovert ones as well. 10. In fact, your friends disagreeing about whether you're an introvert or an extrovert is probably a very good sign that you're an ambivert. 11. Small talk is something that annoys you, because while you can do it, there are instances when it feels a bit insecure. 12.  13. Too much time spent alone can leave you a bit downcast, however, and you're concerned that that's not very productive. 14. And some of the best weekends of your life have been when you didn't go home for three days. 15. Thinking before you speak isn't a problem for you, most of the time. 16. You have a tendency to balance out whoever you're with. If you're with someone loud, you'll be quieter. If they're quiet, you'll compensate for that. 17. You're known to be quite intuitive and good at picking up signals that other people can miss. 18. Often, you just find yourself observing what's happening around you. 19. And at other times, you'll be getting involved in the moment. 20. So in the right context, you love attention, but more often than not, you don't want to be the person everyone is looking at. 21. So if you can't figure out whether you're an introvert or an extrovert, maybe it's because you're actually an ambervert.


حالہ کی ہے؟ پہلے پکابلے کے لئے جانتے ہیں 420 گرمز بھائی ہے دیکھے جو بت تیسی یہ برش کریوی بت تیسی آج آپ کے سامنے بھائے بڑے دنوں بعد آئی ہے بڑے دنوں بعد کوٹ ساب کے سامنے بت تیسی آئی ہوگی کوٹ ساب نے بھارت میں اپنا پہلا مقابلہ جو جیتا ہے یہاں پر کمبوڈیا گا رہا ہے تو شونیہ سے کلکتا پہنچا ہے بھائی بی کے سٹیڑیو میں مچ دیکھا ہے اور وہ جا رہا ہے ابھی پرس کنفرنس میں جہاں پہ شاید 420 گرمز پہلی باری ایک اور سٹی مچ سے بات چیت کر پائے گی اگر ایسا ہوا تو میرے ساتھ یہاں پہنچ سوٹلی بوم بھائے اور ایک بچلی بوم بھائے دونوں بجائیں گے اور آپ کو ہم آپ کو یہ دکھائیں گے رینی بھائی تھوڑی ایک سائٹمنٹ ہے before we get into the nitty gritties اگر ایسا تھا first half second half how they were opening up 3 point 2 nil job done I feel three point was important but the only thing is next two matches will be way tougher than this last time we have talked about this is the match where we don't have to think much but then the worrying point is اگر جو ہمیں ہمارے پر اپنانس کو بہت افغان اور ہونکوان کے لئے یہ سب سے بہت سکتا ہے لیکن اسی طرح ہی دیتے ہیں جو تیم کمبوریہ ہم دیفنڈنگ دیتے ہیں جو سب جانتے ہیں لیکن یہ بہت سکتا ہے لیکن یہ سب سے بہت ہی دیتے ہیں ہمارے پر اپنی مجھے سر اشواخ، بتاؤ جی تین انگ کا آگئے ہیں، بتیسیہ بہر آگئے ہیں کیسے کھلیں، جیسے کھلے چلو وہ تو بات کی بات ہے بھائی اگر ہم لوگ آسٹوالہ جو اپنے یوٹوپ کھول کے دیکھو امرہ چند میں نے بھولا کہ دیس کینڈ اپ مجھز سیٹ پیسیز پے دیسائڈ ہوتے سمتائنڈ تو one of the reason ڈرٹن پلیر میں کھلا را پایا سیٹ پیس کی وجہ سے تو I think it's important ڈو مجھے لگتا تھا کہ بہت سرٹیجی جو ڈو گول کرکے you know like ڈو پیچھے ہٹ گئے اور اسٹیم میں اس کمبوڈیا میں تو کچھ تھای نہیں یار وہ مطلب پیچھے بیٹنے کے لئے تھای نہیں even up ڈیکھو one on one ڈو two versus two ڈو بھی ہوا وہ بھی انہوں نے ہمارے پلیر کو بھول دیا like they were I'm not I'm not but that's the fact I'm criticizing but that's the fact like they have no clue up ڈونٹرن کے یاد اور اور اور یہ ویمارے بہت محمود جو بہت اہم we are very ڈٹکی انوڈرلی ڈ کی جو ایک بہن چیز گرنے گا اوہ نا لائی نا اوہ Bleacher ڈی دین دہو ڈی ڈی انڈی فاییی بہت بہت66 بڑے ایک بھل ساتھ نیچلے گا ایسپیس لیو اس خطر اپنا اند رونا میکنی مبا نمار اور مبا ڈیرار و ٹ انہ حول لیو رچا جنڈلی when you're coaching teams and you have a team you're playing against that has knows the difference in quality and is happy to sit back so much where you're giving them so much time and space on the ball that you're not doing anything till the final third اقصر you suppose that is when people the teams that are attacking them that time I'm saying like an India team then it gets a little tougher because you're not doing anything anything is just passive kind of football sideways و reacted overseas and suddenly you have to do something to open them up on. You've got those five people in front of you did you see a bit of that in the first Forestan think pretty much people like Liston andwives are attacking pressure like پر ایک امام کے ساتھ بنا ہم ویرانید وی بیدasedیت كے کیا تھا کہ ہم ممتعایت پر بیجنگہ کے لئے میں بھی کہتا ہوںование vé Zhenb a کی تین پیچھے چھوڑیں گے تو چیلے جائے گا انور اور جھنگن کو بہت زیادہ ہمیں وہ سمجھتے ہوava کیا انہوں کو کبھی پر دیکھ لے رہے ہیں امام ہمشاهوں کے سمجھتے ہیں桜 ہمیں سمجھتے ہیں ممتعایتوں کے لئے هم بھی بھی بھی رہے ہیں بھا رکھتا میں لے رہا ہوں میں لے رہا ہوں اور میں کھیک لے رہا ہوں وہ پینلٹی مارکے چلے جاتا ہے پر اس کے پاتھا ہیڈر اوڈ سو سو سر تایم ان اگر دیکھنے دیکھنے کے لئے اور اگر وہ پہلے پہلے پہلے آپ کو حقا رہا ہوں ہم کوئی بہت ہی نہیں ہے ہی نہیں مطلب آس پاس اس گول تو اگر آپ ایک گفٹ گول کیونکتا ہے کیونکہ وہ کسی مارکہ نہیں تھا انہوں نے سکن گولا کے لئے بھائی نہیں تو مجھے لگا سر آپ ایک باری فرصہ کنیٹ کرلو ری کنیٹ کرلو تھوڑا آپ کو انٹرنٹ بہت شیکی ہو رہا ہے جیدیب سر ہمارے ساتھ آجائیں گے تو ابھی ہمارے چھیٹری چلے گئے ہمارے چھیٹری چلے گئے رینیڈی بھائی کیسا لگا آپ کو چھیٹری چھیٹری اگین رینیڈی بھائی اس براؤ تیار میں نلائے گا اس بہت دیتے ہیں اسی لے لگا چاہیز ہے حکم میں cứ تاکہ کرنے کا ضرورت ہے سیمیول سیل سیٹری ہے لگا چاہیز ہے لگا اوندرِ چھاہیز ہمارے جو مجھے جو پھر ہوناہیں tomorrow ایک باری لگا ابھی جو کنیٹ کرنے کے لئے سب کے جانتے ہیں ایک سامان چاہیز ہے بھی مجھے اگر اب نہیں کھلو گے اسٹیم کے ساتھ تو کب کھلو گے بہت than they didn't get the, I think Manvi didn't get the much playing time also and for me it was a little bit strange to see Liston playing in midfield even Glenn Martin was playing at times ahead of him I don't know what match plan was like maybe coach had his own strategy but personally I would have loved to see one one one playing up number nine and you know like trying to get in into those loose balls or to those crosses where we have seen a lot of them came in the second up but no one was making those kind of runs where you know like Sunil how he anticipates where the ball will come and you could see left side couple of time Udanta made a great inside run with the solo run with the ball and a good crosses also came from both sides but unfortunately nobody was there to finish those off so I think yes as Renidhi bhai started earlier بھائی چلو یہ تو kind of warm-up match تھا but great we got three points and I'm expecting all the other two teams will beat them and as seeing this earlier I saw you know you know I think everybody have seen Hong Kong and ڈروپ پھر گیا ہے سا ہنگ کھون کو دیکھ کے اب تو you feel I personally feel they will also beat them ابغان اپنانستان will beat them because ابغانستان will be much much physically stronger so having score you know scoring more goals would have been perfect idea but yes things are going to get little bit tougher after seeing Hong Kong especially I feel they have two really good up front players number 10 and number 9 who was coming in and giving space to someone like us to then come in through the oval app where do you suppose that was coming from you suppose there's a spree game nerves that you haven't won in a long time you're chasing a result is the result that's important so you also played out the 11 that he's played because he's not played out the most informed 11 he's played Thapa who's not the most informed player he's played Brandon who's not the informed player Manveer is not your most informed player when it comes to international football he's played your most experienced 11 he's gone in with your most experienced 11 at the international I don't think the rotation or let's just say the initiative taken by the players was such a drawback it is looking at the way these guys are set up اگر 5 and 3 کے ساتھ کھلو جگہ کام پر یہ ساتھ کرنے کے لے so if you look at the fact that Roshan was given free license either go down the flanks, cut it and shoot so you saw him trying to take shots from distance quite a few times then Mishra was attacking down the flanks جب ہی بھی رoshan کے پاس بالتا ہم نے دیکھا کہ منویر بھی اندر آ رہا تھا مطلب he's coming closer to the striker position coming up and holding those positions اس کے لے I think when you start to commit so many numbers forward you need numbers behind the ball as well to receive it and continue rotating the ball اگر پورے آت کے آگے چلے جائیں گے پھر پیچے سے defend is رہ جائیں گے so even to rotate the ball quickly around you need players in the second layer which is where I think Thapa and Brandon were seen staying a bit behind over there so maybe that was the reason primary reason behind the movement and choices that we saw and Distin again I think he has the ability to look for spaces ability to receive the ball under pressure and take people on تو ہاں پہ میکھو لگ رہے یہ سب کانسیٹریشنز گئے ہوں گے overall just in terms of how it unfolded in the first half ارے مجھے لگتا اپنے ہوستہ بھی گے ہاں چلے گئے رینیڈی بھائی رینیڈی بھائی tell me honestly now let's جب تک ہو آئیں گے how impressed you was for the it was actually for from the performance of whole team yeah brother it's you know the three point was needed like you said you know when you get three points I feel that you know that was most important him but then again with the game they have played we have seen against Bangladesh the same thing we struggled to open up today again when they were defending even though we scored from a penalty and one good header from Sunil we still struggle to open up right so now when we are struggling just imagine if Hong Kong scored early and they defend or if Afghan scored early and they defend how we are going to break that wall so it's a difficult it will be a difficult too difficult match it's not going to be easy so now that's my warring factor for me so I hope you know we we play better at the same time if Afghan don't give us too much of respect and if they come up that will be a good luck for India just imagine if they defend now it but Afghan has to come out now Afghan the good thing about is when they have lost today so they will come out and take so that's where we are going to get space and and it is going to be very difficult you know like different for Hong Kong also they have to decide whether to attack India or sit back because you know like we I personally and we know we still are you know like consider that we are higher rank than better better team how they will do how do you see that going like how important will be now this next match after seeing this performance what do you feel like about the team see next see today's match gives me give today's result give me a very uncomfortable feeling because now Hong Kong has won Hong Kong have won now there are more than one team two teams who are who have ambitions in this group see by the time we thought that by the time we'll go and meet Hong Kong the ambitions will be over but it is not going to be like that so today at least a couple of more goals I would have been very happy because this Cambodia could be the could be the could be the could be the target of every other team and they would they could they would be able to they might score more than more than two goals that's that's the feeling I'm getting because given the way that Cambodia played and all of you have seen what kind of team Cambodia is it's an it's like in what we say I like him maybe in India so I think now see Afghan Afghanistan will also come back will try to come back Hong Kong has got an ambition now in they have beaten the most perhaps the toughest team in the in the group one of the toughest in the group so as what ishfaq has just asked me I'm very uncomfortable at the moment no not because of anything else so all of us seen what kind of football they played but even with that I think we could have won four nil four nil would have given us a cushion but two nil somehow is giving me lot of bad feelings but it has a it this this because Cambodia is a is a team scoring against them can upset the entire group that is that is a good point that's a good point and you know what that that was one of the reasons I thought Sunil was not happy being taken off that was another reason he's being vocal in the bench as well yellow card yeah that's true that's a good point actually i actually i'd like to apologize my internet اور بیبی کے ساتھ لڑائی ہوگی تو گیمز چلتی رہتی ہیں ابھی میری بیبی کچن میں آئی پانی پینے جاتے جاتے انٹنٹ آف کرکے چلے اسے گئتے گول کیا گول معا رہا ہے یہ دیکھا ہے بہت ہی کیا جی میں جانتے ہیں کہ آپ جانتے ہیں جانتے ہیں ہونککانگ اور ہونککانگ ہونکانگ نہ دا تو بہت ہی دیکھے ایک لیوڈی لیوڈ دیکھیا ہوں گا تو مطلب تھوڑا فائیٹ ہے اب اس میں at least has stopped to walk away اوڈیون what i mean to what i mean to say at the at the start of the at the start of the league as we start of the tournament this we thought there are there India is the best team and one more thing will will be there with some little bit of ambition that is of than now the third team has come in the fourth team is so i won't say a substandard but the sport team is so inferior to all other three teams that everybody will start targeting that team for a for a goal difference for a goal average all these things put together مجھے لگا ہے کیا گلوب تھوڑا ڈرور ہو سکتا ہے that that's what that's what the feeling i'm getting and i don't know لکھا ہؤہănہ صفیح طرح حکم بھی لگا ہی جان mustarding high حalesool اگہ圈ینا بہت ایک اچھے بات بولی اگر بہت ای جان اس کے لئے مومئے جان اسے مارا تو ہے you know اس نے کہ نہیں مارا just that it didn't work today but at the same time when you get space wingers لوگ لے کافی plus point اے اور when we have a player like listen and man beer اور من بیر ہم لوگ سب معلوم ہے من بیر جب space رہنے سے کتنا اچھا کھل سکتا ہے اور when there is no space we talk about this before where من بیر کباز اگر آگے میں space نہیں ہوگا تو he's not that technically really really sound that he will do something so that's why he click when Habas was there when Habas when Habas place place counter attacking game that they've got they've bought listen and man beer they've got the space so then this is why we were talking about against Afghan we may we may get this but today there is no space at all کھا جائے گا آپ جا ہوگا بھی تو there's like two blocks of line at defending so there was no space at all so اس میں انڈیا خراب سوہ رہا تھا ایک بھی at such chances create new rather than except one or two here from here actually chances of it not clear never rather it was difficult for for indians and it's not because earlier when we play higher ranked teams and we say okay we're playing higher ranked opposition it's too tough for us now you're playing a lower ranked team and a lower ranked team will generally set up brother brother ہم لوگ نے پہلے بارے میں بات ہوا تھا after playing draw against Qatar I said you know the most toughest match will be against Bangladesh not Qatar Qatar we didn't have anything to lose we will defend but to open you have to have to be if that won't happen then it won't open if you need individual quality players which we don't have that enough of course yes you can say this is a passer but still we still have to go a long way in terms of opening up opening up a different level we all have been doing whatever I was watching the game and thinking about Cambodia Cambodia go attacking play Khel Leme will take twenty more years maybe fifteen years Cambodia go I'm telling you because and I'm thinking whole my life maybe before Bob Houghton we played those type of game before and I'm tired of that and I'm thinking about Cambodian players and I'm feeling but to reach to Indian level they have still have to play fifteen more years to get Indian level I feel just imagine India after playing a defensive and to play attacking game we still have to wait for another ten fifteen more years also for India so we are on a process like you said we are that's the only way we cannot hide that are there not players in the second half who kind of tell you that if you bring them up they give you some things and okay yes the argument is there that Cambodia is already battered by then second half they looking tired as well but you had an ashiq you had anudanta who will of course will give you good options on the bench but why not start with these guys because they have that thing they have something that Ranidhi was saying will show you at least they showed it today overall I mean if you're talking about tired legs I don't know if you watch the first half of the Hong Kong and Afghanistan game 15 minute کے اندرے لوگ چلنے میں بھی مشکل ہو رہا تھا I mean that's how nackered they were so once sunset came in the flood lights came on the game was very different Afghanistan جو first half میں دیکھا second half میں started to see them come in a lot also and it's not that یہ جو کمبوڈیاں کا پتہ نہیں مطلب the whole unit has been so well attuned to maybe defending deep ان کو آنے دو کھلنے دو ادانتہ بھی آئے گا اشک بھی آئے گا starting them and things have you if you look at the pace of the full box that Afghanistan have got they won't have any trouble dealing with them if it's a 1v1 foot race Afghanistan کے مین اشوز وہ بٹم ٹرائنگل میں مطلب ان کا جو سنٹر باکے and defensive midfielder جو ہے وہاں پر you're looking at very aging players players are not agile at all but on the flanks up front these guys are not I mean some of you are going to be afraid کہ آرہتے ہیں we are going to get beaten for a pace or maybe some of you like آشک ادانتہ a listing and stuff are going to trouble us too much we guarantee we'll have a big advantage in the counter attack should Afghanistan come in پر وہ لوگ بھی اپنا گیم کیسے script کریں گے وہ بھی دیکھنا ہے how are they going to go about ایسا نہیں ہوگا کہ پہلے منیٹ سے یہ لوگ چڑنے والے پورے آٹنو لوگ آگے بیش دیں گے it's not going to be that way they might have their own plan to maybe coming with 3 points in the game and it doesn't necessarily mean that they're going to go all out attack مطلب Afghanistan نے جو last پندرہ ملٹ میں جو گیم کھیلہ اگر یہ لوگ وہ شروع سے کھیلے گے then it's going to be big trouble for us especially dealing with that sort of combination play their passes started looking a lot more settle they started looking like a much more settle team but now first half ان کے پانچ passes بھی ہو رہنی دے without pressure they were looking completely gone even basing on basing this on let's say what we have seen the second half and what we have seen Afghanistan play maybe let's say couple of hours before that unfolded there's no way of correlating کی یہ کرنے سے یہ ہو جائے گا کیونکی کافی مطلب کافی کچھ دیکھنے ملہ in the second half especially from Afghanistan they were a couple of goals down and things but they were for sure exposed in the central area اگر وہاں پہ ہم لوگ problems create کر پہنگے that is لجسے سنیل کے پیچھے آگے پیچھے جو دو central midfielders if they can supply those ball آئی نہیں رہتے آگے پلوٹ کری دیا تھا وہاں پہنے جائیں گے بھی کدھر بھائی مطلب اگر کمبوڈیاں نے آٹ لوگ بھیج دیا there is nowhere else to go forward if listed and manvira coming inside and playing there is no place for the midfielders to come in and join the attack because they come in and combine closer to seenil and then you get the fullbacks taking up the wide areas لیکن یہاں پہاں it's going to be more of a traditional 4-3-3 should they go with the same formation on here midfield role coming in making those runs beyond the striker all of that will be relied on a lot more because Afghanistan is a totally different ball game take physicality as well take the speed and they play football here are the 3-5-3-2 you would stick with this playing 11 not entirely behind seenil there should be a bit more of let's say attacking attacking incision or maybe brandon is given that license and soration these guys thapa given the license then it might look very different I mean it can be the same place different roles maybe جیدی سیر what do you suppose he's going to repeat the same 11 you might see a different 11 given you're playing higher opposition better opposition I have not seen Afghanistan I have not seen Afghanistan at all so next match is Afghanistan playing Afghanistan I have not seen the Afghanistan match at all today I only saw this online that they have lost to one so very difficult to say what he is going to do today whatever he tried to do I don't think it worked even he looked frustrated at times so I think he will go for some other combination because he has been doing it for the last 2 years he has been trying some combination of the other I think he will go for a different combination I don't know what it is but I have a feeling he will go for a different combination that's what we have seen over and over what do you suppose because for a change to personal or you persist with a winning combination you have a winning combination brother I feel there will be some changes at the back here we are talking about attacking game but I think we will Swas's boss will come in and Quotal they will come in because coach will want to have a proper back line but today they have tried with Rosen we have already talked about it he didn't have the best game but I feel it was okay for him again the same thing as Mishra still the experience is neither international football so I think boss will come back Swas's boss and as Sunil listen Manbir I think he will still keep them this is what I feel behind them like Suresh looks so good today Suresh for me not really honestly I never Suresh for me is a right back Suresh is never a player if you want to break the lines if you want to do something Suresh for defending yes if you are defending against Qatar if you are playing against UAE it's fine but if you are playing against with an opponent where we have to score score score I think Suresh we need more a better passer from there I feel Suresh yes he can run a lot he can run a lot but I will bring the guy from Yesir Yesir I will bring Yesir in if you want to play but again Afghan Suresh will play against Afghan because we need to defend also we are not going all out attacking so that's why there will be changes again Afghan so we have to defend also so we need to put up your experience defender in that's where Swas's boss and Qatar will come back again so we are not going to see this line up tricky tricky 2 days for the management there is one saying don't make too many changes in a tournament in that 2 over 3 game tournament you have a winning combination you continue with the winning combination don't unsettle the camp but here we are and I think all of us agree that you might possibly see 2-3 changes going into the next game I think but that always happens yeah پہلے دیکھیں گے پہلے دیکھیں گے کون کون فٹ ہے I think that's very important who is 100% fit as Rene Deeb I said I think for Afghanistan کے ساتھ میں آچ a coach will definitely look for physicality I am with Rene Deeb I سوریش نہیں ہے who will play those between the line passes he will break the play and mainly will play to depend on our side pass because that's what he does but we need somebody with a defensive quality also so I personally will go what Rene Deeb I said the defense line that I feel like there are there is a chance of Suresh Glenn and maybe if he put Yasir or Sahal behind Sunil either either one of them will do I like Sahal today because he did the chasing and that and because I was in personally he has improved that physical part and he is the one who can receive the ball between the lines very nice and that's his strength and I cannot see wingers changing until and unless somebody is injured until and unless he wants Ashik instead of Manveer from the right side and to play one guy as an inverted winger because Ashik has that physical presence and the speed who can unlock but I cannot agree more with what Richard said the weakest part of the Afghan is their defense to those midfielders who are a little bit slower and who conceded those two goals today because of their poor play and only two players got mainly involved to break them down was number nine and number ten they were very good in that and I think that's a good good example for Indian team how good and patient Hong Kong was and they pressed them high surprise press what we say when they thought that they are not pressing and they pressed and then one ball almost next to that center circle and open them up not once or not twice many times it happened in the game the first fifteen minutes which was selling I think I was messaging in our group also both the teams looked dead so that was maybe that was the part later on I didn't see the second half much I went to play my senior tournament which we play 5v5 because I have to recharge and then it happens it is very necessary to go to the field but I think because in midfield we need little bit physical presence because I don't think the players who played today tactical reason they will be they are good players but they might lose the plot in physical presence again by the way we have come to talk about changes our soldiers press conference can you tell any Bhai joining us from the YBK this was in Kolkata you talked to the coach and the coach answered you he is just a mute spectator press conference no no in fact he pointed out and said he is raising his hand one minute first Taliyam this has been talked about three years of problems he was in a very different mood today at the press conference with the comfortable wind so he came out and said many of the same things he has been saying in the last few days but obviously the manner was much easier because he has the three points now on the board his team have the three points on the board do you want to take you through what all he said tell us before you came we were all discussing if the same 11 is going to play and a majority of us think that no there are going to be quite a few changes does someone ask him anything on the 11 are you going to change in these two three days time what are you going to do couple of injury concerns one is to Roshan who was playing right back today for a change left a little bit of hamstring issue there and Thapa as well he is coming back from injury and picked up another knock today so in fact his team had said he wanted to take him off at half time but kept him on for a bit longer than that so maybe depending on how things go because there is only two days break between now and the next game so maybe those two will be changed I think also Suresh's role in that he played today may not be the same in the next game because today the plan was to press high and like we saw I guess and with both Sandesh and not being the fastest players around I think he wanted someone with a great engine to cover for that and I think that's pretty much exactly the job Suresh did so those might be the changes one thing he stressed on was that India need to start learning how to play without Sunil Shaitri and he pointed out to his own players saying that they are getting in the right positions but when they are receiving that final ball or they are finding themselves inside the box then they are a bit unsure what to do so he went on to say that now a lot of time has been spent on these players so they need to start paying back deliver on their potential he is throwing down this thing to them he is saying yes once again also there was a bit of a half joking mention that he basically said I wish them good health that they stay healthy and that all the money that they are getting paid doesn't get to their heads that they manage to keep that so obviously that's something that he was somebody asked him about Afghanistan actually quoting the Afghan coach saying that last two times India and Afghanistan played India got lucky he was lucky so his response was pretty cocky as well he said maybe he wasn't watching the games he is talking about us those who criticize our game don't understand football so anything else was it a packed pc but a lot of journalists asking questions by pc standards i think there would be atleast around 50 journalists unfortunately i had to come up before the players walked out through the mix zone so i didn't get a chance to meet any of the players but then i guess the show must go on but you tell me that 420 grams first question what was the question tell me this is the only question because in the post match press conference you get to ask one question this is the only question if you have a plan to overload and your full backs are getting injured what would you have done he said luckily they are young and unfortunately he said that he took Russian off also as a precautionary measure because he told him not to go forward because it was a comfortable situation to nil up Cambodia were playing with 10 men in their own half so there was really no issue but because he is young and excited and wants the ball all the time he was still going forward and taking shots and putting in crosses so he was forced to take him off so that just to make sure the injury didn't get any worse were you asking about taking out Sunil no of course it was obvious because he got a yellow like i mentioned because he wants the team to start i think Steemach gave the impression that he is preparing the side and he wants us to also get the impression that he is preparing the side for the Asian cup during a qualifier but if you don't get there then what preparation will you do then you will play Calinda but in his mind i think one third of the job is actually done but that's what he is saying we will see a very different looking team because he comes around in 23 so obviously players like Apuya, Vikram Patap who else is there Rahim Ali all these players he mentioned but he also did Suresh, Roshan and Akash for the work they did today saying that they looked like they have been playing senior level football for quite a while so that was a positive from his perspective because he is smiling a little after that and lastly also i mean in general not really missing his words in any sense again pointing out to the kind of debacle that happened before the last 3 days with regard to tickets and unfortunately we saw the result of it today despite everything despite all the challenges late issuing of tickets online ادھا سیدیم تو بھر گیا تھا ادھا سیدیم would be easily 40-35 yeah yeah so i think around 20-30,000 people were here and you could see that it clearly made a difference there were periods of play when not much was happening a lot of square passing back passing keeping the ball waiting but and the crowd was also reacting to that there was a bit of whistling and all of that happens in Calcutta very quickly it happens five minutes but the weather is not at all ideal i mean you guys have played in this weather a lot so you know exactly what it's like it's really sapping weather a couple of guys i was speaking to who said he wanted it in the bowl itself it's hard to breathe oxygen is not reaching the brain at the right time and all that so those issues are there so you need breaks i guess from time to time you need to catch your breath a little bit i guess they have to so you have to vary the tempo and i think overall he'll be pretty happy with how his guys have done ہم TV پر دیکھ رہے تھے ہم TV پر دیکھ رہے تھے تو اپنے کو لگ رہا تھا کہ مطلب آپ کو تو مطلب کھلی چھوٹ ہوئی ملے میں آئے ہو آپ پانچو جی ہمارے فریس بیل تک بس ایک لڑکی نے بڑا اچھا ایک دیلوگ لکھائے یہاں پہ اپوزیشن بوکس is the لکشمن ریکھا فر انڈیا کیونکہ بوکس کے پاس آتے آتے پھر سڑنلی اپنے نمبرز ہیں کہ آپ کو سپیس ملنے نیوانا آپ تو دیکھ رہے تھے نببے نببے منٹ ہو چکے گے یا ایٹی five last five minutes of the game even at that point they were playing with 10 کیمبوڈیا were playing with 10 men in their own side ایک ہے جس کوanna ایک ستی outی منٹ بھی ایک سٹنلی ایٹی دوسرہ۔اہ ایٹیس ایٹیس ایک ستنی ایک ستنی اس دن لی کہا ننی آمری کمیٹا آمری جب یہی ملنے جو ایٹیس ملنے بیل تک لڑکی اور کہا اپنے نمبر تک تو اس میں بھی تھوڑا زادہ ہی سوائگر تھا اتنا I'm not sure ہم نے اتنا confidentی اتنا orthoretically اس میں کیا دومنیٹ کیا کی you know we should have been playing with that kind of of of confidence or whatever it was and سٹی مچھ also said that like a fair result for this game should have been at least four four gold difference that's what I wanted to ask you before I go to رینڈی بھائی is there a sense in the ڈیم کی کم گول مارے you missed an opportunity to hit at least four five yeah definitely but although the coach said that we had four five clear chances I didn't see I didn't see خلاف بھی وہ کہہ رہے تھے ہم کے تھے ہاں وہ مجھے دیکھیں نہیں four five clear chances ڈیکھے بھی نہیں مجھے دیکھے ہاں chances تھے no doubt but I mean اب جھیٹری پاچ گول تو نہیں مارے گا ہر گیم میں and سارے چانسے ایک آشک کلیر چانس ملاتا بھی چاہتا بھی آشک تو جب there was no one moving only ڈیم میں سب کو بھولا تھا بھائی یا بود دھا گاڑن آیا وہ یہاں پر walk کرنے کے لے ہو کیا رہا ہے چلو آگے چلو آگے make some space رینڈی بھائی is that what he needs to address in these two days is that and can it be addressed if it can't be addressed than what you do you you you are playing against a team that will come at you so you will find space and that is your best opportunity you reckon that yeah I feel that I feel that this is the best responsibility and this is the best time to win against Afghan because they will come out a lot of players will be coming out to score because if they don't score if they don't win against India they are almost out like his fuck said so so it will be a good match for India and today is not the match where you know we cannot send a though gold to see the high house I go up are you know it's going to be a totally different mess like Richard also mention and it will be a good match for us to see also if India can really do it or not so then we will have a lot of things to talk about after the Afghan match but not today today there are three points good work from India but we still have a lot of work to do and it's a big big headache for the courts your true media professional کیونکہ آپ نے کیا طریقے سے end کیا تھی آپ بود بھائی ہی بولنا پڑے گا آپ کو good bye رینڈی بھائی thank you so much for joining us ہمارا بول رہے ہمارا سیمس like a happy camp when it's come up time but I'm I'm really you know like you want to hear that that in your wingers to pullbacks to not to move ahead and all that why why not more goals I was really shocked and surprised to hear that I think personally and I think that was a telling part actually unfortunately press conferences میں وہ چانس نہیں متا ہے to back-and-forth نا because ہی روشن بہت پیثم کوٹل تو now you that that is clearly you are shutting the game down you are you are putting an end to the game more or less so you're kind of counter counter being counterintuitive to your own like you've got on ادانتا you've got on Sahel with a view to perhaps create more in the attacking third and then when you are it's time to change your full back you're bringing this guy انہوں تھوڑا انہوں ہوئی گیا تھا پھر last 10 minute میں بند ہوئی گیا تھا اگر پہلے مور باک پاس is in my love ball rather than scoring one more goal as جایدیب دا سید like this was an opportunity because میرے سب سے بھی ایک ایسا تیمے where other teams actually tell me one thing is hong kong playing before you know like 3 o'clock match again before a 5 o'clock match on the same day on the same day yeah hong kong comboed yeah first game wow that that that is again a match you know like that will have an impact on the second match also trust me that kind of match نا کتنے مارے گے may be نہیں مارے گے who knows man many ball now see football i don't know it is the make they will try to score more goals you you don't think even it will be easier for them to break 10 when they are staying behind it's not going to be easier but i think we need to you know like wait for that match and that will be a big match again you know like that can decide hong kong you know like how they will set up against india richard when you're part of a team and ارسپیکٹر the quality of the team and how you want a game you want a game after a long time صرف and and you're part of a camp and you're all staying together how does that sort of uplift body language how does that uplift the next two training sessions and just the vibe in the entire team going forward نی بیننگ is huge vibe i mean there's no replacement for it جو بھی موٹویشنیل ویڈیو سپیچہ دی سب کرنا جیتنا لگی فیلنگ رہتا ہمیں i think ishwak and runny d can elaborate on it more than anybody else but of course i mean جو بھی اینجی چاہیے اگلے دو سیشنس کے لے اگلے مجھ کے لے to get a sense of clarity ابھی جو کوش بھی بول رہے سب لوگ یکن کرنا شروع کر دیتے آپس میں جو توکس رہتا ہے and you're watching the next opponent with a lot more intent so you get a lot more let's say drive and focus to bring in all your energies to meet the next stars but what ishwak also said was you are ابھی دو مچہs back to back ہونے والا ہے by chance مطلب ہوگا نہیں کہ آپ بول نہیں سکتے ہیں گر hong kong نے ان کو four zero ہر آ دیا five zero ہر آ دیا یہ سب بھی it'll start playing on your mind then all that but again the momentum takes them forward تو اگر hong kong کے ساتھ بھی بیننگ مومنٹر میں ڈیا کے ساتھ بھی رہے گا so i mean this across the group or whatever i think there are six groups playing now right for the air c qualifier جس نے بھی جیتا i mean you know three match format where everything is at stake then اس میں it's a totally different feeling کہ ابھی دو مچہ باکی ہے out of nine possible points you've got the first three جو بھی بولو تیکٹکس چلا نہیں چلا full box کلایا نہیں کلایا یہ ہوا وہ ہوا جیتنا جیتنا ہے بھائی مطلب ابھی اس کے بعد آگے کا جو بھی مومنٹم چیے یقین چاہی اس میں ہا جاتا ہے مطلب it gives you a lot of دیکھ سے گرونڈنگ اور سینٹرنگ دو تیکنے کے لئے بلکو لہ جیدیو سر آئیو لیل جلسا وائنی سر آج وہ کام کر رہا ہے جو آپ اتنے ٹائم سے کر رہے ہو ہمارا بھائی بیٹ کیا ماش دیکھا اس کے بعد pc پہ گیا اوٹر بشلیشن ہو رہی ہے آپ بہت اچھا ہو رہا ہے that's why i'm keeping silent لیکن وہ جو افغانستان جو افغانستان ماش کی بات کر رہو نا چی وہ میرے کھل سے وہ ایزی نہیں ہوگا کیونکی جو حکر حکر ماش ہوتے ہیں نا وہ سمہ و دی اوٹر because of the current system of indian football ڈنین فور بولا سب سٹر پلائنگ دیکھ کیونکی جیتنا ہے نہیں تو نا جیتیں گے تو آج مر جائیں گے یہ جو ایک ہوتا ہے کیونکی آپ کے پروموشن رلیگیشنی ہے that is one thing you don't have any any any knockout tournaments around the country so splitting i'm not i'm not see i'm not coming back to coming back to again to my favorite topic but some like as i told you i'm not feeling very comfortable with whatever is happening because this was that a sense in the stadium as well especially after having seen افغانستان in hong kong you're mute by but i can't really speak for the stadium but i did speak to a few people few colleagues in the press box and yeah there was a bit of like what is going on kind of feeling wasn't as a short i mean the thing is i think other than that one shot from distance that repeat had to deal with you didn't have to do anything through the game there was no pressure on india's goal so it was such a comfortable kind of game from that perspective that yeah no one really expected a gold blood but at the same time there was if you're saying like if you're referring to that electric kind of vibe that you get when a team is playing well irrespective of whether they're scoring goals or not that that wasn't there full marks of the crowd though the crowd tried really hard they did everything they could to lift every time you know there was a drop in momentum or they were like playing these square balls back passes the crowd started getting after the players to kind of push on push on push forward move ahead so full marks to the crowd and i think definitely for the افغانستان game there will be even more people who will turn out so that will add a little bit even more i think if if 30 or 1000 turns up today i think we'll definitely see figure closer to 50 for the next game so yeah i think we should be good too i mean frankly none of the teams today on the pitch except for the two goals that hong kong scored especially the second goal from that striker that turn and finished into the bottom corner apart from that none of the teams on display today really showed a kind of fluency to their game or any kind of real domination or you know it was all fairly standard جیدیب سر ہیں وہ بھی جلدی اٹھیں اور ایک ہمارے دوست ہیں جو سٹیڈیم میں جو سارے چار پڑھے سویں گی تو سارے چار کا تاکہ لگ رہا ہے یہاں پہ سب کا اشواق before we leave sir what would you like to say any closing comments because we are meeting again on Saturday night after India Afghanistan I think let's hope for the best سل만 ہوتا ہے you are not getting the audio audio is getting high want to listen to the audio ok just try fixing if you can if you can't no problem we'll let you go sir no problem there richard you want to say something before heading out جیدیب سر جرنلیس پوڈنٹو بیو what is the big talking point the story the next 2 days in the build up to Afghanistan for you the build up to be Afghanistan match I'm not too sure about it ایک سوال جوہب دینے سے پہلے مجھے یہاں سے نکلنے کے لئے بولا جا رہا ہے بھائی بول دو اماری مانگے پوری کرو پیچھے والا سڑی سے جانا پڑے گا اگر آپ کے پاس یہ نہیں ہے تو مطلب اگر اندیوٹر بند ہو گیا تو تو مشکل ہوگا اگر پانچ منٹ آرے گے تو رسی پکڑے کے نیچے جانی پڑے گے بھائی ایک 11 آری کو ملتے ہیں اس سے پہلے کچھ کرنا ہو تو پہلے آپ مال مصالہ تک hands down سے مال مصالہ تک کیا شاہیا ہوا بھی دو دن کا چاو تریننگ پی jestem بھائی خریتا ہوں سری آپ اے تک سیو صحیحا ہے جیدیو صحیحا آپ کی اپنے حالی ہے پیچھا myself اگر اندیوٹر جو غرفنے کے لئے ایک مضاقی ہے بہت ایک وجہ نہیں ہوجاتا ہے ، ولوہاں ایویف اور جو دیکھا ہے رہا ہے ، ہم اس کے حضرہ پہاہل کرسکتے ہو کہ ایسا سقینے کو سب دائی'tا ہے ، بہت زیادہ میں ایسا ہوتا ہے ، میں سب ہی چادہ اسا لیا کہ ہوں ، چونکہ اےہ ہم افتعار ہوتا ہے ، آپ رو ہی기에 ہی بھی گھائے ، اس کی حصائف یہاں ہے کہ ایک پہنچ ہے کے دل اردان ہے۔ جو دن ہے اپنے ساتیڈے کے اپنے کانفردنس کامس بیٹھنے گا آفردی افغانستان گیم ہم لوگ پھر ملیں گے جی افغانستان کے بعد پھر سے ہماری کھانی آپ کے سامنے آئی گی اور آپ دیکھے جی ہماری دیڈیکیشن کو اپنے کبھی کوئی اُنگلی نہ اٹھانا ایک فومن انڈیا کابٹن سارے دستہ کمارے لے ویٹھ کر دیں ایک فومن انڈیا پلیر


Namaskar dear learners. My name is Chainika Sanapati and I am from Maninam Devan School of Management Krishnakanta on Lukovice State of University. Welcome to the second part of the video on the unit labor environment from the course business environment. By now you have got some idea on the concept related to labor market principles of labor legislation and also the definitions of labor welfare. So in this video we will discuss on the industrial relation the concepts of industrial relations then also the importance of industrial relation why it is important in an organization and also we will discuss about trade union the concept of workers participation in the management and also we will discuss at the end of this video the VRS and golden handshake. Let us now discuss about the concept of industrial relations. So the term industrial relation comprises of two terms that is industrial and relations. So the term industry refers to any productive activity in which an individual or a group of individual is or are engaged and by relations we mean the relationship that exists within the industry between the employer and the employees and the workmen. The term industrial relations has a broad as well as narrow outlook. So originally industrial relations were broadly defined to include the relationships and interaction between employers and employees and so from this perspective industrial relations covers all aspects of the employment relationship including human resource management, employee relations, union management or labor relations. But now its meaning has become more specific and restricted. So accordingly industrial relations pertains to the study and practice of collective bargaining trade unionism than labor management relations. So let us now discuss some of the definitions of industrial relations. In the world of Leicester industrial relations involve attempts at arriving at solutions between the conflicting objectives and values between the profit motive and social gain, between the discipline and freedom, between authority and industrial democracy, between bargaining and cooperation and between conflicted interest of the individual, the group and the community. Thus industrial relation can be defined as a coin having two phases that is cooperation and conflict. This relationship undergoes change from thesis to antises and then to synthesis. Thus the relationship starting with the cooperation soon changes into a conflict and after its resolution again changes into cooperation. This changing process become a continuous feature in the industrial relation system and makes the industrial relation concept a dynamic and evolving one. Let us now discuss the scope, objective and need of industrial relations. Based on the definitions that we have discussed industrial relation the scope of the industrial relation can be outlined as a labor legislation that is relationship between the labor union and management. Then employer-employee relations that is relations between management and employees, the role of various parties, the mechanism of handling conflicts between employers and employees in case if there any conflict arises. The main and the primary objective of industrial relation is to maintain and develop good and healthy relationship between the employees and the employers or operatives and the management. Thus the objective of industrial relations can be stated as establish and foster some relationship between workers and the management by safeguarding their interest, avoid industrial conflicts and strike by developing mutuality among the interest of the concerned parties and keep as far as possible strikes, lockouts and garrows at bay by enhancing the economic status of the workers, then provide an opportunity to the workers to participate in the management and decision making process, then raise productivity in the organization to curb the employee turnover or absenteeism and to avoid unnecessary interference of the government as far as possible and practicable in the matter of relationships between the workers and the management. There is definitely a need of industrial relations and the need of industrial relation has arised to defend the interest of the workers for adjusting the reasonable salary or wages. It also helps the workers to seek perfect working conditions, then the workers, employees are concerned with the social security measures also through industrial relations. So industrial relation is also needed for achieving the democracy by allowing workers to take part in the management as well. Industrial relation encompasses some factors that influence behavior of the people at work. Some of the important factors are the characters. It aims to study the role of the workers' unions and employers, federations, officials, shop stewards, their industrial relations officers or managers or mediators, consulator etc. Then institutions, it includes government employers, trade unions, union federations and associations, then government bodies, labor courts, tribunals and other organizations which are direct or indirect impact on the industrial system. Then methods, methods focuses on collective bargaining, workers participation in management, then in disciplinary procedures, then grievance reversal machinery, then dispute settlement machinery, revision of existing rules and regulations or policies and procedures, hearing of the code labor tribunals and then the contents. It includes matter pertaining to employment conditions like pay, hours of work, leave, with wage, health and safety, disciplinary action, lay off dismissals, then participation in workers' participation in management, then collecting bargaining. So, these are some of the things, factors that includes in the contents. As we have discussed about industrial relation, here it is very important to discuss about trade union also. So, let us now discuss about the meaning of trade union. So, the trade union are voluntarily organizations or association of workers formed to promote and protect their interests through collective actions. Thus, a labor union or trade union is an organization of workers who have joined together to achieve goals in areas such as wages and working conditions. The union negotiates contracts and conditions with employers keeping employee satisfaction high and protecting workers from unsafe and unfair working conditions. Thus, the primary for purpose of the trade union is collective bargaining. Under the trade union act 1926, the term trade union may be defined as any combination where the temporary or permanent formed primarily for the purpose of regulating the relationships between the workers and the employers or for imposing restrictive conditions on the condition of any trade or business and includes any federation of two or more unions. Let us now discuss about workers' participation in management, its meaning and some of the definitions given by the scholars. Workers' participation management is a system of communication and consultation either formal or informal by which employees of the organization are kept informed about the affairs of the undertaking or through which they express their opinion and contribute to the management decision process. Workers' participation in management provides a chance to employees in organizations decision making process. The workers' participation may be at shop level, departmental level or at the top level. The workers' participation in management implies the willingness to share the responsibility and accept commitment by the workers in executing decisions of the management with consultation of the workers. The workers' participation in management conducted through the mechanism of forums which provide the association of workers' representatives. Let us now discuss about the levels and forms of workers' participation in management. So the level of participation of workers in management is number one, information participation of workers. It ensures that employees are able to receive information and express their views pertaining to the matters of general economic importance. Then consultative participation of workers under this kind of workers' participation in management, workers may act as consultant in the matter of workers' safety, health and their welfare at workplace. The associative participation of workers, this kind of workers' participation in management is the next level of consultative participation. Under this participation of management, morally the management accepts and implements the opinion of the employees. Then administrative participation of worker, under this kind of participation of workers in management, worker take part in discharge of managerial functions. Then decisive participation of workers, it is the highest level of workers' participation in management where the employees and the management together take decision on the matters related to the workers, welfare and production related issues. There are certain forms of workers' participation in management. Number one, the joint consultation model. Number two, joint decision model. Number three, self-management or auto management scheme. The number four, workers' representation on the board. So what is joint consultation model? In this consultation model, the management consult with the workers before taking decisions. The workers represent their views through joint consultative committees. Then joint decision model. In this form, both the workers, the employees and the management jointly decide and execute the decision. Then the self-management or self-management scheme. In this model or form, the entire control is in the hands of the workers. The workers manage the organizations themselves. Then the workers' representation on board. So under this method, the workers elect their representative and send them to the board to participate in the decision making process. Let us now discuss about voluntary retirement scheme that is BRS and Golden Handshake. Voluntary retirement is legally tenable and forms an integral part of public policy. This scheme is voluntary on both sides, the employer and the employees. The voluntary retirement scheme package is offered to the employees as an incentive to retire earlier than their normal retirement age. And the BRS package usually contains generous retirement benefits for certain employees. The main purpose of BRS is to downsize the number of employees on payroll or adopt a changing business environment. Let us now discuss some of the cost constraints and benefits of BRS. Costs and benefits to the company. A company introduces BRS with a view to reduce its surplus labor. If a company or an organization can reduce its workforce through retrenchment, it has to pay compensation at the rate of 15 days salary for every year of completed service. So companies employing more than 100% cannot retrench their employees without giving prior notice. Then consultation with the employees or union or paying compensation under the law. And also obtaining prior permission of the appropriate government. The extent of BRS amount is dependent on the number of factors like relative health of the enterprise, the real cost in terms of intangible elements, moral and motivation. Let us now discuss about golden handshake. A golden handshake is a clause in an employment contract that provides the employee with a significant severance package in the case that the employee or the executive losses his or her job through firing, restructuring or even scheduled retirement. This can be in the form of cash, equity and other benefits like stock options. Golden handshake are offered only to a high ranking executives by major corporations. We can take an example of golden handshake like it is usually offered to a director, senior executive or consultant who is to let go before his or her contract has expired. This situation is most common after the event of mergers or takeovers or buyout. So dear learners, we have come to the end of this part of the video on the unit labour environment. So in this unit including both the parts of the video we have gone through the concept of labour market, we have gone through the concept of labour legislation, also the what is called industrial relation, the concept of industrial relations is important. Also we have learned about workers participation in management, the concept of VRS and golden handshake. So thank you so much for watching this video. We will also come up with other units related to management. Thank you so much for watching.


My fellow Americans, later today, Nancy and I will be going to Andrew's Air Force Base to be with the families and friends of four American Marines, four young men whose bodies are being returned after they were murdered by communist guerrillas in El Salvador last Wednesday night. We will carry with us all of the grief and sorrow and rising anger of a nation whose patience has been stretched to its limit. I will speak to the country and to the loved ones of those brave men who defended our freedom. But before we go, I must also speak to you about important deliberations that are now taking place in Congress. We've made considerable progress this year in achieving the spending reductions needed to bring down the budget deficit and keep our economy growing and producing new jobs. The Senate has passed a plan for $56 billion of budget savings, which would also allow us to keep most of our defense rebuilding program on track. We all owe a debt of gratitude to the Senate for their courage. Unfortunately, we cannot say the same about the plan passed by the House. It is not a true budget savings plan. Many of its so-called savings are simply phantom cuts. Further, the House makes no meaningful effort to shrink this gargantuan federal spending machine that gobbles up your taxes and divvies them out to a multitude of special interests. Unlike the Senate, which has proposed real, substantial and permanent reforms, the cuts of the House budget here are not enough and certainly not permanent. The freezes and other one-time measures the House proposes are not solutions that would permit us to get a handle on federal overspending. They would only postpone the inevitable. And what's even worse, in these perilous times the House budget would send a signal of weakness by cutting purchasing power for vital defense needs.  And this is why we've taken an additional step. This week, I appointed a special bipartisan Blue Ribbon Commission to review defense management and procurement. So yes, we can and must eliminate waste, but it is sheer folly to blindly weaken ourselves when our adversaries are conspiring and working so hard to bleed in cripple America. It is time to stop treating our defense establishment and intelligence agencies like enemies and concentrate our attention and anger on the true enemies of freedom and democracy in the world. For the past two weeks, the House and Senate have been meeting in a conference committee trying to come up with a final budget for the next fiscal year. I'm sorry to report that they haven't made much progress. So far the House has turned away from realism on defense and refused to accept the many program reforms and permanent savings in domestic spending that are proposed in the Senate version. And as is predictable whenever sufficient will is lacking to make the tough decisions on spending, calls are raised for tax increases. Well, if I must, I'll repeat it till I'm blue in the face. I will veto any tax increase the Congress sends me, and I'm pleased to say I have been promised the votes to sustain that veto. All of us have a great deal at stake in the outcome of these Senate House appropriations or negotiations for the sake of both our national security and our economic well-being. If the conference committee reports a budget that achieves substantial and permanent changes, it will pave the way for continuing the low inflation and falling interest rates that will keep our economy growing and keep Americans working. If on the other hand, the process breaks down and the Congress can't do what's right on defense or on controlling domestic spending, then the consequences will be very bad. America will be seen as too weak to respond to threats, and all the progress we've made in our economy will be placed at risk. I'm asking for your support to make Congress understand this is a moment in our history when all of us should pull together and put our national interest above partisan politics. The challenges we face are big, but not too big if we Republicans and Democrats unite for a stronger and safer America. We still have time, so let's get started. Until next week, thanks for listening, and God bless you.


So, last time you recall we were talking about the master equation for Markov processes and just to refresh you your memory we said consider a conditional probability density that the system is in state some state k at time t given that it was at j at time 0 and this quantity this set of quantities obeyed a set of couple differential equations which was of the form d over d t of this was equal to on the right hand side you had a summation over all possible intermediate states. So, l equal to 1 to n w k l p of l t j minus w of l k p of k t given j k and these quantities were the transition rates to go from the state l to the state k and there was a constraint here it said that l not equal to k and this is what I call the master equation it is a couple set of first order differential equations for this quantity and of course the initial condition could be anything you want you care to specify since we are talking about conditional probabilities the initial condition is p of k 0 j equal to delta k j. So, the task is to solve this set of equations given that initial condition and then you have a whole host of probabilities okay now notice that I wrote this rewrote this as I wrote a column vector. So, I said let p of t be a column vector with elements p of 1 t for each j etc up to p of n t j in this fashion and then this equation became d p of t over d t equal to a matrix w acting on p of t and this matrix w as you can easily verify has the following elements w k j equal to w k j for all k not equal to j all off diagonal elements were of this form and the diagonal elements w k k was equal to minus the sum of all the other elements in that row okay. So, this is equal to w for a given k k is 1 for example it is w 2 1 3 1 etc etc. So, it is w l k summed over l 1 to n l not equal to k. So, we have this picture of a matrix where each column each row adds up to 0. So, the determinant of w is 0 now w has real elements all the off diagonal elements are either 0 or positive and the diagonal elements are all negative just go back to this equation let us write this equation for instance for the case when k is 1 okay and let us suppress the index j that is not necessary here. So, essentially you have a equation like d over d t p of 1, t equal to on the right hand side you have to sum over all k 2 3 4 etc etc. So, it is equal to w 1 2 p of 2 t plus dot dot dot plus w n sorry I put k equal to 1. So, 1 n p of n comma t minus this quantity here which is just a sum over l leaving out the index 1.  So, it is clear that all the off diagonal elements of this big matrix w are precisely w 1 2 w 2 3 and so on so forth multiplying p 2 p 3 etc column vector and what multiplies p 1 because after all what does this equation imply it says p of 1 t dot dot dot p of n t the d over d t of that equal to w times p. So, that is w 1 1 1 p of 1 p plus w 1 2 p of 2 t plus dot dot dot dot dot etc on the first column and then similarly for the other guys so d p 1 by d t is this fellow here and w 1 1 as you can see is minus of all these just writing this out explicitly okay. So, the important thing to remember is that the off diagonal elements of w are the transition probabilities transition rates and they are non-negative they are either 0 or positive okay if 2 states are not directly connected then that particular w happens to be 0 okay. We are making some assumptions here which I have not technical assumptions about the nature of this w matrix we will talk about it later on when I give you special cases of it there are there could be situations where we are talking about the generic case in other words we are talking about the Markov process in which you can reach any state from any state no matter where you start there are no subsets of states which are you know closed among themselves and so on. So, we are taking the general case where all the w's exist and then you have transitions possible now you must remember that it is entirely possible that you may not be able to go from say state 6 to state 8 directly there may be a 0 transition probability but given enough time you may go from 6 to some other state 5 and then 5 to 8 and so on so that possibility exists of course and that is really what happens most of the time because we will look at cases where you may be able to jump only from a given state to neighboring states on either side and yet over a period of time the system wherever you start will reach any other state okay. So we have this w matrix and then we wrote down a formal solution to it and that was just the exponential of this matrix w so we had d over dt p of t equal to w times p of t and this implied that p of t was e to the w t is equal to e to the w t times p of 0 whatever that is and in the case we are talking about this p of 0 is a column vector in which the elements are all 0 except for the jth row which has got 1 because you are starting with the state j okay. So the task reduces to finding this quantity here and the statement made was what sort of time dependence can we generically expect and the answer is you expect things to decay in time to some equilibrium distribution and we already know what that distribution is we have some idea of what it is because remember that determinant w equal to 0 implies lambda equal to 0 is an eigenvalue of w you can actually prove more than this you can show that the 0 is a simple eigenvalue that is not a repeated eigenvalue generically moreover that it has a right eigenvector which will be the stationary probability distribution and in the simplest cases we are looking at it is a unique vector what is important is when you want to identify the column the elements of this eigenvector as corresponding to probabilities we want to make sure that the elements cannot be negative okay. So we need a guarantee that this eigenvector has elements which are not only real but also have are also non-negative okay there are theorems which assure us of that so one of them was the statement I made that the eigenvalues of this w can never have positive real part and the reason I said was due to this disc theorem which said that if you give me a general matrix M and this was the famous Geshe-Corin disc or circle theorem and what it says is we give me an n by n matrix M then take its diagonal elements and mark those points in the complex plane and take the sum of the module I of all that off diagonal elements in that row add them all up and draw a circle about this center point of that radius and element the eigenvalues are guaranteed to remain inside these are on these discs that was a statement this is not a hard theorem to prove because look at it here is a simple way of doing this suppose lambda is an eigenvalue then it says M times some eigenvector u equal to lambda times u now let us look at a particular eigenvalue lambda and let us look at a corresponding eigenvalue lambda and corresponding eigenvector u then suppose this u is of the form u 1 u 2 etc and let us say the kth element in it is the largest in magnitude okay so this fellow has elements u 1 u 2 up to u n and let us suppose that some element k this fellow has the largest magnitude in magnitude over all these of all these elements then if you write this element down it is clear that m k j u j must be equal to lambda times u k I write this down for that element out here and there is a summation over j running from 1 to n so let us take out the j equal to k element and put it on the right hand side and then it says summation j equal to 1 to n j not equal to k m k j u j equal to lambda minus m k k on u k now take modulus on both sides then it immediately tells you that modulus of lambda minus m k k times modulus of u k I will transfer it to the right hand side equal to summation j not equal to k summed over j m k j u j over u k modulus but of course this is less than or equal to summation j not equal to k modulus m k j times the modulus of this because I take the modulus inside the summation I get maximize the sum itself but these numbers are guaranteed to be less than or equal to 1 because we took this to be the largest right so this is less than equal to summation j not equal to k modulus m k j that is the disc here because it says this Eigen value is inside us or on the circle of radius m k k whose radius is given by this so this region is a disc and you are guaranteed the Eigen value is inside or on that disc okay so all the Eigen values of this m are either in or on the union of all these discs or the Gershkor and discs okay there are further refinements to this for example if one of the discs is disjoint you can show that that disc has at least one Eigen value etc definitely has an Eigen value and so on okay. Now what we need is just one part of this theorem applied to this matrix W remember that we had this W whose off diagonal elements jk were all W jk these guys were all positive numbers and the diagonal element k was equal to minus summation j not equal to k W jk so that immediately tells us that 0 is an Eigen value in the Eigen value plane and all these numbers the diagonal elements are all at negative values because these are non-negative numbers inside here so this equal to minus modulus W kk and so you immediately know that the centers are all sitting here and then this look like this each disc looks like that it touches 0 therefore the real part of lambda less than equal to 0 for all so the Eigen values are such that e to the minus lambda t could at must dk to 0 except for the 0 Eigen value where it remains at 0 there is no T dependence at all therefore W is a relaxation matrix things relaxed to the equilibrium state and what is that given by well that stationary distribution is not difficult to write down so the stationary distribution corresponding to lambda equal to 0 satisfies p state W d of course it satisfies dp stationary over dt equal to 0 which must be equal to W times p stationary so it is the right Eigen vector corresponding to the 0 Eigen value of W since each column of W adds up to 0 it is immediately clear that the uniform Eigen Eigen uniform row vector is an Eigen vector a left Eigen vector 1 1 1 1 1 etc. But this is not a symmetric matrix so the left and right Eigen vectors need not be the same in general and the right Eigen vector is indeed the equilibrium distributed the stationary distribution is that clear now how do we find it well you need to put in this condition and discover what it is so let us put that in and if I write out what W is and let us call this p of p stationary p 1 p 2 up to p n it is stationary there is no time dependence so I would not put in a t index at all there is no t dependence it is the single time probability independent of t right and what is that given by well we have a summation l running from on to n l not equal to k W k l p of l minus W l k p of k must be equal to 0 for the stationary distribution again it is a couple set of equations simultaneous equations linear in all these fellows is there a guarantee that this will have a non-trivial solution it is a set of homogenous equations and when does a set of simultaneous homogenous equations have a non-trivial solution when the determinant is 0 which indeed it is we know determinant W is 0 right so it is got a solution right it is got a unique solution and you need to find that by solving this set of equations here whatever it be so this problem reduces to an algebraic problem nothing more than that so this thing will lead lead you to implies you can find this now there are some important cases where you can write the solution down explicitly remember it is this sum that is 0 summed over l but you could ask what happens if each of these terms is 0 inside the sum okay then you get a very special kind of distribution okay which corresponds to saying that term by term this sum is 0 and that is called detail balance so since it is so important in physical applications let me write it down it is called detail balance implies that this quantity Wklp of l equal to Wlkp of k for each kn for every pair this is true pair wise and of course if that condition is true then immediately you know that this that is going to give you the stationary distribution without doing much solution at all and what is this actually saying it says wait for a long time get to the stationary distribution let p of k be the probability that you are in state k then that multiplied by the transition probability rate that you go from k to l must be same thing in the reverse order so here is the initial state here is the final state if you interchange the two you get just this guy here so the flow both ways pair wise is exactly the same the weighted flow of probability mass now this should be a curiosity just a curiosity except for the fact that systems in thermodynamic equilibrium physical systems satisfy detail balance provided the underlying dynamics has a property called time reversal invariance I would not get further into the details of this at the moment but just to tell you that it is a very very important special case there are lots of physical systems under very general conditions which satisfy detail balance in which case this thing is immediately true and what will that tell us it gives us the ratios of all these probabilities so you choose any one of them say p1 then you can find p2 p3 and so on in terms of this p1 and how would you determine p1 itself you normalize the probability remember you have to normalize right so remember that you definitely need this summation k equal to 1 to n p of k must be equal to 1 so we know all the ratios p p2 over p1 p3 over p1 up to pn over p1 and we know p1 itself from that set of equations provided you have a normalization condition there is got to be one inhomogeneous condition which is what this is and with this normalization you can find all of I leave it to you as an exercise to show that in the general case for arbitrary n when you have this detailed balance condition valid then this will imply this will imply that the solution p of k looks like this it looks like 1 over and this is a well known form so it is worth memorizing it 1 plus a summation l not equal to k 1 to n ratio I could verify this so there is a very simple formula essentially an algebraic formula for the stationary probability distribution of this Markov process in the stationary Markov process in the case when detailed balance is valid and then it is just that simple algebraic formula of there what happens if the rates are all the same the rate from l to k is the same as a rate from k to l what do you think would happen now you are saying not only read the balance you are saying that look this rate is equal to that rate that tells us this must be equal to that the probability is distribution must be a uniform distribution there are n states you are in the steady state and each of them is equally probable so what is the probability of any one of them 1 over n and indeed that is true because if these rates are all equal this cancels gives you 1 there is a summation here except for 1 index k so this is n minus 1 you add it to 1 and you get a 1 over n okay so this goes over but when you do not have that when you do not have that extra condition that the rate transition rates are also equal then of course you have a non-trivial solution in terms of all the transition rates now let us look at the simplest case the simplest possible case is when you have just 2 states possible and this is such a famous case and it applies in so many places it occurs in so many places that it has got a special name to itself it is called the dichotomous stationary dichotomous Markov process corresponds to n equal to 2 just 2 possible states. We can write down what the solution is in this case because that stationary distribution is utterly trivial in this case you have summation over l and for any given k it runs over only one other value for 1 or 2 right so l k etc run over value is 1 to 2 and you have w for the stationary distribution you have w say 1 2 p of 2 minus w 2 1 p of 1 should be equal to 0 because there is nothing else to sum over if I said k equal to 1 I have this and I sum over l there is only one other value 2 and similarly you have w well you have essentially this equation and nothing more so this is what we call w 1 2 and let me call this p of 2 equal to w 2 1 p 1 here so p 2 is this fellow 2 is this and p 1 plus p 2 must be equal to 1 so this must be equal to 1 minus p of 1 and what does it lead us to it gives us explicit solutions it says w 2 1 over w 1 2 plus 1 p of 1 equal to 1 or p of 1 equal to w 1 2 w 2 1 2 is a rate transition problem rate to go from 2 to 1 and similarly p of 2 equal to w by symmetry that is it those are exact solutions for the stationary distribution of course we also have to write the time dependent solution for p of t we have just solved the problem w on p stationary equal to 0 and we have this but now think about it a little bit and you see immediately how physical this solution is because what we have is a process and we cannot draw this let us draw this is a process which has a function of time it takes on two states possible now we need a symbol to say what the values of this random variable are which can take two possible values let us call those values to constant c 1 and c 2 for example so let us say c 1 is sitting somewhere here and c 2 is sitting somewhere here then what it does is it starts in say state 1 goes on for long time so that any arbitrary instant of time you can put the origin of time and then it abruptly makes a jump to c 2 and then goes on for a while it makes c 1 and then it does this etc. So this is c 1 and that is c 2 two states it is a two state process and in each state the value of the variable is either c 1 or c 2 and it keeps switching back and forth randomly between these two states so you can now imagine can easily imagine how many possible situations this will model immediately anything which has got two possible states either on and off or a passive state and an active state you name it a huge number of applications where this model will work the simplest possible model now what is the rate or average rate at which it switches from one to the other so we have already said that we have said that w 1 2 is what we call w 1 2 is the rate from at which 2 to 1 switching is happening so let us call this lambda 2 the rate at which the system switches state if it is in state to the rate at which it switches to state 1 and similarly to 1 is a rate at which it switches from 1 to 2 then according to what we have here it says p 1 must be equal to w 1 2 that is lambda 2 over lambda 1 plus lambda 2 and p 2 must be equal to lambda 1 over lambda 1 plus lambda 2 now what is the physical meaning of this lambda 1 and lambda 2 if you look at this picture you see that it stays suppose it had started like this somewhere it says stays for a time interval in state 1 random time interval another random time interval another random time interval etc and the average over all these things is the mean residence time in state 1 so if you say what is the average in between switches from state 2 to 1 in between what is the average time it spends in each each time it reaches state 1 let us call it some tau 1 so average residence in state 1 let us call it tau 1 and similarly the average duration of a stay in state 2 let us call this average equal to tau 2 then clearly the switching rate is just the reciprocal of these things right so it is clear that lambda 1 tau 1 equal to 1 over lambda 1 tau 2 equal to 1 over lambda 2 so it says this time is obviously equal this is equal to tau 1 over tau 1 plus tau 2 and this is equal to tau 2 over tau 1 plus and that is exactly what you would expect physically because now you would say huh if I look at it as a function of time and I ask I put my finger on one particular point in time I ask what is the stationary probability that it is in state 1 or state 2 well the probability that it is in state 1 will be the fraction of the time that it spends in state 1 over a long period of time and similarly for state 2 and they are precisely proportional to the mean residence time in state 1 divided by the total residence time these are the fractions okay so if we have a simple physical interpretation of what is meant by the equilibrium distribution for a dichotomous Markov process it is just the ratio of the fraction of the mean mean residence time in one of the states divided by some of the residence times in both the states okay. So it is physically very clear this is what is happening we still have to solve this problem of the time dependent problem we still not dealt with that but the stationary distribution is completely clear in this particular case. Now even if you have a three state process the formulas that you write down in general without detailed balance are not so trivial they are quite involved they get more and more algebraically more complicated but when you have something like detailed balance then of course it simplifies enormously but the most popular model is the dichotomous Markov process in this case now what is what remains is to ask what happens as a function of time what happens when you put in the time dependences everywhere and this is what happens we need to solve this problem by going back and saying d over dt so we need we write the solution down p of t is to the w t p of 0 and we need to know what is w and w was equal to w 11 w 12 but w 12 was the rate to go from 2 to 1 on this side which was lambda 2 and similarly w 21 was the rate to go from 1 to 2 and the diagonal elements are minus those guys so that is w the transition matrix and we need to find the exponential of this matrix so you square it you cube it and things like that and find out what is the exponential but matters are made a little simpler by noticing that w squared is minus lambda 1 lambda 2 lambda 1 minus lambda 2 this is w squared and what that equal to its lambda 1 squared plus lambda 1 lambda 2 so take out a lambda 1 you get lambda 1 into lambda 1 plus lambda 2 and then minus lambda 1 squared minus lambda 1 lambda 2 so again take out a lambda 1 and then on the other side you get minus lambda 1 lambda 2 minus lambda 2 squared so it is minus lambda 2 lambda 1 plus lambda 2 and then finally lambda 1 lambda 2 plus lambda 2 squared so that is lambda 2 plus lambda 2 so we can take out the lambda 1 plus lambda 2 and write this as equal to lambda 1 plus lambda 2 times lambda 1 minus lambda 1 that is just minus of this guy out here so this is turning out to be equal to minus and then a w itself okay now the rate to go from 1 to 2 is lambda 1 and 2 to 1 is lambda 2 and the average rate is half the sum right so let us define the mean transition rate lambda is lambda 1 plus lambda 2 over 2 so it says that w squared equal to minus 2 lambda w that of course immediately makes the problem of finding the exponential trivial because it says w cubed is proportional to w once again and so on so forth so where does it get us it says e to the w t is the identity matrix plus w t plus t squared over 2 factorial w squared which is minus 2 lambda w and then t cubed over 3 factorial and then w cube but that is w times w squared and so on so it is minus 2 lambda whole squared w etc all the way so let us write this as i plus let us take out the w let us take out the w and then let us write this term as minus 2 lambda w t divided by 2 lambda write it in that form so this becomes over minus 2 lambda a minus 2 lambda take out a minus 2 lambda in this fashion and then inside I have minus 2 lambda t minus 2 lambda t whole squared over 2 factorial plus dot dot dot I took out a minus 2 lambda so put let me put that back in here so that matches this power out here but what is this fellow e to the minus 2 lambda t minus 1 right so let us erase this 1 minus e to the minus 2 lambda t and get rid of the minus sign and it is over right now we can write the full probability distribution down completely I leave that to you as an exercise to write this down so you should be able to write down p of now let us let us put in the values that we have for this process so you should be able to find p of c 1, t given that you started in c 1 p of c 2, t given that you started in c 1 how would you find this what is this guy equal to this is e to the w t on the initial matrix and what is the initial matrix if I start with c 1 what is this equal to it is equal to 1 at equal and what is this 0 so all you have to do is to apply that to this fellow all you need to do is to apply this matrix which is a 2 by 2 matrix because we know about w and I apply it to this fellow and read off these two numbers and similarly p of c 1, t c 2 and p of c 2, t c 2 this column matrix is equal to e to the w t that is this matrix acting on 0 1 and you can write the full matrix now by the way just to check since we have this statement here if you let this if you let t tends to infinity if you let t tend to infinity be better recover the values that we already had for the equilibrium distribution what happens to this guy it becomes a stationary distribution p 1 p 2 right so you have p 1 p 2 should be the limit of e to the w t on the initial state whatever that state is whether it is in 1 or 2 we do not care now what is the limit of e to the w t you can read it off from here yeah so we know that the limit t tends to infinity e to the w t turns out to be the identity matrix plus w over 2 lambda because this goes away so you have 1 0 0 1 plus w over 2 lambda and now you have to tell me what is 1 over 2 lambda what is w by the way it was lambda 1 here lambda 2 here minus lambda 1 minus lambda 2 added to this guy out here and this is lambda 1 plus lambda 2 so what does this become equal to lambda 1 plus lambda 2 so it is lambda 2 again a lambda 2 and then a lambda 1 and a lambda 1 1 over 2 lambda times that on whatever initial state you want to put down now one of our articles of faith is that as time increases the initial value should not matter so whatever distribution I should still get the equilibrium or stationary distribution to be the same thing so whether I apply it on 0 1 or 1 0 it should not matter it should not matter at all otherwise I am in trouble right in fact I could have had a of this and 1 minus a of the other so let us do that and see what happens so suppose the initial state this fellow here had been some a b with a plus b equal to 1 non-negative numbers such that a plus b is 1 so we apply it to a b and what do you get you get lambda 2 a plus lambda 2 b so lambda 2 comes out and you have a plus b which is 1 it goes away so this indeed gives you lambda 2 over lambda 1 plus lambda 2 and lambda 1 over lambda 2 independent of a and b well independent of a b is 1 minus a so that corroborates the requirement we had that the stationary distribution should not depend on the initial distribution at all okay so it does it does cancel out this thing does that is why you had the same element both places out here and that is exactly the this is exactly the equilibrium distribution we discovered earlier okay but you can write the time dependent one out here write this out explicitly I leave you to do this little bit of algebra but you get expressions what is that so what is the decay to equilibrium what is it going like there is a constant part in these probabilities which gives you the stationary part and then there is a part which decays there is only one more eigenvalue and what is that other eigenvalue 2 2 minus 2 lambda minus 2 lambda so the correlation time you expect the correlation time in this process is going to be 2 lambda inverse and again that corroborates what we are going to find the correlation time explicitly I am going to define it in a minute but you see it is this time scale that is the correlation time in a very specific way we will see that the autocorrelation will die down with this exponent out here but what is this guy equal to this is equal to 1 over lambda 1 plus lambda 2 right which in turn remember this is it is equal to tau 1 tau 2 over tau 1 plus tau because this is 1 over tau 1 that is 1 over tau and what is this number what sort of mean is it it is the harmonic mean of the individual residence times right so we have this very simple relationship which says in a dichotomous Markov process with mean residence times lambda tau 1 and tau 2 in the two states the correlation time of this process time on which it loses memory in some sense is the harmonic mean of these two individual times now let us define correlation well some things can be written down immediately and then we will if time permits do this or I come back to this a little later we will write the answer down at least in equilibrium we will write the answer down so I ask now what is the mean value of this process let us call that process X so what is the mean value of X X has values C 1 and C 2 the sample space of X comprises the two values C 1 and C 2 and the system is switching randomly forth back and forth between these two values with mean residence time tau 1 and tau 2 respectively in the two states so what do you expect is the average value of X X stationary X stationary is with respect to the stationary distribution by definition this is equal to C 1 P 1 plus C 2 P 2 by definition the stationary or t tending to infinity average has got to be this because P 1 P 2 are the stationary probabilities and C 1 C 2 are the corresponding values therefore this is the weighted average and it is a normalized probability and what is this equal to not surprisingly this is C 1 tau 1 plus C 2 tau 2 over tau 1 plus tau 2 or in terms of lambdas it is C 1 lambda 2 plus C 2 lambda 1 over lambda 1 plus lambda 2 what is the mean square going to be the same guy but with squares right so it is C 1 squared tau 1 plus C 2 squared tau 2 over tau 1 plus tau 2 again this is the stationary and what is the variance going to be so what is delta X that is the difference between this and the mean squared stationary delta X whole squared stationary what is that going to be that is equal to this minus the square of this fellow now the square of this is a first of all if I take this minus square of that there is a tau 1 plus tau 2 multiplying this over here so let us quickly do that it is C 1 squared tau 1 plus C 2 squared tau 2 tau 1 plus tau 2 minus C 1 squared tau 1 squared plus C 2 squared tau 2 squared plus 2 C 1 C 2 tau 1 tau 2 the whole thing divided by tau 1 plus tau 2 squared so some terms definitely cancel out we can write down a very simple formula and that is delta X whole squared in the stationary state is equal to first of all the tau 1 squared cancels with this guy the tau 2 squared cancels with that and then you have a C 1 squared tau 1 tau 2 a C 2 squared tau 1 tau 2 and then you have minus 2 C 1 C 2 tau 1 tau 2 so this is equal to tau 1 tau 2 that is it okay now what is tau 1 tau 2 over tau 1 plus tau 2 it is it is the correlation time right so there is a direct connection between this what happens if what happens if C C 1 C 2 equal to minus C 1 this becomes a square of whatever value so sometimes it switches between plus 1 and minus 1 or something like that then the formula simplify that is called the symmetric dichotomous process we will talk about that little while later but what happens if there is time dependence so the next question to ask is the autocorrelation the generalization of the variance and I will do that tomorrow we need to generalize this to ask delta X at any instant T 1 delta X at any instant T 2 what is that equal to that generalizes the variance but this is a stationary process so this thing must be a function of T 2 minus T 1 or something so I might as well look at delta X at any time 0 and then call this just T what would this be if T equal to 0 it should reduce to this right so it is this time something or the other and you expect the memory is going to drop as a function of time exponentially with the correlation time which is 2 lambda inverse so what do you expect this formula to be what do what do I expect this to be in general that is equal to this multiplied by e power minus 2 lambda so the dichotomous Markov process is exponentially correlated and we will prove this we have to define the correlation time correlation self-auto correlation more precisely we will do that and then take it from this point tomorrow.


Well every year the Brainerd Lakes, Pequot Lakes and Cross Lake Chambers host a banquet to celebrate the accomplishments of the local businesses in the region and to award one lucky business for their entrepreneurial spirit and accomplishments. This year's Business of Excellence Award goes to Just For Kix, a local company that focuses on dance and creating opportunities for youth. Just For Kix now serves more than 23,000 dancers across the nation. The creators of the company, Cindy and Steve Klau, credit their strong team and family values for the success of their company. We work well together and it all came from you know hard work, we believed in work ethic, humility and honesty and because of all that we've certainly had seen a lot of success and we appreciate all that. This year for the first time the Chambers also presented an award to an individual who achieved exceptional business success in their lifetime. Stuart Mills Jr. was awarded the Business Legacy Award although he was not able to attend the ceremony. His daughter says he's honored for the recognition. I know that he so appreciates receiving this from everybody because again I feel like it's the entire community acknowledging my dad and I so appreciate that everybody's come together to acknowledge him and recognize him and thank him. About 450 people attended that awards ceremony. If you've enjoyed this segment of Lakeland News, please consider making a tax deductible contribution to Lakeland Public Television.