الحمد لله رب العالمين الرحمان الرحيم ملك يوم الدين وشد أن لا إله إلا الله وحده لا شريك له إله الأولين والآخرين وقيوم السماوات والأرضين وشد أن محمد عبده ورسوله الصادق الوعد الأمين صلى الله وسلم عليه وعلى آله وصحبه أجمعين أما بعد إن شاء الله تعالى today we're insha'Allah going to speak about and we're going to reflect in a series of bars over the verse of Allah سبحانه وتعالى فوربك لنا سألنهم أجمعين we're going to contemplate and we're going to ponder over that verse إن شاء الله تعالى الله سبحانه وتعالى He says in Surah Al-Hijr ayah 92 to ayah 93 الله سبحانه وتعالى He says فوربك با يولود لنا سألنهم we will ask them and the noon in لنا سألنهم has an emphasis on it it has to keyed on it an emphasis لنا سألنهم we're going to ask them أجمعين each and every one of them أما كانوا يعملون and they're going to be asked about that which they used to do so in that verse الله سبحانه وتعالى is telling us that we're going to be asked about every single action that we have done so insha'Allah وتعالى the way we're planning to ponder and contemplate over this verse is beathen الله الكريم by bringing places where we're going to be questioned الله سبحانه وتعالى He says in another ayah ولو شاء الله if Allah willed سبحانه وتعالى لجعلهم أما لجعلكم الله would have made you أمة واحدة Allah would have made you one nation ولكن يُضِلُ من يشاء الله misguides whoever he wills ويهدي من يشاء أن الله guides whoever he wills ولا تسألون and you'll be asked and you'll be asked and you'll be asked عما كنتم تعملون that which he used to do you'll be asked صورة النحل آية 93 in another place الله سبحانه وتعالى He says فلنسألن الذين أرسل إليهم ولا نسألن المرسلين الله سبحانه وتعالى He says صورة العراف آية 6 فلنسألن we will ask الذين أرسل إليهم the ones in which it was sent to them ولا نسألن المرسلين and we will also ask the messengers we'll also ask the messengers also الله سبحانه وتعالى He says in another verse لا يسألوا الله is not questioned عما يفعلوا ذلك which he does وهم يسألونه but the people and the creation are the ones who are going to be questioned all of those verses they have roughly the same meaning as you can see each verse is emphasizing the point which is that you and I are going to be questioned and the only one who is above questioning is who الله سبحانه وتعالى last lesson the reflection we spoke about the first time that the person will be questioned is in there is in there grave when the angels come to you the famous hadith and Imam أحمد narrated in his musled من حديثي البراعب العازب رضي الله تعالى عنه that the prophet said عليه الصلاة والسلام that the angels they will sit and they will say to the person مر ربك who is your lord and the person will respond by saying ربي الله my lord is Allah سبحانه وتعالى the believer فيا قولانين and the angels will both say ما دينك what's your religion and then he will respond by saying the believer ديريا الاسلام my religion is Islam فيا قولان له than the two angels say to him ما هذا الرجل اللي بعث فيكم who is this man who is brought out from amongst you this messenger فيا قولوا the believer will respond by saying هو رسول الله it is the messenger of Allah صلى الله عليه وسلم then a caller فيا ينادي منادن a caller will call out في السماء from high above and then he would say صدق عبدي my slave has told the truth he has uttered the truth فأفرشوه من الجنة place for him a laying from jannah وأل بيسوه من الجنة and clothing from jannah وفتحوا له بابا إلى الجنة and also open for him the gates of jannah and doors of jannah so this hadith it shows us that the believer is going to be questioned and the same is for the the disbeliever he will also be interrogated and he will be questioned also the day of judgment the prophet عليه الصلاة و سلام he told us that the person's legs will not move from his position the day of judgment until these questions are put to them and from those questions are what was it that you used to worship the person will be asked and the second question that he will be asked the day of judgment is what did you obey from the messages that were sent to you and those two questions the first question being what was it that you were worshiping what was it that you were worshiping and the second question being what did you obey from the messages that were sent to you is the two parts of the testimony of لا إله إلا الله ماذا كنت تعبود what was it that you were worshiping is what is لا إله إلا الله and the second question ماذا أجبتم المرسلين is what و أشد أن محمدا رسول الله so the person has to worship الله سبحانه وتعالى and they have to worship الله with sincerity and sincerity is that you do this عبادة this act of worship only for Allah سبحانه وتعالى you do not associate partners with Him in it as the poet said فحدر يا فطين sincerity is is to purify your heart is to clean your heart إخلاص لله صف القلب من إرادة سواه that you do not intend you do not want through this action you are doing other than الله سبحانه وتعالى and be cautious of being a person whose heart is tainted if a person gave you a cup and the cup was clean it was not clean and they told you to drink from it would you drink from it if the cup was dirty and then a person poured a cup of tea in there for you a cup of juice in there for you would you drink it the answer is no is because the utensils that we eat from or we drink from have to be clean prior to whatever is going to be put on it or put in it and the same applies with the person who is coming with the action before you think of doing anything good the heart has to be clean from everything and it has to be detached from everything else other than الله سبحانه وتعالى الله سبحانه وتعالى so you pray and you worship him alone and when you're worshipping him you do it with two pillars complete humiliation you humble yourself completely and you completely are in state of love for him سبحانه وتعالى as ابن القيم says in his نورية رباعدة he said رباعدة من الرق الذي يخولي قوله فبولوا برق النفسي والشيطاني that they ran away from that which they were created for the people were created to be slaves of who slaves of الله رباعدة من الرق الذي يخولي قوله they ran away for the servitude in which they were created for and they became slaves for who they are نفس الشيطان you're always going to be a slave of something regardless of whether you like it or not the best thing to be a slave for his who الله سبحانه وتعالى if you're not a slave to Allah you become a slave to what your own wings and desires and you worship yourself الله tells us in the Quran فإن لم يستجيبوا لك فعلم أنما يتريعون أهواءهم if they don't obey you on Muhammad and they don't follow your path then what you need to know is that they are what they are following desires أفرأيت من اتخد إلهه هوا he worships his own wings and desires and after a period of time because your heart is yearning for Allah and your heart wants Allah after a period of time as the person is dwelling in the desires and the person is in it for so long they become suicidal and they no longer want to live anymore and a lot of these people you see they commit suicide they no longer can live just like your body needs carbohydrates and it needs vitamin and it needs minerals so does the heart need its creator it needs who الله سبحانه وتعالى and if it doesn't have it just like the body dies if it's not given the amount of carbohydrates that it needs and the protein that it needs and the minerals that it needs the heart and the body will die and so will the heart as well so the first question that you are going to be asked is ماذا كنت تعبت who are you worshipping and the second question that you are going to be asked is ماذا اجبت المرسلين have you obeyed the messenger that was sent to you نبي الله محمد what did you obey him did you follow him in everything or were you a person who picked and chose when you wanted to take him if it was something you wanted then you followed him and if not you didn't you won't be able to answer this question ماذا كنت تعبود if you were worshipping besides Allah and you will not be able to answer this question which is ماذا اجبت المرسلين you won't be able to answer it if you haven't lived by it if you are not one who followed the Prophet عليه الصلاة والسلام you followed him in what معرفة him معرفة who he is وعملم and also follow him in action عليه الصلاة والسلام وطاعته in terms of obedience you know who he is if somebody asks you what's his name محمد what you know who he is and it's very sad you see many Muslims today but as officially it's one of the saddest things you find many Muslims who know artists rappers they know musicians in which they see as role models they know their ins and their outs he will tell you this football player how much he was bought for and how much he was sold for and what team he's been playing for and how many years he's been how many years he's been playing for that team he knows it but if you ask him about the Prophet عليه الصلاة والسلام he doesn't know about him is there really a strong answer for you the day of judgment regarding when you're asked ماذا أجبتم المرسلين also what you're going to be asked the day of judgment as the Quran tells us is وإنه لذكر لك وليقومك that the Quran is a dhikr أي شرف لك وليقومك أزيبنا الجليرا نا النام البغاوية نقرت بي منشن وإنه لذكر لك أي شرف لك the Quran is an honor for you محمد and it's a شرف and an honor for your people but then Allah what did he say وَسَوْفَةُسْ أَلُونَ and you're going to be asked about the day of judgment so the Quran is from the things that we're going to be asked the day of judgment we're going to be asked did you implement the Quran where you won who lived by the Quran and so if you become a person who lived by the Quran the Quran will become for you فَا يَقُونُوا حُجَّةً لَكَئِ will be a proof for you it's going to be a proof that's going to argue for you the day of judgment the time when you're in the most need or you've forsaken the rights of the Quran and so it becomes a what حُجَّةً عليك it becomes a proof against you the day of judgment you become a person who had boycotted the Quran وقال الرسول يا رب the prophet صلى الله عليه وسلم he says oh my lord إن قومي تخذوا هذا القرآن مهجورات that my people they boycotted the Quran that was sent to them and they turned away from it ابن القيم has a great book called الفوائد it's not his بداع الفوائد it's another kitab which is called الفوائد this is only one for you and in this book الفوائد by ابن القيم he speaks about what it means to boycott the Quran it means to boycott the Quran to boycott its knowledge you don't know what the Quran is saying to you if a person send you a text message on your phone one of the first things that you're going to try to do is understand what they're trying to say to you if you know it's an important job that you're looking for but it's in another language you will try to find somebody to translate it for you and you would want to know what message they are sending you because it's your job you're going to get the job or if they have declined you and said they're not going to give you the job the best book ever sent down is the Quran the best book you can ever find is the Quran and Allah is commanding you something in it and you don't want to know what it's in it the prosperity of this world and the hereafter is connected to it for you your joy and your happiness is connected to it and you abandoning and turning away from it is the misery and pain and agony in which you will endure for the rest of your life Allah says in the Quran ومن أعرض عن ذكري فإن له معيشة ضنكة ونحشره يوم القيامة أعمى قال رب لما حشرتني أعمى وقد كنت بصيرا قال كدالك أتدك آياتنا فنسيتها وكدالك اليوم تنسى and the person ومن أعرض عن ذكري the one who turns away from my Quran the remembrance of Allah the one who turns away from me which is the Quran فإن له معيشة ضنكة that person will live a very hard life in this world you're gonna live a very hard life and on the day of judgment the same way you turned a blind eye towards the Quran you'll be resurrected literally blind you turned a blind eye to the Quran you gave no importance to it no consideration so the day of judgment الجزاء من جلس العمل the way and the thing you deserve is for you to what it is for you to be resurrected and brought back to life blind so the person says قال رب ليما حشرتني أعمى وقد كنت بصيرا oh my lord why have you resurrected me why have you brought me back to life blind when I was a person in the world who could see and then Allah says قال كدا قال كدا لك أتتك آياتنا like this our verses came to you you had eyes you could see our verses came to you and you turned away from it you chose to not look at it you chose to not contemplate over it you chose not to ponder over it وكدا لك اليوم تنسى and today you will be abandoned and left but the one who lives by the Quran علما وعملا واعتقادة he learns about the Quran he implements the Quran and follows the instruction that the Quran gives him and he also believes in the Quran he has unwavering conviction in the promises the stories and information in the Quran he has unwavering conviction that person is going to live a good life in this world and here after that waits him is a good life Allah says إنهم أجرهم بيحسن ما كانوا يعملون this life you are going to live a good life living a good life doesn't necessarily mean that you are rich you might be قليل اليدي you might have little in your hand and Allah سبحانه وتعالى what he gives you in this world is not an indication that he loves you or hates you what Allah gives you in this world in terms of wealth is no way an indication that Allah loves you no if Allah doesn't give you something it does not indicate that Allah hates you because in this world Allah gives to who he loves and he gives to who he doesn't love and he says it in the Quran إعطاء الدنيوي to gain something in this world has no relationship and it has no indication that Allah loves you no does it show that Allah hates you you see a believer who has no children and a disbeliever who has so many kids and this believer has been looking for kids 20-30 years in his marriage and he's never got it and this disbeliever as soon as he gets married his wife is pregnant but the giving and the prevention is all based on love and hate the day of judgment as Allah said in the ayah that I recited وَالخِرَةُ عِنْ دَرَبِّكَ الْمُتَّقِينَ the hereafter is only for the believers the ones who are going to find prosperity and good in the hereafter is what the believers so just because you see and this is something that happens to us Muslims we see a person who is blessed in this world driving a good car he's he's wealthy, he's well-off and it makes us leave what is most honorable for us our capital you're a soul man you're a dean, you're a religion you would leave it for something Allah gave to this person in this dunya when in reality as I said it has no indication that Allah loves this person or hates them so what you're going to be asked brothers is the Quran many of us the Quran has just become something we decorate on our house how many people have you visited whose houses have ayatul kursi on the wall and if you ask them read ayatul kursi from the top of your head they have no knowledge of it no do they know it they've never memorized it but it's decorated on the wall the Quran wasn't sent for that the Quran was sent for it to be in the hearts Allah says in the Quran about the Quran who went down with this as a shield from the that the Quran is verses that was sent down to be in the hearts of the believers the Quran was not sent down so it can be stuck on walls it's meant to be in the heart look at the Prophet when he recitation the ayat and he started to read مع جيبريل when the Quran first came down what did Allah say to him لا تحرق به لسانك لتعجل به إن علينا جمعه وقرآن what does Allah mean that we are going to gather it for you محمد meaning in your heart there's no need for you to have to read with جيبريل the whole Quran we're going to place it what we're going to place it in your heart so what does it mean that we have to come with the Quran as I said first of all knowledge of the Quran and we know it we memorize it we try to give importance to the memorization of the Quran and the second is the meaning and what is in it because the Quran was not sent down for you to only read it and this is a problem that many Muslims face يقيمون حروفة they establish its wordings ويضيعون حدودة but they forsake its boundaries you see a young kid in this message sometimes he's memorized the Quran he's half and he's in the toilet urinating standing up this is a problem this is a problem because the Quran was not sent down for you to just read it الله says in many places أفلا يتدبرون القرآن أم على قلوب أقفالها أفلا يتدبرون القرآن ولو كان من عند غير الله لو جدوا فيه اختلاف كثيرة كتاب انزلناه إليكم مبارك ليتدبروا آياتي كل of those places Allah is telling us that the Quran was sent down for you to what to contemplate and ponder over it and to contemplate and ponder over the Quran it means that you understand what it's instructing you with you can't ponder over something you don't understand ولذلك عمر بلمرة إن أبي حاتب he brings it in his تفسير in صورة العنكبوت regarding the verse وتلك الأمثال نضربها وتلك الأمثال نضربها للناس وما يعقلها إلا العالمون عمر بلمرة إذا تابعي he said if I come across a verse in the Quran and I don't understand the meaning in it بكيتو على نفسي I cry on myself the reason is because Allah says واتلك الأمثال here are parables examples that we give you وما يعقلها and no one truly digest it and understands it وما يعقلها إلا العالمون except those who have knowledge and when you don't understand the Quran it shows you are the opposite of a person of knowledge you're an ignorant individual the most valuable book you don't even know it I ask every one of you who today is the iPhone if you go to the settings in iPhone and you look at the apps that you use on your iPhone they've got this process that you can do which is to go through your settings and you can look at every single app how much time you spent on it your WhatsApp your Facebook your Twitter your Instagram you can find out how many percentage has been used from your phone they'll tell you how many minutes that you've been using it for check how long you've spent on your Quran app I can assure you you'll be shocked how much time you spend on Twitter how much time that you spend on what Instagram how much time that you spend on your WhatsApp and how much you spend when it comes to the book of Allah سبحانه وتعالى والله if the Muslims today the way they use their phone and the way they keep their phone so close to them if they done that with the book of Allah I can assure you you will not be in the situation that we are in today فمن ضيع القرآن anyone who forsakes the Quran فليما سواه أضع he is verily going to forsake everything else what value do you hold what honor do you have if you forsake and what the thing that Allah said in it is your honor وإنه لذكر لك اي شرف لك ولي قومي this is where your honor lies but you've chosen to what you've chosen to turn away from it so you'll be asked about the Quran the day of judgment ولذلك I think it was مجاهي ديبنو جبرين when he came to the ayah يتلونه حق تلاوتي he said يعملونه يعملون بالقرآن حق عمله that they're going to implement the Quran the way it deserves to be implemented and مجاهي ديبنو جبرين is the man سفيان الثوري who said جاءك تفسير مجاهد فحسبو كبي if the Tafseer of Mujahid comes to you that's enough you don't need to look for anyone else's Tafseer so you'll be asked about that the Quran the day of judgment وإنه لذكر لك ولي قوميك and so for to سألونه you're going to be asked the day of judgment ألمام الطابراني narrated in his معجم من حريتي أنسل that the prophet told us that the first thing that you're going to be asked another narration طابراني's wedding is أول ما يسأل عنه العبد يوم القيامة the first thing that the person will be asked about the day of judgment when he comes is صلاة to who his prayer that's the first thing you're going to be asked فَيُنضَرُ فِيهَا it will be looked into your affairs regarding the prayer how are you as an individual when it comes to the prayer فَيُنصَلَحَد if you pass the test and you make it through with your prayers and you come with the amount that is needed from you فَقَدْ أَفْ لَحَدَ and you have received and gained success and prosperity وَإِنْ فَسَدَدْ if your prayer is short and you haven't meet you have not met the requirement and you've not met the amount that was needed from you فَقَدْ خَابَ وَخَسِرْ that you have truly lost and that day you're in a state of destruction and it's the only day I say brothers that it really matters whether you pass or you fail every other exam that you've gone through before this can always be redone but this day as they say it's crying over spilled milk what has happened has happened is nothing you can do so it's now for you to think about how you are with your prayer the scholars are differing فيما بينهم between themselves طائفة and a group of scholars are saying that the person who leaves the prayer is a disbeliever and leaves the fold of Islam this is a statement transmitted from إمام أحمد رواية العنو إسحاكم بنراهوية أما إسحاكم بنراهوية however you want to say it أبعو بيت قاسبن سلام and others they held that opinion that the person who leaves the fold of Islam he narrates this from that the Sahabah this is كالصحابة لا يرون شيء أن تركوا كفر غير صلا يسر that the Sahabah never used to see something that if a person left they will become a disbeliever other than the prayer عبدوليم الشقيق he brings that from them and he's a tabi' so you're in a situation where some of the scholars whether it is a correct view or not the point is it's a dangerous matter it is the only action that the difference regarding whether you become a disbeliever or not is very strong it's something that should scare you that the day of judgment the prophet said in the Harith the person who leaves the prayer the day of judgment يبعثوا مع قارونة وهامالة وأبيب الخلف the one who left the prayer he will come the day of judgment he has no حبجة no burhan no proof no evidences and he will be resurrected with فرعون قارون هامال وأبيب الخلف the prophet said in the Harith عليه الصلاة والسلام you've been resurrected with صناديب the heads of kufr because you left the prayer you are like a shaytan who refused to prostrate to his lord when he commanded him he refused to prostrate to his lord and you as Imam Ahmed said this you've refused to prostrate to your lord you left prostrating to him سبحانه وتعالى so you'll be asked about your prayer the day of judgment and guess what brothers it is the first thing you'll be asked about the day of judgment the first question there's nothing else أول ما يسألوا عنه عبد اليوم القيامة it is the first thing that the slave will be asked about the day of judgment is his prayer if you get your prayer in line and your prayers are good then you make it through everything else brothers and sisters and if your prayer is short and you have not met the required amount from you فقد خاب وخصر destruction and losses for you that day so you'll be asked about it the day of judgment what you're also going to be asked brothers is your age and your life what you spent and Imam اضطبر اتلمي دي نريت عبد اليوم المسعود رضي الله تعالى عنه that the prophet said لا تزولو قاعدة موبنو عدمة that a person's legs will not move يوم القيامة it is the day of judgment من عين ربي in front of his lord besides his lord the person's legs will not move from his position that day حتى يسأل عن خمسن until he's asked about 5 questions these are 5 questions that you're going to be asked the first of those 5 is عن عمره your age فيما افناء what did you spend your age with you've been living for 30 years 20 years الله gave you a chance to live in this world what did you do for those 20 years how have you spent it وَزِئْ لَهُ الْوَلَعِ were you laughing and you playing or was it جد and اجتهاد you were striving you were working hard you'll be asked about it seconds you'll be asked and the beauty about it all is that Allah سبحانه وتعالى every time he does something to remind you that your time is close and from the things that Allah does سبحانه وتعالى is that he brings white hair into your beard or your head to tell you they're coming closer every time بس الله سلم القرآن أولم نعملكم ما يتذكر فيه من تذكر وجاءكم النبي عبدالله عباسه دماليل is the white beard the warner came to you the white hair is the warner that came to tell you your time is over you're coming there was a time when your white your beard was black your hair was black and now you're starting to see don't say I'm young don't say no this hair is just stress only this is you fooling yourself and lying to yourself the truth is you're closer and closer to your grave people are celebrating the new years that's a year gone by that you're closer to your grave are you celebrating your time closer to the grave or should it be something you're scared of people celebrate their birthdays what are you going to celebrate that you're getting closer to your grave that time has gone by so you're going to be asked the day of Jalmad الله سبحانه وتعالى he says to you did we not give you time to live did we not give you an age ما يتذكر فيه من تذكر did we not give you a time for you to ponder to say to yourself you know what I've misbehaved for a portion of my life 5 years I was misbehaving 10 years I was misbehaving now I need to be sensible now I need to be appropriate now I need to be enlightened and then you still didn't and then Allah sent a warner to you and you know what's up the warner comes in different forms and shapes sometimes it's the white bin even sometimes Fulan do you remember Fulan yeah he's gone he died and what about Fulan he's died and Fulan he died all of those is a sign for you the angel is telling you that I'm coming closer and closer to you the people you knew I've knocked them down I've taken them they are no longer alive I am now heading toward you they say even though it may not be a reality a story but the meaning is correct that a man the angel of death came to him when the angel of death came to him he said to the angel of death how dare you just walk up and come to me like this without telling me or giving me any signs that you're coming get away from me and tell me when you're coming the angel of death said I promise a period of time went by and so the angel of death came back to the man when it came to visit him and it came to see him he said to the angel of death again you gotta come didn't I tell you to when you're coming you give me a sign that you're coming you don't just walk up on me like that he said yes I gave you many signs he said what signs have you given me he said where's your neighbour on the left he said he's dead what about the one on the right he said he's dead dead he said where's your wife she's dead where's your oldest son he's dead all of those people I took down they were your shields in front of you now that they are gone who else do you want me to go for you're the only person left and then when other people die and you take people to the graves this person has got he's received what it was promised for him but the true lesson lies in for you it's a wake up call for you it's you who has to think here and then the hadith mentions you're going to be asked look at the hadith it mentions that you're going to be asked about your life and then within your life you get asked specifically your shabbat you know why brothers why is it شباب is mentioned independent from عن عمري فيما أبلا عن عمري فيما أفلا why is shabab specifically mentioned the reason is because مرحلة الشباب two khasla two characteristics have gathered in you that makes it a greater reason for you to be asked what is it القوة وصحة you have strength and you have health the third khasla is that you're going to be asked to it is al faraq three times and the prophet said in the hadith المؤمن قوي خير وأحبه إلى الله من المؤمن الضعيف وفي كل خير يحبس على ما ينفعك واستعم بالله ولا تعجز أو فما قال عليه الصلاة والسلام that the strong believer is more beloved to Allah than what the weak believer but both of them are good what does it mean المؤمن القوي خير وأحبه إلى الله من المؤمن الضعيف عصم الدعولة ماده يسأل المؤمن القوي here means the shab why is it because he is the one who is physical and his iman is strong نعمتان مغبون مغبون فيهما كثيرا من الناس two blessings many people are heedless about الصحة والفراغ health and free time those three قوة صحة and فراغ three blessings they all combine inside the youth look at you right now brothers you left your house walked out you didn't have to explain yourself to anybody you just had the time to come over and you could sit and just listen to a lecture go when you want to go wake up whatever time you want to wake up you've got that free time you've got health look at your parents they keep complaining about their back their arm, their shoulder, their this you don't complain about that you have قوة strength all of that has made it more of a reason for you to be asked about that مرحان that age واللهي brothers it's a blessing الله has given you قوة الشراء ولذلك المساعدة who wanted to marry or the father the righteous man who wanted to marry his daughter of تنبي اللهي موسى some people they say شعب لكن الله يصحب صحر مدين some people say شعب but it's not authentically transmitted that is right the point is that when he came تنبي اللهي نبي اللهي موسى when he came to this righteous man the daughter what did she say to her father she said يا أبا تستعجله فاذا حاية موسى إن خير من استعجل قوي الأمين فاذا حاية موسى why he's a coward how is he a coward لأن نبي اللهي موسى was what شعب he was a youth and he was a reliable individual are we all together brothers so مرحلة الشباب is a blessing it's the time in your life where all of the good is in you and that's why you will deserve the day of judgment to receive the shade of Allah because with the strength with the free time and with the health there's one thing that covers all of that and makes you not benefit from it which is a شهور and if the person gains control over these desires and he uses those three advantages that he has in the obedience of Allah the day of judgment he will receive a shade are we all together that's why the prophet said سبع يوضلهم الله في ظلي يوم لا ظل إلا ظل 7 الله is going to give them a shade the day when there is no shade from them is who شاب نشأ في ظاعت الله who grew up and was nurtured and was upright in your being سبحانه وتعالى are we all together brothers so you're going to be asked the day of judgment about this age that you have this مرحلة الشباب you're going to be questioned about it and benefit from it brothers benefit from this also من أين اكتسبه وفي معنفقه your money you're going to all be asked where did you get this money from do you get it from drugs do you get it from alcohol where did you earn this money from who gave it to you والله penny will be questioned the day of judgment not a pound not 5 pounds you're going to be questioned pennies pennies where did this penny come from and where did you spend it where did you when you got حلال money you're going to be asked the day of judgment where did you spend it it is sad that we've reached a level that the minds cannot even comprehend the other day I go through my local area I try to go to the youths in where they are I try to go to them where they are where they sit if I see a group of Muslims Somalis whatever they may be sitting together in a place I always try to approach them whether it be in the park whether it be on the corner of the streets I try to go to them and I try to have a dialogue and discussion with them what hurts the most and breaks the heart and brings them an old man to tears is when you see the young kids some of them as young as 16-17 والله is some even younger than that who are drinking alcohol back many years ago when they first started doing this they used to hide it they used to carry that brown bag hide it or they would pour it inside a Coca-Cola bag a Coca-Cola can or whatever a bottle or a change and you think they're drinking Coca-Cola right now they do it right in your face they don't hide it and the kind of alcohol that they drink is the worst alcohol the white people the kuffar who don't believe in Allah and all the day of judgment is the one that they have one sip of the two our young kids they've got a bottle and drink it like it's water they drink it like it's water do you not think that the day of judgment you're going to be asked don't you think you're going to be questioned all of this which you're taking it's a sad reality online it's so sad that subhanAllah in social media you see Twitter Instagram Facebook them coming out recording themselves doing this they put it on social media I know their father Fulan and Allan that's their father he's in the front row in the street or he's praying in the street it's a big problem the day of judgment is questions people will be asked money some kids are buying drugs they're making money from drugs and they're paying their parents rent they're taking that money from their kids and the child thinks in his mind and heart and he's doing something for his parents so when you ask him what are you doing he's like my mom needs me man my dad needs my mom's a single mother I give her money so the money that's taken from Haram it's imported what it's imported into house food وماله منينك تسبح your wealth where did you get it from and where did you spend it وماذا عميلة فيما علم وماذا عميلة and the knowledge that you've attained have implemented it that knowledge you have you will be questioned the day of judgment regarding it also what you're going to be asked the day of judgment is your seeing your hearing your tongue your heart you're going to be asked about all of them الله says in the Quran ولا تنقف ما ليس لك بيعلم إن السمعة والبصرة والفؤادة كل ذلك كان عنه مسؤولة كل أولئك كان عنه مسؤولة ولا تنقف ما ليس لك بيعلم إن السمعة والبصرة والفؤادة كل أولئك كان عنه مسؤولة all of them you're going to be questioned what did you look at if you look at the first problem that everybody goes through which they can't stop the chain of problems that come from it's one of these what you looked at stop looking at what you're looking at also what you're listening to the Prophet عليه الصلاة والسلام when he prohibited music and he called it صوتان ملعونان two types of sound are passed you have to realize it was a music far better than the music that we're seeing today that music which the Prophet referred to as حران and he said it's a cursed music it was at the Prophet's time imagine this music today where if you hear the lyrics the words insults insults filthy language the videos that come with it the matter becomes even worse والدالك عبد الله المشعود in seven إِنَّ الْغِنَ يُبِتُوا فِي القَلْبِ النِّفَقِ that music it's what brings in the heart hypocrisy that a person lives double life this brother that you know is a domestic praying with the people fasting, doing kheb but when he goes outside he's doing something else he lives a double life on social media he's something else but in the real world he's something else do you know what's making him do that music والله I have not seen anyone who listened to music except he is as Allah said about them in the Qur'an about them what did he say he said about them لا يأتون الصلاة إلا وهو they don't come to the prayer except that they're lazy the brothers look at the prayer the youngsters listen to music the reason why they feel lazy is because of music because hypocrisy enters your heart it's impossible you know what music is called it's the ruqi of shaitan and the Qur'an which is the ruqi of Allah they both can enter one heart can they can fire and water be in the same heart at the same time simultaneously أبقى الله الله refuse that one has to be God and the other one has to go follow this up and watch what I say brothers إبن القيم says something powerful he says music is what made girls who are chastis take their hijabs off إبن القيم says that and come on the street and do prostitution when you say prostitution I don't mean she makes money out of it she becomes a woman who every guy sleep with her the same with the guy إبن القيم said a society whose zina increases in and homosexuality increases in is when music is brought to them homosexuality increases in are we all together brothers and zina increases in a society where what I'm saying the music إبن القيم is talking about is nothing like the one we're talking about today always keep that in mind always keep that in mind it's much worse now now they clearly telling you do this zina the rap is telling you I do this zina I did this to this woman and he's telling you rather some of the people who've come into the scene these artists some of them they came and they became famous to what زينا فلانا and فلان only became known because of a video or a sex tape that leaked the Muslim girl فاطمة زهرة آمينة عيشة that you see is looking up to this fat girl this woman who became famous through what a sex video look how much ولذلك الله سلم القرآن وستفزز من استطاعت منهم بصوتك وأدلب عليهم بخيلك ورجلك وشاركهم في الأموال والأولاد وعيدهم وغايةهم الشيطان بلا مرواء الله tells Iblis when he kicked him out of jannah and he told him to lean in jannah الله says to him وستفز من استطاعت منهم بصوتك any individual you want to use your voice to misguide them مفاصرين they said that the voice that شيطان is going to use to misguide the people is music that's the voice he's using what you're hearing is that when you stop listening to music and you stop letting your ears hear it is when your heart is going to realize that you feel alive you're going to feel alive and that's why the person who listens to music on the time of the messenger is cast صوتاني ملعوناني two types of people are cast two sounds are cast صوتون اندل نعمة a sot which is music when the person is enjoying themselves and the next one is brothers صوتون a sot when the person is going through hardship, calamity that the person does but in that case the prophet told us that the people who listen to music and our musicians and rappers and our singers, Allah is going to deform them He's going to make them into pigs and monkeys look at it today look at the rappers that the people are watching today they become animals recently one guy came out with his name, remind me he made a track with one music that he made he became platinum what was it again? just one you know it don't act like companions yeah panda the music was called panda or his name was called panda is it panda? it's panda is panda right? don't worry your guys are not here and they are not going to say anything if you brothers pay attention to this if you look at him as a person brothers show me as a person just look at him والله I will show the uncles إن شاء الله he is deformed he is mentally tapped you will never think to yourself that this person is والله he is mental and he became number one this is what they look up to the thing is a joke the reality is that it's a joke not even those who listen to understand what the guy is saying they don't know what he is saying والله they listen to music they don't know what he is saying he screams no one knows what his lyrics are and what he is saying are my lying brothers be honest yeah he had to do an interview to tell the people the logic behind his music and what he was trying to say and he said can I are my lying brothers that's the reality it's reached that level of حبكة that it's become that sad and that pro so the day of the day what you listen to what you watch and what you listen to is the channel that goes towards your heart what you see is what goes towards your heart are you with me brothers والذلك the شريعة told us to lower our gaze and it told us what we can listen to and what we can't listen to because all of these things are going towards your heart and once it goes towards your heart والفرجوا صدقوا ذلك أو يكدبوا the person listen to music the lyrics coming in he sees these things he becomes desensitized and that's it all he now looks for is fulfilling his شهوة and his desires one of the things that you are going to be asked the day of judgment and it's the final one is كلكم راعين وكلكم مسؤولون عرعيتي everybody is going to be asked about the responsibility that they've been placed over them fathers are going to be asked about their children fathers are going to be asked about their children fathers mothers are going to be asked والله if you take a person and you tie them from the back and you throw them into the sea and then you say to them you tie a person from the back and you tie them from the legs and then you say to them be careful don't let the water touch you is that possible and you throw them into the sea the parents who brought their children into this society and this environment who are telling their children you need to behave yourself this method this example is what relies on the reality are we all together when you throw your child into this society and then you say oh don't act like Chris or Michael be like Abu Bakr or Umar it's very hard to say that unless you've changed the whole atmosphere for him and you've created a new atmosphere for him are we all together and how could that be done it can be done that's what Allah SWT he said to Musa and Haroon وجعلوا بيوتكم قبل what's قبل it means a place Allah has remembered make your houses a place Allah has remembered imagine your child is outside at school 6 hours as a child little kid little kid and the child 6 hours he spends outside he comes home you don't even talk to him you say eat sleep go wake up go to school again wake up 10 years go by you really think this is your child physically but mentally who is what now when social workers come or one day my dad used to say a lot he says a lot he used to say why are you upset when the social services come to take your kids they raise the child they nurture the child it's their child they educated him they paid for his education they may have even paid for his food and his housing they've just taken their child back the child is only yours by name it's a problem it's a reality are we all together so one of the things I believe my father my father he did was very good which is every day before we went to school before we left the house before we left we prayed one of my brothers would lead my father would pray behind us as soon as he finishes my mum would go into the kitchen and she would prepare the food and my dad would sit down and he would talk to us until the food gets ready we eat then we dress up we go to school who has from the first stage before I go to school fresh when the mind is who's taking the persons who's taking the mind my father he's putting the first information into my heart and my mind as soon as I woke up I went together and then as soon as I come from school I'm always waiting for him so he's pouring out the Quran teacher's waiting for me at home he's going to pour everything out which was wrong and he's going to pour in my head everything that's what that's right in a society if you take care of your child like that inshallah they've spent 6 hours on your child you need to spend 12 hours are we all together but you bring a 52 inch plasma television one thing we never had in our house never was television we never ever had television in our houses my dad never brought television to the house 6 hours they took you and then another inside the house they're going to take you again are we all together what is it called vision they're programming you you can't think for yourself the whole point is that they have control over you do you not see that this post-colonial media outlet that we have that the media only let out everything around us it's perpetrating one concept it's only one thing that's been said to us BBC Muslims are like this Muslims do this Islam is a big religion why is those 4 questions what do you believe about women's rights what do you guys believe about this 4 questions all the time are we all together think about it are we all together the whole why is my religion restricted to 4 questions 5 questions what do you guys always want to ask to show you that they have the ability to do that to be programmed are we all together before they bring you into the television or they bring you on the radio I listen to LBC sometimes and sometimes they talk about topics which are very tough so then a person calls in and he wants to speak on the LBC and wants to convey his message first of all you've lost from the get go because before they let you in they'll talk about ISIS okay we have on the studio what happened your speaker is very low your voice is very low the studio of voice is very high are we all together so everything is about programming the people and the message is only being directed towards one way so the way that we can always win brothers is that we have to go back to Allah and know what the topic today was about and the I that we started which is and those were some points that I could think of today I went very long you know why? because we missed last lesson so we made it one hour today 50 30 or 30 right an hour 60 minutes right so it's 30 or 30 if I said anything wrong if I said anything wrong if I said anything wrong if I said anything wrong


Hi and welcome to the session. I am Deepika here. Let's discuss the question whether the following is an AP. If they form an AP, find the common difference E and write three more terms 0, minus 4, minus 8, minus 12 and so on. We know that in an AP every succeeding term is obtained by adding D to the preceding term. So D found by subtracting any term from its succeeding term that is a term which immediately follows it should be same for an AP. So let's start the solution. Our given list of numbers is 0, minus 4, minus 8, minus 12 and so on. We have say 1 equal to minus 4 minus 0 which is equal to minus 4. Again a3 minus a2 is equal to minus 8, minus of minus 4 that is plus 4 which is equal to minus 4 plus a3 is equal to minus 12 plus 8 which is equal to minus 4 plus 1 plus ak is the given list of numbers given list of numbers common difference D is equal to minus 4. Now the next three terms are minus 12 plus D that is minus 4 which is equal to minus 16 and minus 16 plus D is minus 20 and minus 20 plus minus 4 is equal to minus 24. Our answer for the above question is yes the given list of numbers forms an AP with D is equal to minus 4 and the next three terms are minus 16 minus 20 and minus 24. I hope the question is clear to you.


So that's exactly what I heard in the video, but pretty much stay where you put it too. So I Don't know weird Shea bear here It's more paranormal stuff. I don't know if you guys noticed or not, but in the last paranormal video When I was sitting here talking that door right behind me opened up and you can actually hear the click of the door handle Turning which I'll loop that for you a couple times and then I'll play the unedited Version of it the raw footage that I recorded right here on this camera and We'll see what you guys Think about that little story night for last I was in the garage smoking a cigarette and Little story on that as you know, I know Little story on that as little story on that as hey guys shave every 1,000 here Today I've got something Else that I'm going to kind of put under the paranormal stuff Little story night for last I was in the garage smoking a cigarette and Little story on that as you know, I don't smoke in the garage So there I don't smoke in the house. I smoke in the garage So the other night, you know when when I go in smoke I just kind of watching security cameras. Maybe see if I can see animals, you know, I've seen I've seen armadillos and stuff in there So I just kind of watch and make sure because I'm up late. I don't sleep a lot so just make sure the house is okay and The other night was watching I caught something on camera too that I'm going to put in here for you and then I'll narrate through The camera itself when I show that footage, but I had to share this with you guys. So and It's just Interesting me. I mean, I don't hold a lot of stock in the orbs. We all know that but This is pretty cool. So take a look at it and see what you think See, that's pretty interesting. So, you know, let me know in the comments below what you guys think it is I mean like you seen it it definitely wasn't a bug. So I don't know what it was so all right guys Hope everybody enjoys your weekend coming up and remember comment rate and subscribe and Click the click the bell icon so you can get notified of when I upload my next videos So thanks again guys. Thanks for watching. I appreciate it. Shea bearer the myth a man legend. I'm gone for now Bye-bye guys. Take care So, you know, that's That's pretty compelling guys Excuse me Snickers the cat was over here on the bed beside me and Bruno was outside on his leash and I always closed the door because air conditioner so loud I didn't notice it until Monkey got home. She wasn't here. She was at work. So when monkey got home She likes to watch my videos. So we watched it and I caught it. I said, no, no, no, no Wait a minute. So I backed it up. She was like, what was she was looking over here at the You know right there she was you know looking at what's going on behind me, you know and So she had noticed it and I played again. So watch the door. So that's it's pretty disturbing My niece noticed it But I didn't notice it until I Was watching it with her because I didn't I don't always play every clip all the way through If I'm not going to be like doing much editing in that clip I really have no reason to so I didn't notice it through editing, but I did afterwards. So Here it is again, and I want to say thanks for watching guys. I appreciate it. Shea bearer the myth man a legend I'm out for now. Take another look at this and see what you think.


The floor may not be a robot. Igaonotarabe was a Japanese signal hack event used to be posted and told on image boards with the purpose of scaring people, being the most popular case during the mid-2000s. All this event can be summarized and read below. During a broadcast from TV hack Ido on May 14, 2005, thousands and thousands of TVs were showing residents the same content as well, news, sports and everything that would be normal that day. Everything was okay until the problem started at 6.31pm, when the TVs gradually went dark. At first, the residents thought it was just a signal failure, but something more disturbing would happen after a simple signal failure. After the TVs went strangely black, a man with an extremely black face appeared on a webcam, showing only his smile. The residents became frightened and uncomfortable. At a point they started hallucinating and becoming paranoid in their brains, and then committed suicide. The event spread throughout the Japanese internet. After an anonymous Shiteraba user commented on the case that happened to his older sister, who was supposedly one of the victims. And so, the Shiteraba thread is reposted on feudal channel, two channel, BBS Pink and others, with the description saying, translated, the smiling TV, and then using the threads link until September 2005, when thousands of reposts has been deleted for unknown reasons. And still nowadays, the case has never been solved.


Okay. Thank you very much for coming. And this is joint work with Morita and Sina, both from Georgia Tech. So let's start by seeing what circuit switching is. So the motivation for this comes from switching or routing in data centers. And you'll see in a second why there's like the, either it's optical or wireless, for example. But on a high level, what we have here is a collection of senders and a collection of receivers, right? So these are the senders and these are the receivers. And at any given time, we want it, we want actually to decide which sender sends information to which receiver, right? And each receiver can receive information from at most a single sender, and each sender can send information to at most a single receiver. So essentially what we're looking for is a matching, right? So this matching, for example, dictates which sender sends information to which receiver. And we keep this matching for some duration of time. And then at some point, we want to switch to a different matching, okay? Which dictates the different fronting in the data center. But what happens in modern, let's say, data centers and networks, is that if you use optical methods or wireless methods, this switching actually incurs a cost. And this cost is actually cost, what we call the switching cost, which means that there is some fixed amount of time where nothing can be routed or essentially nothing can be sent. And the goal, the high level goal in circuit switching is actually find a sequence of matchings that maximizes it, maximizes the total data that you can send in a given fixed time interval, okay? So let's see what is the formal definition of the problem.  We also get a demand matrix. So for every sender I and receiver J, DIJ denotes how much data needs to be sent from sender I to receiver J. We also get the size of the interval or what we call the time window, which is W. And we also get the fixed switching cost. So every time we change a matching, there's an interval of delta time that nothing can be sent in that time. So before we formally define the objective, let's see what the solution is, or in other words, what is the schedule in this case. So this is our time window from 0 to W. And let's say we first choose matching M1, you can see it here, and we wish to send data over this matching for duration of alpha one time. And once we're done with that, we need to pay the fixed switching cost or delta time. And then we can choose any other matching we like. Let's say for example M2, so which is a different matching. And let's say we wish to keep this matching, transmitting over this matching for a duration of alpha two. And then again we need to pay the fixed delta switching cost, choose a different matching, pay delta, and so on and on. But we cannot go beyond the interval or W time on total. So this is what the schedule is. So in other words, the schedule is just a collection of pairs, or you might call these configurations. And a pair is a matching, let's say ML, and a duration alpha L. And a matching, sorry, a schedule is feasible if the total durations plus the time it takes to switch doesn't go beyond W. So this is when a schedule is called feasible. And the goal is to maximize the total transmitted data. So think of a specific edge, let's say you can think of AMD as a complete bipartite graph. So let's say edge ij. So this tells you the total duration that are matchings that contain the specific edge were chosen, right? So this is the total alpha L of all matchings ML that contain the specific edge. But it can happen that for some edges this duration is more than the demand. So in this case we actually cap the total transmitted data by the demand because we cannot send over a specific edge more than the demand. So this is essentially a truncated linear function. And this is our goal. One interesting point to note is that this function, if you think of it as a set function over all these configurations, is actually a similar function, a monotone similar function. So what is known about this problem? So first of all, Leon Humdy actually proved that this problem is NP-hard. And they actually proved that the different problem is NP-hard. They proved that the problem of minimizing the total time that is needed in order to satisfy all the demands, that is NP-hard. But once that problem is NP-hard, this immediately implies that our maximization problem is NP-hard. Otherwise, if this is in P, then we can solve that problem as well. So we know that probably we cannot get an exact solution. So recently, Borja, Alizade and Vishwanath had several interesting observations about the maximization problem. The first observation, as some of you might have guessed already, is that this problem is actually a special case or it's captured by what is called the samolar knapsack problem. So in the samolar knapsack problem, we're giving a universe of elements and a monotone samolar function over the elements and sizes to each of the elements. And the goal is to pack elements whose total size doesn't go beyond the size of the knapsack and maximizes the samolar function. And in our case, all these configurations are actually the elements. So this is the first observation they had. And the second observation they had, that if all the demands are very small, and by small, I mean they're at most, let's say, an epsilon fraction of the entire interval, then the greedy algorithm gives you almost one minus one over e approximation. And this is kind of interesting because the greedy algorithm actually doesn't work for the samolar and knapsack problem. But here, they had the extra assumption that actually the demands are very, very small. Okay? So another thing that will be important to today's talk is what is known in general for the samolar knapsack problem. So this problem, to some extent, has been resolved. All these, let's say, four algorithms that are written here essentially give you a tight one minus one over e approximation. So there's a classic work of a cooler most and all, which was immediately extended afterwards by Sviridenko, that actually showed that if you enumerate, let's say, over most three elements in the ground set, and then extend that, greedily, then this gives you a tight approximation of one minus one over e. This line of works, and actually there are more works, but these are just, let's say, the more well-known works in this area of Badmidiur, Vondrak, and Neneguyen, they aim to find test algorithms that also provide a tight approximation of one minus one over e. The problem with all these, at least in our setting, is that all these algorithms, including these test ones, require some sort of enumeration over elements from the ground set, or in other words, they need to know at least one or two elements that are in the optimal solution. So what can we show about the problem? So we can show that for every constant epsilon, there's a polytime algorithm that gives you an approximation of one minus one over e minus epsilon for the circuit switch problem. Again, for now, we're only dealing with the offline case. So what is our approach? So first, let's start with what is wrong with using or what is hard with using the known techniques. So the first difficulty I mentioned is that if you look at some of our knapsack, then the ground set has exponential size, even if you enumerate over all the durations, because the number of matchings, this is a complete bipartite graph, is exponential. So all of these algorithms on all their algorithmic, let's say, techniques actually fail, because if we need to guess or enumerate at least one element that is not or two, this cannot be done in polytime. The second approach is that, okay, someone can say, okay, this is some other knapsack, but we have a very specific some other function. It's not a general one. And the function inside just truncated linear, right? So for every edge, we have a linear function and we truncate it at the demand. So maybe we can write an LP around this directly, but at least there are two natural ways of formulating linear program relaxations for the offline problem and both have an unbounded integrated gap. And the reason is that both of these relaxations can actually cheat by smearing the solution and actually ignoring delta, the switching cost. Because without the switching cost, if delta is zero, then the problem is easy. So the first relaxation actually finds a distribution over matching for every time step. And the other one is more directly related to the knapsack problem where we choose these configurations that satisfy the knapsack constraint, meaning that the total, the sum of the alpha plus delta for all these, the chosen configuration times the CW, but all of these actually fail. So what we do is actually look at how large the switching cost is. So if the switching cost is small, let's say not more than an epsilon fraction of the entire window, we can show that greedy, the simple greedy can be analyzed in a better way than it usually is and we can get the required approximation. And if the switching cost is large, more than an epsilon fraction of the window, then in this case, the first thing you can note is that the number of matchings is at most one of our epsilon, right, the number of configurations you choose and epsilon is fixed. So there are a fixed number of matchings. This is not enough because even if we know that the optimal solution has a fixed number of matchings, we still cannot enumerate over those because there's an exponential number of matchings. But instead we show that you can actually enumerate over the durations of the matchings of the configurations. And once you know the durations, then the problem becomes very easy to tackle. Okay, so I'll show you these two ingredients. So what happens when the switching cost is small, let's say it's most epsilon fraction of the entire time window. So what is the, so I said that the greedy can be analyzed better in this case. So what is greedy here? So we start with an empty solution, there are no pairs we chose. So as long as we did not exceed that time, we choose the best element and an element is a pair of a matching and a duration. So how much do we gain if we choose M alpha? So for every edge in the matching, we gain the duration, but we need to cap it at how much demand is still remains for that edge, right? We cannot exceed the total demand.  And we divide it by the size in the net stack or in other words, the duration, which is alpha plus delta. Okay, so this is what the greedy algorithm implies for this problem for circuit switching. And it was shown by Bodger et al in the same work that actually solving this is easy, finding the best configuration that can be solved exactly and it just reduces to maximum weight matching. Okay, so the question is, are we done? So we have greedy, easy to well define. So the answer is not, is that greedy is not well defined yet. So the question is, what happens when the last configuration we choose that's called MR with duration of R exceeds W? Okay, so let's see how that can happen. So let's say we chose R minus one configuration so far. And now we choose this configuration, as you can see the duration of R plus delta exceeds W. So in this case, we use another property of the problem, a very specific one, is that in session we can inflate or deflate elements. So this is not a general net stack problem. So we just in this case deflate the duration of the earth matching. So once we add the switching cost delta, we end exactly at W. Okay, another thing that can happen, actually the only other thing that can happen is if we entered here and we add the earth matching, we still exceed the W, but there's no way to fix this, right? Because W on its own is enough to cause the violation of the length of the time interval. So in this case, we just throw away the earth element. And throwing this throwing away of elements actually is what ruins the greedy algorithm for the net stack problem. But we still do this anyway. And so what we can prove, so for abbreviation, if we instead of writing that expression, I'll just say that f of the schedule S is the value of the schedule. What we can prove is that the value of the greedy algorithm is at least one minus one over E minus, think of this as order epsilon factor of the optimal solution. So always some optimal solution. And how do we prove this? So we prove this by using what you might call resource augmentation or actually looking at optimal solutions that have smaller time interval allowed. So the first step is to show that the greedy is actually very good compared to the optimal solution on a smaller time window, smaller by how much by an additive delta. So we can just remove one delta out of the allowed time and look at the optimal solution for the reduced interval, then greedy works very well, gives the one minus one over E. So this is what you might call O tilde. But the question is how good this O tilde is. And you can prove that O tilde is almost as good as the optimal solution. And actually the way we prove this, it actually works not only for optimal solutions, take any interval S for W and let's say S tilde is the optimal value for the truncated interval, sorry, it's truncation of S, then you don't lose more than a factor of one minus two delta over W. So if delta is small, this actually is close to one. This is what happens. So when you plug these two things together, you get this result. So this takes care of the first case where the switching cost is small. What happens when the switching cost is large? So in this case, because let's say K, the number of configurations we have in the optimal solution, is at most one over epsilon, which is a constant, we can enumerate over the durations. So let's say the optimal durations are alpha star one up to alpha star K. So how do we handle the fact that we know the durations, but we have no idea what the matchings are. So now that we know the durations, I'll show that it's very easy to write a linear programming relaxation. And then we're just going to use randomized rounding. And the relaxation, what it does, it assigns for every duration instead of a single matching distribution over matchings. So what will be the relaxation? So L is the index of the durations or the number of configurations we have in the optimal solution. So for every, let's say for the Lth duration, we have something that is at most a distribution. If this is strictly smaller than one, then think that with the remainder, the one minus the sum, we return the empty matching. So there's a distribution for every duration alpha star L. And now we just need to see what is the contribution of an edge ij from center i to receiver j with respect to this distribution. So first of all, it cannot exceed the demand. And here it cannot exceed. We go over all, essentially all matchings, over all distributions for all durations, the probability of choosing that matching that contains the edge ij and the actual duration which we guessed, which is a constant now. So this is why we can formulate this linear programming relaxation because these, the durations are known, are not variables. So this is it. This is a very simple relaxation. We just minimize the total contribution of all the edges, maximize, sorry, the total contribution of the edges. And so one thing that is left before we get to the programming is how we solve this because there's an exponential number of variables. So what you do is you just write the dual and see that the dual separation we're called is maximum weight matching. So this can be solved precisely using, for example, the ellipsoid algorithm. So once we have the distributions for every duration, alpha star l, from this relaxation, we use randomized rounding, which means that for every duration, we pick matching m with probability exactly what the distribution from the relaxation dictated. Okay, so how do we analyze this? So we need to lower bound this expectation. And the expectation is the contribution of the edge ij, which is, let's say if i is the indicator that matching m was chosen for duration l, right? So I sum over all, all matchings in this duration that contain the edge and their duration. Right? So this is the total time that was transmitted, which is random variable over edge ij, and we capited the demand. The issue here is that we want expectation of a minimum of two things. And the min function is a concave function. So this will give us, if we change the order of the mean and the expectation, this will actually work in the other way than what we want. So the question is, how do we analyze this? So you can analyze. This is a very nice exercise, but at some point we figure out that this was already done. So we're not sure this is even the first place this was done, but this gives you exactly what you want. You have a very specific concave function, and you want to lower bound its expectation as opposed to upper bounding its expectation. And what do I mean by that? I just want to switch the expectation and the mean function. So this, for example, was done by Andelman and Mantour. This is a paper about some AGT problem. So if you have N indicators, independent indicators, some the capping parameter B and B, capital B and B want to be in the non-negative coefficients, everything here is non-negative. So I want to lower bound the expectation of the linear function of the indicators, capped to B. All I want to do is actually change the order of the mean and expectation. So you can do this with the loss of 1 minus 1 over E. But this is a very nice exercise. For example, it was done here. So once you get that, we're done. We show that even in the case where the switching cost is large, we get an approximation of 1 minus 1 over E. Okay, so this handles the offline case. So the title of the talk promised something also about the online case. So let's see what it means online circuit switch scheduling. So with every time T, a new demand matrix, let's call it DT, is revealed and is added to all the unsatisfied demand we had before, right? And once this demand matrix is revealed, we choose a matching and translate it for some period of time. But we, unless we're already in this, let's say, delta time interval that nothing can be transmitted because we already switched a matching, okay? So for simplicity of presentation, and again this can be done without loss of generality, let's assume that time is discrete. So it's one, two, three up to some capital T, and that the demands are also integral, okay? So if the demands are integral, we can actually view the demand matrix as a multi-graph, a bipartite multi-graph, okay? So let's see what that means. And we'll see what that means. Let's say as a thought experiment it will be easy to see this in the online case where there's no switching cost, okay? So these are, let's say, the senders and these are the receivers as before, and say the first demand matrix we get is this. So for example, you see that the demand from sending from this sender to this receiver, there's a demand of three because there are three parallel edges. And here, for example, sending from this sender to this receiver, there's a demand of two, and here a demand of one, and there's also demands of zero, etc. So we view the demand matrix as a multi-graph, a bipartite multi-graph. So first of all we add it to the unsatisfied demand wave so far, so there are no demands, so this is what we have so far. So intuitively, if there's no switching cost, let's say delta is zero, what seems like the best thing to do is to choose the largest matching, right? So we choose the largest matching, let's say, these red edges, and we for, because time is discrete, we broadcast over these, over this matching for a single step, so we remove one edge. So every edge in the matching is actually removed. What happens now with t equals two? There's a new demand matrix, d2, let's say it looks like this. So we add it to the unsatisfied demand, so this is what we have so far, and again we choose a matching, let's say the red edges, and because time is discrete, we remove the chosen edges, and there's d3, and we add it, there's a matching, and so on and on and on. So this intuitively seems what you should do when there's no switching cost. What you can actually prove is that when there's no switching cost, this greedy online algorithm gives you a competitive ratio of half, okay? And the proof of this, which I won't go exactly into the details, actually relies on the fact that the offline version, when there's no switching cost, is easy. You can solve it exactly. So the question is, at least in the way we prove things, it seems like half is like a bound we cannot go beyond, get something better than that. So this raises the question, is there a connection between, say, the online problem and the offline problem? And what we can actually prove is that you can reduce the online problem to the offline problem, even in a black box manner. So what does it mean? So it means that if you have an offline beta approximation for the offline problem, when you choose some integer, say k, which needs to be at least three, then there is an online algorithm that gives you an approximation like this. The point is that this algorithm uses a window which is slightly larger than the W allowed. We deviate by an additive k times delta. One thing that is important to note about this is that this, let's say reduction, is poly time. So if this beta approximation runs in poly time, you actually get a poly time algorithm, an online algorithm, which is not always the case, because sometimes when in the online setting you just want to handle unknown input and you don't care about the running time of the algorithm.  And another thing to note, what happens, let's say, if we don't care about the running time, so offline we can always solve the exponential time. So beta equals one, right? So if beta equals one, you get something that is very close to half, essentially, right? Then this is the half we got when there was no switching cost. So if you plug in the result we have for the offline case, we get a competitive ratio which is roughly e minus one over two e minus one. There is some epsilon loss and we deviate, additively deviate from W by time of order delta over epsilon. And another thing that we can show, and that's not very hard, is that one can ask, okay, this is cheating. You gave the online algorithm more power, a larger window. The fact is that this is unavoidable. So there's no non-bi criteria online algorithm with finite competitive ratio, right? So if you want any finite competitive ratio, you must deviate from the time window W, okay? So I don't know, again, if there's some lower bound on the size of the deviation, but there must be some deviation in the window size, otherwise there's no finite competitive ratio. So this in some sense justifies this. Okay, so a few interesting open questions. So there are more questions than this, but I think these two questions are very interesting. So the first one actually relates to the hardness of the offline problem. So I mentioned to you that Somolar knapsack has a tight 1 minus 1 over e approximation, tight in the sense that there's a hardness result. Our problem in some sense is a special case of that, right? There's a specific Somolar function and we can also inflate and deflate the elements. We don't know whether the hardness result of the Somolar knapsack applies to our special case. One issue here which makes this problem interesting is that the hardness of Somolar optimization problems is usually information-based and we're talking about the offline case. So maybe we need to translate this to some complexity or something it's not clear. So these are like two incompatible things in some sense. And the second interesting question is it seems that even if you have beta equals one, at least in our method, we cannot break the half barrier for the competitive ratio. And I think it will be very interesting to show that there's actually better algorithm in the sense that probably you won't reduce the online problem to the offline one, but then you gain by showing an approximation better than half. So thank you. So what is the delta of the function of how different the two languages are for each other? Actually that's a good question. I don't know. The reason delta is fixed is because I didn't go over all the previous works and there are like also practical works that deal with this from people that actually work on data centers, people that say publish in sitcom and things like that. For them delta is fixed and they have like physical reasons like that. But from a theoretical point of view it's very interesting. Actually maybe at some point I should talk with those people and see if it makes sense in terms of the application. But I have no idea what happens when the switching time depends on let's say some distance measure between the two matchings. Thank you.