This is the man in black here again to introduce Columbia's program suspense Two of Hollywood's most deaf players are with us tonight. Miss Geraldine Fitzgerald and Cedric Hardwick Miss Fitzgerald and Cedric are here to match wits in a suspenseful tale by John Dixon Carr called Will you walk into my parlor? If you've been with us on these Tuesday nights, you will know that suspense is compounded of mystery and suspicion and dangerous adventure In this series are tales calculated to intrigue you to stir your nerves to offer you a precarious situation and then withhold the solution until the last possible moment and So with will you walk into my parlor and the performances of Geraldine Fitzgerald and Cedric Hardwick We again hope to keep you in Suspended just how far does any man trust his wife or his fiancee either for that matter An English bazaar a garden party in the grounds of Layton Hall in Kent one fine summer afternoon before the war Layton Hall is the home of major in Mrs. Grant always ready in the cause of charity There's the stern red brick of the hall rising above oak trees Against green lawns of the stalls and the swings and the roundabouts and the coconut chives They are not well patronized now Because a summer storm is coming up and the wind is whipping at the tents flapping the gaudy banners in a fantastic manner and sending the spectators hurrying away in search of shelter But over in a far corner is the fortune teller's tent gaudy in purple and gold yet with more than just a suggestion of mystery Beside it is a miniature shooting gallery presided over by major grand himself Near the center of this bazaar is the bandstand where the village musicians play lustily to keep the patronizers from leaving But as the wind rises it seems that only two of them are oblivious to the coming storm For they are in love the young man is tall in sport coat and flannels the young lady in a flowing gown of a startling beauty which suggests a halo a startling beauty that glows against the gray of the sky The paint of the tent She has her hand on his arm for protection against what you have nothing just For protection I want to get my fortune told before we leave Mary the wind I'm sure is going to pour in a minute I won't take long. We'll beat the storm wait and see I hate to drag you away from the match But I do want to visit him. You don't believe in that rubbish. Do you Mary? No, I don't suppose I do. I never can resist getting my fortune told Well, I suppose it's a woman's prerogative and they say this man is all very good They say it's marvelous how he can tell you all about yourself. You know that already, don't you? Oh, Phil darling? Please don't be so unimaginative. All right Mary. I'll be good Who is the fortune teller by the way? There's his sign on the 10th the great Omar Parmas than crystal-gazer sees all knows all no I mean who is he in real life friend of the majors? Maybe the major could tell us there He is now Please Phil we don't we don't have to go there. Do we go where to that shooting range of the majors?  It's right next to the fortune teller's 10th Mary and we can't insult our host Coming major look at the major.  Oh, you know, it's nothing like that Phil I'm much too much in love with you only all the old cats in the village are probably saying awful things about me Now what the devil could they be saying about? Are you young rascals you young so-and-so? Give me a hand each of you and many congratulations. Thank you Thank you very much major. We feel rather pleased about it ourselves Please I do and you young woman you come over here And then you have every one of us Britishers at your feet what you do But snarie a fellow American when he's helpless and away from home And do I love being snares? Yes, old girl. It looks as though you had your man where you wanted him Now tell me your secret. Are you a demon in disguise? Please major Grant. It's an awfully good design She is please major, please Phil No, nothing, but it's getting dark and the wind's rising it's going to pour any minute now Oh a moment before you were the one who said not to worry. Oh, that won't matter my girl The show's nearly over anyway. We did pretty well if I do say so myself We came over here really to see the fortune teller if you don't mind letting go my hand You won't let me go Not until you patronize this charity As a preparation of polishing off your husband after marriage. Why not try a few rounds with a rifle? Of course, what kind of a truck you are. No, please now now here's a neat little model winchester 61 22 caliber. Yeah, try it.  You just fire away and see if you can hit the target. Yeah All right, if you insist I don't watch out Bullseye you fit the electric light in the roof You're not supposed to aim at that Speaking of dying if that's her style of target shooting down if I'm not gonna crawl out from under this counter and stand behind her It isn't funny Phil. I'm sorry, but I can't go on with this. Here's the rifle. All right here. I Sorry, Mary, but no, it was going to affect you like this.  Well, why don't you go ahead darling?  You're a very lucky young fellow man. I hope you realize that. Oh, I realize it all right I am hope this fortune teller doesn't keep her in there very long. Yeah Why the sky it's getting black as pitch You're not careful. This wind is going to blow all your tents into the next county. All these tents are pretty securely peg young fellow I think we can risk it. It's so dark that Wait a minute look there. Yeah, well The fortune teller's tent He's got a light inside and you can see his shadow against the tanned it Like a shadow screen Looks it has Mary going in how she's sitting down across the table from I say you know You happen to know who the fortune teller really is no as a matter of fact. I was going to ask you No, I'll tell you a little secret.  No, he knows a lot about human nature that my lad is inspector Brandon He's a specialist in poison cases. They say never forgets a face Is anything wrong? What's he saying to Mary? Look at those shadows Mary's jumped up and back to wait He's pointing his finger at her now. She's backing out of the tent look major. He's following her. Can you hear what he's saying?  What was he saying to me? saying to me Nothing at all really Only the usual thing about a happy life and a little illness, but nothing serious and why were you so frightened? I wasn't frightened. Oh no, Mary. I'm sorry. I saw your shadow on the wall of that tent and I heard you shrieking I Think I'll go in and get my fortune told and see what all this is about Why not? I Felt a drop of rain on my head. It's going to pour down in a second. Hadn't we better run for the house? You go on up to the house Mary. Oh Phil. I don't want to be by myself All right, then dear there's the major here given this gun will you I'll be with you in a moment I'm gonna see that faker fortune teller I come in Thank you Sit down in the chair opposite to the first time in the date of your birth Then look at the crystal on the table in front of you just a minute inspector Brandon Do you mind if we drop the mumbo jumbo? Well, as a matter of fact, I'd like to drop it. It's been a bit of a strain talking like Hamlet's ghost Well, what's on your mind? Maybe it's only the heat or my own nerves, but What were you saying to miss Sherwood miss miss who the young lady was just in here my fiancee What's wrong? Why did you jump like that? Do you say fiancee? Of course, why not? I look here, mister. Oh, my name is Lester Philip Lester. And what did you say her name is? Mary Sherwood Here, what's all this mystery? Tell me mr. Lester She lived here in the village for very long No, only about six months and how long you've been engaged to her believe me. I have a reason for asking that How long have you been engaged? Well, you're weak tomorrow, but weak tomorrow She by any chance invites you to dinner at her house tomorrow night dinner has she Yes, as a matter of fact, she has but I don't see you know who this Mary Sherwood really is No Well, I'll tell you she Inspector Brandon ah Never stand with your shadow against light. You're hit. Yes, I'm terrible sorry But Phil shouldn't have given me this dreadful rifle to hold all I did was touch the trigger by accident I I hope I haven't hit anything in the quiet village of Sutton later that same night after the unfortunate accident that couldn't be helped a Rather white-faced young man Philip Lester slips down the road Pauses in front of the door to the in starts to enter and then changes his mind He looks over his shoulder and then walks around the building being very careful to stay within its shadow He slips in through the side door and makes sure that no one sees him He makes his way quietly up the stairs to a darkened passageway outside the bedrooms Glances at the number on the first door and then hurries down the hall Stops in front of room Come in specter brandon I thought Yes You're sitting up and taking knowledge and thank you Scooting inspector what I heard you were still unconscious and not expected to live Yes, that was the report that I was stuck to styles to give out, but why I had my reasons mr. Lester As you can see fortunately I was the recipient of only a flesh wound across the left shoulder it he bled a little but not much Uninspective poor Mary's nearly frantic.  Let me ring her up and stay away from that telephone why because Because I want to tell you a few things about miss Mary Sherwin The first place.  Three husbands and one fiancee whom she didn't bother to marry First the fiancee they made mutual wills in each other's favor Exactly a week after the engagement following dinner at her house. This fellow was taken ill He died before morning into tannic convulsion Specter that's ridiculous Mary well, she's so young and it is young perhaps, but I don't believe it Don't take my word for it I've sent Sergeant Lambert to London for foul You can see photographs and fingerprints.   Yes, I'm fairly well off. Have you and this woman made a will in each other's favor Mary wouldn't need to do that. She's got plenty of money and a collection of jewels worth I don't know how my quite agree, but you haven't answered my question Have you made a will in each other's favor? Yes, who's just one of that yours or hers? I don't remember we started talking and agreed it would be a sensible idea But it shocked you a little, didn't it? Are you wondered why it was necessary? Specter A minute ago you were talking about photographs and fingerprints well Who don't mean Mary's been on trial she has been on trial three times Yes, three times and under three different names, but she was acquitted. Yes because she had a cast on alibi There you see wait She was acquitted simply because the prosecution couldn't show how the poison was administered


Dear students, I am Dr. Muhammad Ali Bhatti and I will teach this course of macroeconomic analysis. This is an advanced course of macroeconomics. I have been teaching this course for the last so many years. I have taught this course right from the intermediate level to the PhD level. Before this course, you have taken a few courses of macroeconomics. So, let me introduce what is this course. We can define macroeconomics as the study of the behavior of the economy as a whole. In this course, we will study the structure and the performance of the economy and government policies that affect the economic performance. Dear students, you know that microeconomics and macroeconomics are the two main fields of economics. There are many common ideas between microeconomics and macroeconomics and methods are also common between these two. But the main difference between these two fields of economics is the level at which we study the economy. In microeconomics, for example, we study the utility maximization and the profit maximization, consumer behavior and the firms behavior, whereas in macroeconomics, we study consumption but not the consumption of an individual and similarly the production of a firm. Rather, we study consumption at aggregate level, aggregate consumption, aggregate production, aggregate output, aggregate investment. So, these are the topics of macroeconomics. So, how do we aggregate them? We calculate the national values from individual values. The way it is done is that we take a representative agent and the individual who represents the economy can also be a firm or a consumer. So, we represent the individual's behavior as the behavior of the economy. So, what are the main topics, main issues which we will study in this course? The most important one is the long-run economic growth. You know that in the world, some economists are rich and some are poor. Rich economists maintain a good living standard for their citizens whereas for poor economists, it is difficult to meet the basic needs of their citizens. So, how can we differentiate from the perspective of macroeconomics between rich and poor countries? If you look closely, you will see that historically rich countries are the ones who had extended periods of economic growth in the past. Whereas, poor countries were either not given a specific period of economic growth and if they had performed well economically in history, then the other ones also had declines which they have offset. So, this is the basic difference of growth. Growth rates are very important and this is a very small growth rate that has a wide impact on the long-run economy. So, our issue is that how can the economy improve its growth rate and improve its living standard in the long-run and maintain it. The second important topic which we will discuss in this course is about the business cycle. The business cycle means that in the short-run, there are a lot of sharp fluctuations in the economy. In the economy, there is a lot of boom, there is a lot of speed, there is a lot of economic activity on the entire economy and there is a lot of employment and so on. But sometimes, in the economy, there is a state of recession. Recession means unemployment is high, people are not getting employment and this is how the market demand decreases. So, these fluctuations obviously have a lot of impact on the economy. They have an economic impact, they have a political and social impact. So, as a macroeconomist, we think and see why these recession and these boom come, what are their causes and how can we control them. Another important issue is unemployment. You are all aware of unemployment. I think this is the most important issue because of its economic consequences, its social, political and a lot of other dimensions. So, unemployment is an important issue and no nation can afford to stay at a high level for unemployment. So, we will study the unemployment, what are its types, what are its causes and how can we control it and keep it at a minimum level. Similarly, there is a very important issue of inflation. Why do prices increase and how can we control these prices? And how can we control the economy of prices? So, inflation is also a very important issue and it significantly impacts a common person's life. So, this is also an important topic of this course. International economy. You know that we are living in a global village.  They have to keep their economic relations with the rest of the world. Whether it is an American economy or a small economy like Afghanistan or Pakistan. So, what are the effects of this international economic linkage? What is the effect of international trade? What is the effect of borrowing and lending? What is the effect of foreign direct investment? We will study all these issues. And finally, macroeconomic policies. What is the role of the governments? How can they control their economy? How can they control their policies? How can they control their unemployment, inflation, employment, and lifestyle? So, we will study the policies of the government, fiscal policies, monetary policies, and other economic policies. Thank you very much.


People are always comparing that life to someone else. My God, that person's only 21, they already made a billion dollars. And you're like, oh no. Everyone had a different journey. Thanks, Daddy. Thanks, Daddy. No, some of them actually made billion dollars through whatever they were doing. My only fans. But not only that, I've seen a lot of young entrepreneurs inspired me. I've seen some young persons just like 20s through whatever and just like coaching, online coaching, and helping other people. I'm like, wow, he's so young. And I wish I can do that. There's a lot more now than it was back then. Definitely, information is so accessible now. Thanks to the internet, right? And that's where the kids are like, now they're all on their phones. And the parents are like, don't go on their phone. I'm like, no, go on the phone. As long as you're looking for the right things. Yeah, yeah, yeah.


But get this, this is buried in the New York Times piece tonight, but I found it very interesting. He's a decorated colonel, by the way, in the Iraq war, but because Colonel Vindaman emigrated from Ukraine, along with his family, when he was a child and is fluent in Ukrainian and Russian, Ukrainian officials sought advice from him. Here we have a U.S. national security official who is advising Ukraine while working inside the White House. I find that astounding and some people might call that espionage. Welcome back everyone. Over the years, I've watched the declining sanity of many in the so-called mainstream media, but few come close to the sheer craziness of never-Trump or Nicole Wallace. Her latest breakdown came as she whined about her business competitor Fox News and a few of its hosts who had been criticizing the Democrats' latest whistleblower in the Ukrainian scandal. The supposed scandal here is that former Bush attorney John Yu questioned if this whistleblower's actions didn't amount to espionage. A fair and justified question, especially seeing as how we're now finding out he was listening in on phone calls, but no, Wallace seems to think that the veteran and purple heart status of this whistleblower puts them above any scrutiny. Isn't that kind of an interesting angle on this story? I find that astounding and some people might call that espionage.  Have you ever noticed how much the Democrats in the media love to put forth people that they see as above criticism? Then when criticized, they unleash days or maybe even weeks of outrage and hand ringing, along with the typical claim that criticizing the individual somehow applies to an entire group of people. Though he passed a background check, it's obvious that those who hate Trump are rationalizing pretty much any sort of action to undermine him or take him out of office. We've seen this corruption first hand from the FBI and the CIA, so why not this guy? The point is, a journalist asking questions is always okay. The reaction from Nicole Wallace types leads me to believe that they're not interested in asking or getting answers that don't lead to the outcome they want. For that matter, who really cares what Nicole Wallace thinks? She clearly has an agenda and still pretends to be a journalist. For example, she wants to actually claim that Trump said he wants to exterminate Latinos. You don't have a president, as you said, talking about exterminating Latinos. Wrong. Not only was she lying when she made that claim, but her guests just spewed lie after lie and she didn't even attempt to correct any of it. The first being, words and actions throughout his presidency, he's basically declared open season on Latinos, but it's not just the language he used. You mentioned calling Mexicans drug dealers and rapists when he came down the escalator. That was day one. Then it escalated into attacks on Latino journalists. Then he ramped it up again to the invasion, the warning people of the caravan, and words like infestation. For one, I've never once heard Trump attack Latinos, and I did an extensive Google search looking for any example. I couldn't find one. Second, Trump never called Mexicans drug dealers and rapists. He said specifically that some illegal immigrants are drug dealers and rapists, and that others are good people. He was being very specific and definitely not talking about all Mexicans. Then she claims that Trump attacks Latino journalists. Instead, he was very critical of a pro-illegal immigration activist who pretends to be a journalist. Not all Latino journalists, just one. And this isn't even up for debate. The journalist in question admits that he's not objective and is an activist. What do you mean by that? Because you come out specifically and say, neutrality is not an option, even for journalists. Explain. But let me ask you that. But I'm saying that neutrality is not an option. But there again, attributing criticism of one Latino journalist and applying it to all Latino journalists. Next Wallace claims that Trump warned the country about the coming caravan and called it an invasion. As I've pointed out before in past videos, not only did past administrations call it an invasion, but even the Mexican government has called it an invasion in the past. And most importantly, it actually fits the definition of an invasion. She then makes this vague claim about an infestation, a claim that has been debunked to death. Trump called MS-13 gang members an infestation. If you have a problem with that, you probably have some kind words to say about al-Baghdadi. In conclusion, Wallace is just a hack. She can't get through one paragraph without spewing lie after lie. She's just another hypocritical, holier than now, dementia case that has become common place in the DNC media. Thanks for watching. Make sure you head over to my Teespring store and check out some of my wife's awesome designs. If you want to support this channel, please consider subscribing to me on Patreon or SubscribeStar. You can also send me a donation on PayPal and I very much appreciate it. With YouTube demonetizing just about everything I upload, it's only thanks to my supporters that I'm able to continue doing this channel. You can find all the relevant links in the description and the pinned comment. Thanks for watching. Keep coming back.


Hello, I'm Cédric Olivier from Orange. I'm Linux Foundation Networking Board Member, a CNTT officer and OpenAV Functis Project Technical Leader. So thank you for joining OpenAV and CNTT in Orange AFP. This ONES session will first describe Orange CI strategy and I will highlight how Orange is leveraging OpenAV and CNTT in an ongoing RFP. So first, as a good introduction, here are a couple of guidelines regarding our strategy. So of course we want to automate most of the network operations. One simple example, we are currently programming former test plans to... mostly previously executed by hand to reduce the verification period after a new equipment or a new software release. It's worth mentioning that automation is the factor of mandatory as soon as we are referring to the new network architecture, such as NFV, because they leverage on cloud technologies based on over provisioning and also because of the new software release rate. We are switching from a classical equipment release rate every year, every two years to open source software release rate around six months or less. So we must deploy and test as much as possible to bring determinism and to be able to follow the new software releases. About testing, a key rule is we want to test all the software layers independently. Testing only the VNF is not able. We must verify OpenStack right after its deployment before onboarding and testing the VNF. It's of course more than a help to identify the root cause. If the issue comes from the VNF of the infrastructure, but it's also about responsibilities as soon as we are dealing with multiple actors, whatever it's about, OpenStack, Kubernetes or the VNFs. One important aspect is we want to run all deployment and verification jobs in our continuous integration chains. We don't want to set up a new CI chain for a new VNF. We want to assemble the deployment job and the testing job inside our CI chain. Somehow we don't want to duplicate the open source model where all projects define their own gates and diverging on their job-based tools. Here, what we want is to assemble all the Spark test cases available. It could come from internal development, from a range. It could come from open source as integrated by Functest. Or it could be proprietary testing as proposed by VNF funders. It means that we have defined an architecture good enough to assemble Spark test cases. Also, we want to be able to instantiate the CI chains everywhere in our group, in whatever the affiliate and the deployment model, leveraging on centralized services or local services. To do so, we don't want to reinvent the wheel and leverage best open source tools and practices. The biggest open source project has built amazing gates and we can leverage the knowledge, the practices to benefit from this open source project. Here, we don't want to reinvent the wheel and if a feature is missing, we will directly contribute to the UBSIM project instead of forking other bad practices. So, mainly, we want to integrate smoothly and we want to deploy everywhere fastly. So, how does open source help? We are already contributing to multiple open source projects and one very good example is OPNV, where we are first contributors from DZero. OPNV opened a platform for NFV as deployed and testing open stack for years, day after day. This is multiple installers. So, OPNV has built a full continuous integration chain composed of Jenkins, a test database, an artifact repository to ensure that we can build and test open stack or Q&A tests every day. So, there are a lot of OPNV projects in which we are interested and involved. For instance, FungTest. FungTest offers a collection of virtual infrastructure test suites. FungTest is about 3,000 functional tests, three-hours API and data plane benchmarking and three VNF automatically onboarding and tested. It's more than enough to give a confidence to the deployment and to ensure that all the open stack operations are working well. Of course, FungTest also offers integrated upstream test cases for verifying Q&A tests as well. There are a second OPNV project which we are leveraging on cross-testing. Cross-testing is part of our network automation journey simply because it lets the developer work only on this test suite without diving into CI CD. So, cross-testing helps assembling sparse test cases simply by providing a common test case execution and manages all the interactions with CI CD components. It provides a unique interface for GitLab and Jenkins, a simply docker container to execute and a test case name. It stores all the results into a single test database, MongoDB, and it automatically pushes all the artifacts to an S3 repository. So, cross-testing offers a common test case execution. There is a cross-testing CI, the continuous integration part, simply leveraged on the common test case execution to allow building a full CI CD tool chain thanks to a simple test case list, simply docker containers and a test case name. So, cross-testing CI allows us, for instance, in OPNV to write all the Jenkins jobs needed to verify the OPNV test tools in the existing CI tool chain, but it also helps us to deploy the full CI CD tool chain in your laptop in a couple of commands and minutes. Cross-testing CI allows us different models such as the centralized deployment, distributed deployment, or also a mix of them. And it feeds our needs for affiliates, for instance, where we could deploy a local CI and continuous integration chain if it helps or if there are constraints which force us to do so. CNTT is a much more recent open source initiative created by a lot of operators such as Orange. CNTT Common Infrastructure Telco Taskforce defines a reference model, a reference architecture for OpenStack and Kubernetes, which is onboarding and test VNF at the end. CNTT also defines conformance suites, essentially based on a fun test, and playbooks to verify the conformance of your deployment regarding the CNTT documentation. All the CNTT playbooks are leveraging cross-testing CI, deploying locally a full CI chain, running all the modatory test cases in CNTT and a full check of your deployment. Orange is the first contributor in OPNV, as I mentioned before, and a key actor of CNTT will keep contributing on this open source project, but we are of course expecting more contribution to help regarding the amazing scope. Feel free to click on the different links and any help is welcome regarding the different call for contributions. CNTT or OPNV in Orange, here are a couple of RFP requirements extracting from an ongoing one. There are three key requirements regarding our discussion today. The first one is we ask for the full CNTT reference conformance for OpenStack results and outputs. So we are asking simply to run the CNTT-ALC1 playbook and to send us the zip file at the end, dumping all the test data and the artifacts. So we don't ask the full compliance simply because CNTT asks for a lot of modatory features and it may be possible that the ecosystem is not able to deliver all the modatory features. But it's up to Orange to check the result to identify what is about a missing feature, what is about mismatches in version, missing API or simply big bugs in the system on the test. So I will describe in the next slide the Orange CNTT-Future about ALC1 which is in a very good shape. We ask also the success of FUNCTEST Kubernetes test suite. So here as FUNCTEST Kubernetes is mostly about interoperability testing right now, we considered that we can ask the full success. The same test case list is now mandatory in CNTT-ALC2 BARAC, just released, which takes the same test case list into account. And also we ask for a first BNF test cases running in our continuous integration chain. It means that the vendors must deliver a docker container compatible with cross-testing, which can be executed in our CI chain. And to verify it works, we are running the test cases through cross-testing CI. So as you can see, it's implementing the Orange Principle, just highlighted, and the CNTT targets. I remember a couple of meetings in Prague at the beginning of the year, where multiple operators and authors ask to see CNTT deliverables in RFP. Orange is already doing that. So just a quick highlight regarding the latest Orange CNTT-ALC1 field trial. So first, it helped detecting a couple of issues in CNTT-ALC1 just before the Baldy release. Two features were missing in Orange as a product at the beginning of the field trial, so Cinderbackup and Nova instance password. They are now part of the products. And it remains 10 single test failures out of the 2000 included in AC1. They are mostly about Cinderbackup, which was late integrated. And beyond for my func test role, maybe JujuPC must be announced to pass proxies as we saw during the Orange CNTT field trial. So Orange is very, very close in good shape to pass the full compliance in a couple of weeks. So we are leveraging all the current CNTT conformance suites, but we see a couple of features which can help CNTT. So first, we do integrate much more benchmark in CNTT conformance. In AC1, especially, we could have this benchmarking, which could be a very good help regarding the infrastructure performance. So we could leverage Stopper from OPNV, FDIO or DD, a lot of technical solutions. It would be great also to have KPI regarding benchmarking in CNTT AC1, which are currently missing. Regarding AC2, the Kubernetes side, it would be great to switch from the current interoperability testing to a true CNTT conformance suites. We are running the Kubernetes conformance through func test, which is about 300 single tests. It's far from all the very little ratio compared to the E2E capabilities. So we do now list the Kubernetes modatory features and the single tests, which can be part of CNTT AC2. It would be great also to bootstrap the first VNF and CNF conformance suites for the time being we are focusing on the infrastructure, OpenStack and Kubernetes. But there is a key need regarding the VNF and CNF at least onboarding. So of course, every contribution helps. Feel free to contribute. So a few takeaways. So Orange, Leverage, OPNV and CNTT in RFP. We are also a big contributor in these two communities. Merging one in a couple of days and months. We keep contributing in both specifications in implementation streams. We think both streams are mandatory for the success of NFV. And we are hoping to see all the CNTT actors also involved on the implementation side. So my last message on behalf of my open source roles, I would say we expect more OPNV and CNTT contributions, especially for VNF and CNF conformance suites or initial CNTT targets. So thank you. I will encourage you to try the CNTT reference suites. It's very simple. It's about a couple of comments. I'm pretty sure you will love them. If you're on the line, we have two questions in the Q&A box. You're welcome to go ahead and answer live on the phone line. Okay. Hello. I see the first question. How you intend to validate VNF with your communities on top of OpenStack or by Metal? So there are two parts. At least about onboarding both works in the same way. It's true that depending if you deploy Kubernetes on OpenStack or by Metal, we will have different results. I would say it's up to our next activities. First to characterize VNF and its testing. But at least regarding the VNF onboarding, there is, technically speaking, there is no differences. Regarding benchmarking, I would say it depends. If we look at the Neutron and virtual machine, whatever it's about, SDN or not, we can benchmark in the same way. I mean, if we look at Shaker and VMTP, which are included in SC1, it's about booting client and servers in virtual machines. So whatever is on their layer is managed. There is no technical issue. There is no difference between an agent solution or an SDN solution. So from an SC1, SC1 is written in a way that, we define Neutron Modatory Features. SC1 is testing them. It could be implemented via an SDN controller, via Neutron Agents or VN, for instance. There is no specific logics in the networking implementation. So the last question. You think using SDN is preferred for such a case at this preferred way. From an RA1 point of view, at least regarding OpenStack, we are selecting Neutron Features. So it could be implemented by an SDN or via the classical Neutron Agents. So from an SC1 point of view, we are calling Neutron API, asking for Neutron Features. Both solution works. And we alighted in previous LFND events that the OVN and the classical Neutron Agents passed successfully the performance suite. So from an API point of view, SDN is just the implementation, hoping I'm answering the question. So any new question? So I'm writing in the chat a link about the previous session, an LFND event session about CNDT-HC, highlighting the result with OVN and Neutron Agents. So feel free to have a look. Then no other questions. So thank you all for joining this session. Have a nice OEMS. Thank you.


A tape diagram is a really convenient way of organizing information about numerical and later on algebraic quantities. So what this corresponds to is our concrete representation of a number. So let's suppose we're working in base 10 for right now, and if I want to determine the number of objects in a collection working base 10, well, I have a bunch of things and what I'll do is I'll look for sets of 10, there's one, and I'll bundle them. And I might as well bundle the other one just for convenience. And I'll trade, again I don't really need to do the physical trade, but the important thing is this should not belong in the 1's place, it should actually be over in the 10's place. And I have this as my bundling trade. Now if I drop the place value chart and join the objects together, I still have a representation of the same numerical quantity. But now it looks a little bit more organized and this corresponds to what a tape diagram is. And so for example I might draw a tape diagram representing the number 37. And I could draw a set of 37 boxes and maybe it'll look something like this, but maybe I want it to be a little bit more organized. And I certainly don't want to have to draw 37 boxes, so maybe I'll just outline the units and the sets of units and I'll label these amounts. So I have 37, that's 3 10's, or 30. And then that last set of boxes, there's 7 1's there, that's going to be 7 boxes. And there's a tape diagram for 37. Now there's many other ways we could have drawn this if we were a little bit more sophisticated. We would draw maybe 30 and 7 and we could draw a tape diagram that way. One of the nice things is that these tape diagrams are very useful to giving us a visual representation of a lot of different arithmetic and algebraic operations. So for example I'll draw a tape diagram representing the addition of 34 plus 23, and then I'll use it to find the sum. So again it's helpful to remember the set definition of addition, which defines the sum as the cardinality of the union of two sets. And we're going to put two sets together, one of them with 34 elements. So again I can draw that as a set of 10, a 10, a 10, and a 4. So there's my 34 elements there, and another set with 23 elements. So here's my set with 23, that's 10, 10, and 3. And so I'm going to join those two sets together, I'll glue them together like that. And it's worth noting that I can rearrange the pieces. So maybe I'll rearrange them like that. And then at this point I can just figure out how much I have. I have 10, 20, 30, 40, 50, and 4, 3. I have 57 pieces altogether, and so my sum is going to be 57. Now the thing to realize is what we did there is counting really more than anything else. We didn't actually do any addition. Once we get comfortable with the actual process of addition, we can move to larger pieces for our tapes. So I might draw my tape representing 34 as a 30 tape and a 4 tape. And likewise that 23 tape is a 20 tape and a 3 tape. And again if I have some facility with addition, I really don't need to redraw the tape diagram. I just need to add the pieces that I see. And so here's a 30 and 20 piece, and here's a 4 and a 3 piece. So I can add those pieces together, the 30 and 20, that's 50, the 4 and 3, that's 7. And so all together I have 57 as my sum.


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Let's start the seminar by Mostafa Amin. Oh, Mostafa Amin is visiting us from Rice University. He agreed to give a seminar on dark matter with a short introduction for the students, who are not experts on dark matter. But then later it will be more specific about the vector dark matter model that he's working on. So thanks, Mardad. It's been great. It's been great talking to old friends as well as to the new students that I've met. So I changed my mind a little bit compared to what Mardad just described. So I will talk about this new work on vector dark matter, but instead of giving you an introduction to dark matter generally all the way at the beginning, I'm going to intersperse it along the way, wherever the need arises to give you more details. Okay, so let me start by saying that I'm going to talk about... Most of the talk I'm going to be talking... I'm going to be telling you something about these three papers that are here. And it's mostly about vector dark matter or just dark matter that is made up of particles of higher spin. Not just scalars, but vectors, perhaps even massive tensors. Before I begin, the work is in collaboration with these people up here. On all three papers is Mudad Jain, who's a postdoc at Rice. Hongyi Zhang is on one of them. He's a graduate student and Rohit is an undergraduate and Philip is a research scientist, not at Rice. Okay, let me minimize this. Somebody asked me a question about... What is this going on? It's on my screen.  No. I've lost control. Oh, there, it's back. Let me... I think it'll be okay. High video panel, high floating meeting controls. I think this should be fine now. I tried to remove it, so... So, somebody asked me... When I said I was from Rice, I said where Rice is. I thought, given that this is a cosmology school, I would give my cosmic address. And appropriately, so, we are at the center of the universe. At least SDSS claims so. And not quite at the center of the galaxy, but it's okay. For the whole universe, we are the center. It's okay. We are in Houston, Texas, in the US. And if you want to know more about Rice, just ask me afterwards. Okay, so, before I get into the details of the talk, especially given that there is an audience on Zoom as well, and I know how tired I get on Zoom within the first five minutes, so I will give you the punchline first to start with the talk, because I'm sure half the people will not be listening after the first five minutes. Okay, so, the main motivation of this work for me, apart from the fact that it is a lot of fun, is I want to know whether we can tell something about the spin of dark matter from astrophysical observations. I hope that by the end of this talk, you will be able to tell that these two simulations, that look rather similar, have differences between them, and you will be able to tell that one of them is a scalar dark matter simulation and one of them is a vector dark matter simulation. And there will be a test in the end, so pay attention. Okay, in a little bit more detail, I'm going to tell you that if dark matter is made up of a light vector field, then it contains within it a class of solitons, localized over densities that are ground states of the system. This is not different from scalar dark matter. The interesting thing about these is that these solitons are polarized and have macroscopic amount of intrinsic spin angular momentum. And this is a new thing about these guys. I will also tell you that in these models of dark matter, there is a potentially observable signature in the form of interference patterns. This is wave-like dark matter, so there is observable signature in terms of that, which is different from the case when it is made up of scalar dark matter. Somewhat a little bit more speculatively, even the shape of halos is slightly different. Finally, time permitting, I will also tell you a bit more about the formation mechanism of vector dark matter, as well as these objects. As Mehrdad mentioned, interspersed through this sort of research presentation, I will also give you some pedagogical introduction, short bits of it in terms of things about dark matter, things about differences between particle and wave-like dark matter, a little bit about solitons, and a little bit about the power spectrum of density fluctuations as well. All of these things are required in my talk, so I will just do a slightly longer introduction than normal for these concepts as I go along. With that, let me start the main part of the talk. And again, please feel free to interrupt me throughout. My plan is, so Mehrdad told me the talk is about 10 hours, so I will take a break at five in the middle, maybe for five minutes, because I will need to go to use the restroom, but otherwise, you know, I am sure you will all be here. Okay. Well, given the fantastic work that your lecturers have done for me, my life is a lot easier. Asim as well as Marco have done a fantastic job of introducing density fluctuations and also a bit about dark matter along the way. So I will just start by saying, I think we all mostly agree that dark matter exists and we know it exists because of its gravitational interactions. What we don't know is what are the properties of dark matter? What is this charge? What is this spin? What is this mass? What are its interactions within itself and with the stuff that you and I are made up of? Is it an elementary particle or is it some composite thing made up of many elementary particles together? What are its formation mechanisms? What is this cosmic history? Did it form via thermal mechanism? That is, from a thermal plasma? Did it come about via some non-thermal mechanism? All of these things we don't know about dark matter. Let's start with just knocking out a few things out of here. If dark matter had electric charge, that's no good. We've already seen that if dark matter interacted strongly with photons in the early universe, we would not see the structure we see in the cosmic microwave background, which you will learn more about from Blake next week, or the matter power spectrum, which you heard about yesterday from Asim. The fact that dark matter cannot interact very strongly with photons tells you that the charge of dark matter, the electric charge has to be less than about 10 to the minus 7 of the electron charge. That's what it tells you. This is weakly charged. What about dark matter's interaction with itself or with regular matter, say protons or neutrons? The interaction of dark matter with itself can be constrained, for example, with the help of this beautiful observation of merging of two clusters called the bullet cluster. The bullet cluster is a thing that looks like a bullet. This observation tells us that the self-interaction or the scattering cross-section of dark matter per mass has to be less than 10 to the minus 24 centimeters squared per GeV. This is about a nuclear cross-section. That's roughly what the number is. It's a very stringent limit when you think about its interaction with protons. This is from xenon, and as you can see, this number is going down to about 10 to the minus 40-ish. For neutrons, it's even slightly different. So that's charge knocked off. That's a little bit about the self-interactions or interactions with the sun and model particles knocked off a bit. What about the mass? Here, we reveal that we really know nothing. The mass of dark matter particle is highly unconstrained. It can be as light as 10 to the minus 21 EV-ish. This is really light. I don't actually remember the exact number, but I'm not even sure if the constraint on the mass of the photon is that good. So we are allowed to have massive cold dark matter. That's this light. It doesn't contradict observations. You are also allowed to have masses very high, up to a long scale, or if it's composite, even higher. So there's a huge range of dark matter mass that's available, and we don't know what the mass of this constituent is. Very important for our purposes in this talk, we also don't know much about the spin of dark matter. We don't know whether it's a spin-a-half integer spin, such as whether that's a fermion or it's a boson. But we don't know some things regarding spin. If dark matter happens to be a fermion, its mass better be heavier than 100 EV, which corresponds to saying that the de Broglie scale, assuming usual typical velocities in our galaxy, has to be smaller than 10 to the minus 6 meters. Where does this come from? This comes from the simple fact that fermions don't like to sit on top of each other. They already knew about COVID-A before we did. So they were just socially distancing all the way from the beginning of the universe. And that tells us, that maybe even tells us why they have to be heavier, but they cannot be lighter because you cannot pack so many of them in a given volume. We already know what the mass density of dark matter needs to be in a local neighborhood, about 0.3G V per centimeter cubed. Because of this restriction on how many fermions you can pack into a phase space volume, that in turn gives a restriction on what the mass can be. If it's too light, you cannot make up the mass density in a given region. So that restriction tells us that these fermions have, if dark matter is made up of fermions, it has to be heavier than 100 electron volts. On the other hand, if dark matter is bosonic, it has no such restrictions. You can pack as many bosons together as you want in a given volume. So you can make up the local mass density by just packing on many, many, very light bosons together. To give you an example of how many of these there can be in a typical volume, de Broglie volume, look at the numbers. If I make the mass of the dark matter particle about 10 to the minus 5 EV, this is like a QCDA axion-like particle. You have 10 to the 23 of them. This is humongous. If I make it ultra light, like 10 to the minus 20 EV, this is going to be 10 to the 83. So there are many, many particles. So how should I think about these? Particles stack one on top of the other, all sharing a roughly similar de Broglie wavelength, just stack one on top of the other. It doesn't make much sense to talk about these objects individually. They're just sitting on top of each other. Indeed, the de Broglie scale corresponding to these masses that I've just said is macroscopic. So for an axion-like thing, the de Broglie scale, for a QCD axion-like thing, the de Broglie scale is about tens of meters perhaps. So that's macroscopic. For 10 to the minus 20 EV, it can be one parsec in size. So these are astrophysical scales for these particle sizes. And they're all packed on top of each other. So it seems to make very... So it perhaps motivates us that we shouldn't be thinking of them as individual particles. We should just be thinking of them as all sitting on top of each other, a collection of them together, and we should be perhaps thinking of them as a field, the classical field of this stuff. If you want, you can think of this as a condensate, like a BEC. Yes, they would have too much speed. We want them to be cold as well. You would want them to be cold as well, right? Can you repeat the question? Sorry, the question was, why can't we fill up higher levels? I believe the argument would be that they would not remain cold. They would move too fast if you get to very high states. Yes, I guess... Repeat the question. Sorry, I keep on forgetting. The question was, what are promising candidates for fermionic dark matter? I think you could pick something from Susie if that was something, if your flavor is appealing to you. But any fermion that I can pick that has reasonably weak interactions with the standard model will work. There are some questions in the chat. I also have a question. I don't understand the second equation because the second and third term don't seem to be equal. What do you mean? I mean, I'm just saying that the de Broglie scale for this mass particle for different masses is different. Okay, I got it. Let me ask questions from you. Can we say dark matter has both bosons and fermions since neutrinos are also alike? You could certainly have an admixture of fermions and bosons. Nothing is preventing that. In fact, you could have a whole dark sector that's present to somewhat similar to the standard model. Perhaps it's a prejudice of ours to think that dark matter is simple and made up of just one particle. It could be two particles. It could be an entire dark standard model sitting there. So we don't know. Can gravity overcome the degeneracy pressure due to Pauli's exclusion principle for fermions? Yes, but hopefully not in our vicinity. That happens, of course, when you form black holes. That is happening when you overcome gravity in neutron stars. That's exactly what is happening.  But not for dark matter, typically. For any fermions, why do we see them? The interactions will be very weak, right? You have to produce them. If the interaction is too weak with the standard model, how are you going to produce them? Is dark matter, its interactions are going to be very weak? It has to be very weak, otherwise it would not be dark matter. No, but suppose I have a particle that is completely non-interacting. How would you produce it? It only interacts via gravity. Can you produce a particle? You can't, right? If it doesn't interact, to produce something, it has to interact with the stuff you're colliding or it has via something. Okay, maybe I'll repeat the question and I'll try to answer the way I understand it. So why don't we see heavy fermions, heavy dark matter fermions at the LHC? I think it would be great if we could see them, but if the fermions don't interact much with the standard model, which is kind of expected for dark matter, it would be very hard to produce them there. Does it have to be that way? No, perhaps we would have gotten lucky if we could produce them at the LHC. We haven't, but that doesn't mean that dark matter cannot be a fermion. It's just that its interactions would have been weak. I don't have a favorite. So I wish... I don't have a good candidate in mind, yes. Why would... They don't have to. Photons don't... This is of course a slightly contrived example, but photons are bosons. You can think of many bosons that are non-rat... What would make them collapse, you think? But to collapse, it has to be somehow that there should be nothing preventing... We'll get to this a little bit in some of the examples. You have to have... Gravity just pulling you inwards, and you have to have enough mass for it to collapse. Typically, there is something preventing that from happening. Usually in the case of a field, I'll interpret the question, whether you're asking that or not, is if you have a field, usually there are gradients in the field. Gradients want to spread out, so they push outwards. And that prevents these things from just coming back. There is, of course, virialization. Sorry? Virialization. That's true, but I think if they were completely cold... I thought the question was if they were completely cold. Right. What would happen? Right, let's move on. This will be 10 hours, I think. Sorry, can I ask another related... Can we assume that dark matter field is excitation or dark matter? Let me read it. Can we assume a dark matter field or a potential and a state that dark matter particles are essentially excitations of this field instead of being fermions or both? I think if we... As we all should, if you believe quantum field theory, every particle is an excitation of a field. So I think in that sense, yes, these are excitations of a field. Okay. Let me now say, given all the good discussion we have had and given what I've said so far, I hope I've convinced you to some extent that when we think of light bosonic dark matter, it's not crazy to think about this as a field, a classical field just with particles sitting on top of each other everywhere. Instead of thinking about them as individual particles, and once you start thinking about them as a classical field, wave dynamics comes into play. You can think about linear and nonlinear wave dynamics. You can think about all the wonderful phenomena that fluid dynamicism and other people have figured out, such as interference effects, solitons, et cetera. These kinds of effects, of course, have been seen and have been explored for a long time in the context of condensed matter systems, such as bosonic condensates, as well as in the early universe. So as I said, now coming back to a little bit away from the review part and getting back to my topic. So I want to talk about the spin of dark matter and whether we can distinguish them. Let me tell you that in the context of scalar dark matter, which is spin zero, this has been explored quite a bit. We also heard a talk yesterday about this. People have been talking about QCD axions, fuzzy dark matter, many different names, and people have done simulations of these already on cosmological scales. And this is well explored by now. What we want to talk about is what are the differences if I think that dark matter is a vector field? Why does it have to be a vector? No. Does it have to be a scalar? No. We don't know. Why am I doing it? It's fun. I have no better reason. That's why I do physics. I wish I could tell you this observational exact motivation for this, but there isn't. But there are implications of this, which can be tested observationally. So you could potentially tell what is the nature. So what is the fundamental underlying model that we are going to look at in case of vector dark matter? The underlying model is the following. It's very simple. It's just electromagnetism with a mass added to it. That's it. So electromagnetic field strength tensor, that's G mu nu, capital G mu nu. W is the vector field. I've added a mass term to it. That's what the second term in the action is. And then there is gravity. This is very similar to a scalar field action that some of you might be familiar with. That's the Klein-Gordon action. If you're worried about loss of gauging variance, et cetera, you could imagine that there is a, this is an Abelian-Higgs model. I've integrated out the Higgs, if you want. But this is the model. It's just a massive vector field. And for the moment, I'm only going to consider gravitational interactions, no others. But I want to do dark matter. One of the things we know about dark matter that in the today's universe is pretty non- relativistic. It doesn't move very fast. That means the spatial and temporal scales are slow. There is nothing relativistic about dark matter.  Because I'll get information that I don't need. I will get, so for example, this has a mass. The mass, it's a field. It's a real field. It's just going to oscillate with that frequency of the mass. And that frequency is going to be on the mass scale, which is much higher than the Hubble scale. There is no way I can track that many oscillations numerically or otherwise for an entire Hubble time. So I shouldn't be tracking that. A better thing to do would be to write down the action for the slow degrees of freedom. What I do in detail is you take the real-valued vector field. You split it into a slow part. That's the field psi. And a fast part, which is e to the i m t. I've written down c's and h bars here. I will not refer to them because we don't refer to such things. But I have written them just because talking to different audiences sometimes is useful to have them in there. OK, so the fast part. Can I ask a question? So when we couple a massive vector to other fields, unless we couple it contracting it with a current, we usually introduce a cutoff to the theory. I was wondering when we couple it to gravity, which is going to be important, do we also... In the theory that you wrote down, can I think of the cutoff as in Planck or do I... the fact that I have a massive vector, does that mean I have a lower cutoff? I don't know if for this field there is a lower cutoff. This is just a massive vector field. I guess one way of thinking about a cutoff here is also that I've integrated out the Higgs here. So that will introduce a scale. That's the ultraviolet theory that we began with. But otherwise, I don't think there is... but maybe I haven't thought enough about this. Yeah, I just mean, so if I couple this w... if I wrote down, say, w squared times phi squared, where phi is a real scalar, it means there's a cutoff, and secretly there's a cutoff in the theory. That's true, that's true. But I don't know... I've never seen it... when you couple it to gravity in the minimal way, I was wondering if you knew if there's a cutoff. I can tell you a little bit about it, but maybe if you don't mind, it will take us too far away from the talk. Let's talk a little bit later about this. Thank you. Okay, so I integrate out the fast modes and I write down an action for the slow modes. Is this new? No. This has been done for scalars for a while now. In the case of scalars, this psi is just a complex number at each point in space and time. In the case of a vector, this is just supposed to be three complex numbers. The field is actually real. I'm just decomposing it into this part, and then I'll take the real part eventually if I need to. Surprisingly, this four vectors hadn't been done. I don't know why until recently, but it's straightforward enough. You can also do this for higher spin fields. Phi, by the way, here is the Newtonian potential. What are the equations of motion? The equations of motion for this field are the Schrodinger and the Poisson equation. We've already been introduced to the Poisson equation before. That's the Laplacian of phi equals, you're familiar with it by saying it's 4 pi g rho. The rho here is m times psi dagger psi. Psi squared is your number density. The Schrodinger equation, I'm sure all of you are familiar with, but we have to be careful. It is a Schrodinger equation, but psi does not represent any probability density. There is no probabilistic interpretation here. This is not quantum mechanics. It's the same equation, but there is no probability interpretation here. Psi squared is just a number density. There's no normalization of the wave function here. It's not a wave function in that sense. People sometimes call this a wave function, but I think it's a bad nomenclature to say that. Compared to the scalar case, this is a Schrodinger equation which is multi-component. It has three components here, but otherwise it's the same. You can repeat the same exercise for a spin S field, which has two S plus one components, and the result is the same. This is a very general construction. You can start with the action, but you will end up with a Schrodinger Poisson system if you only have gravity. You could worry about whether in the ultraviolet a higher spin field is well-defined or not, but that's not our concern today. At this level, this is nothing more than just a collection of two S plus one scalars. For a vector, it's just three scalars with the same mass. For those who are interested, here is a fluid version of those equations as well. You can translate a Schrodinger Poisson system into an equation that's perhaps familiar from the lectures on structure formation. You can translate it into continuity and Euler equations and things like that. As always, once you want to understand something about the theory, you should write down the conserved quantities in the theory, because as I'll show you, I do numerical simulations as well, and this is very useful to know these kinds of things are conserved. They're respected by your simulations, and they're respected by the theory itself. Because it's a non-relativistic theory, the particle number is conserved, that's defined in the first line, the energy is conserved, the total angular momentum is, of course, conserved, rotational invariance, but importantly, in this non-relativistic limit, the spin angular momentum and the orbital angular momentum are separately conserved. It's not just the sum which has to be conserved, but they're individually conserved as well, which is very useful for us. Okay, so now let me tell you a little bit about some fun effects about this. My plan here is to do it for pedagogical purposes. I'll first present you with the analytic results. Then I will show you that those analytic results are okay by showing you detailed results of simulations as well. And I will also, for pedagogical reasons, explain the answers to what you would expect from the scalar case. So that's the plan. The first result I want to present is embarrassingly simple, which is great. And this is a result that we should know from freshman or from the first course in waves, which is waves have interference. You take two waves and add them together. Take two scalar waves and add them together. What do I mean by that? The square of the sum will not be equal to the sum of the squares. There'll be a cross term. For a scalar field, this has to happen. You can't avoid this. Now think of a vector field. A vector field has three components. Each component necessarily interferes with the same component from another wave. And if I put two waves into orthogonal components, there'll be no interference. So from this simple argument, you realize that given if you fix a total amount of mass density or particle density in a given region or some average quantity in a given region, then the amount of interference will be lowered in vectors compared to scalars. Does that make sense? You can analyze to a spin-ass field. The more components you have in the field, the less interference there can be because you can distribute the same amount of stuff into many different components, which are orthogonal to each other. I'm showing you a cartoon version below where I have superpose a large number of plane waves. The orange is vector dark matter. The blue is scalar dark matter. The average density is the same in both. You notice that the peaks are higher and the valleys are deeper than the blue compared to vectors because that's what you should expect. Interference is what causes the large excursions. You can do this a little bit more formally, but there's nothing more to it. The amount of interference because you have three components will be down by a square root of three for vectors compared to scalars. You can generalize this as a very difficult homework problem to the fact that this will be square root of 2s plus 1 if you have a spin-ass field. So that's the result there. Next I'm going to tell you about another implication which I really love solitons, so I can talk ad nauseam about these, but stop me if I go off on tangents. Okay. Solitons are these fascinating things that exist in non-linear field theories. Okay. They were first discovered by the gentleman on the horse there with a top hat. He was riding along the canal somewhere near Edinburgh and he saw that a boat came to a stop and created a pulse in the channel. And the pulse, he claimed, he followed it on horseback, did not dissipate. It just maintained its shape and kept on going and he followed it for two and a half miles or something. He didn't use those units and then it disappeared into the woods. And that was a discovery of a soliton in water waves. This is the type of soliton. The theory was developed later. So on the top you're seeing the recreation of that same event done more recently in the same canal. Let me see up there. By the way, solitons, this is not just a curiosity, they're definitely seen in fluid dynamics. They've been seen in optics, hydrodynamics, both are in certain condensates. The green things are places where they've seen them. We would love to see them in high energy physics and cosmology. There are many ideas, many theories proposed that they should be there. We haven't seen, we don't have a detection of them in any form yet. It would be great to have them. Okay. We're going to be talking about a particular class of solitons which are called non-topological, which means they are not, so the solitons generally, why do they exist? They exist because some two opposing things are preventing them from dispersing or decaying away. Something holds them together. Sometimes it's topology. Other times it's nothing to do with topology. It's to do with the configuration itself. When it's got to do with the configuration or there's some conserved charge in them, even approximate, then they're called non-topological solitons. For our purposes there are two types, those that are held together by gravity and those that are held together by self-interactions. There's a long history of this. I won't bore you with the details. But these things, if you look at the real field inside them for each component, it's just oscillating up and down. This is very weird. You would think that they would just disperse away. But some sort of attractive interaction is holding them in place and preventing the gradient pressure that would try to push them apart. So that's what's holding them together. We keep on doing this for a very long time in some cases for cosmologically long time. The scalar solitons here have been known in the literature for a while. These are sometimes called boson stars. They're basically a collection of bosonic particles, a coherent collection of bosonic particles. The real valued field is oscillating inside. The density profile just looks roughly like a Gaussian. You can describe the solution, the non-relativistic part of the solution with the help of this profile times e to the i mu t mu, you should think of as a binding energy per particle, whereas m is the mass of the boson itself. I think something that's important is that the total mass of this object is m-plunk squared over m. That's the coefficient that appears. M-plunk is a huge number. m, which is the mass of the boson, is a very small number. That means this mass is a huge number compared to just the mass of the particle. So it's a macroscopic object. It's not at the level of a quantum. It's a macroscopic object. The same is true for the radius. It's a macroscopically sized object. The thing that's determining why it's macroscopic in terms of the radius is this ratio m over mu. m is the rest mass. Mu is the binding energy for a non-relativistic particle. The binding energy will be very small compared to the rest mass, so the radius will be very big. Even though that ratio is going to be small, it doesn't affect this m-plunk squared over m very much. Good. What types of solitons do you have now that I've told you about a scalar case? You said mu is a free parameter. Sorry? Mu is a free parameter. Mu is a free parameter. You have a one-parameter family of solutions. For any mu, you have a solution. So there are many masses and there are many radii, meaning for a given mass, there's a given radii, but there's a whole family of solutions. Thanks, Bertha. Yes? I mean, it's numerically known, but it's at the level of one ordinary differential equation in the sense that it's just if you have a shooting solution. And if you wanted it, there are very good analytic approximations to that, but there's no, it cannot be written down in terms of simple functions. No trig functions or something like that. You can't write it down. The question was about the form of size solution of the UNX. Sorry. I will repeat from now on. Otherwise, Merda, you can throw chalks at me. Okay. So what do you do for vectors? Now it's simple. You already know about the scalar case. You have to do it for a vector. You just take the scalar solution and get it by a polarization vector. Done. That's your vector soliton. You know from electromagnetism, you can think of polarization in terms of circular polarization and linear polarization. Those are your bases. So let's think of the epsilon that I've written, multiplying the profile or multiplying the full solution as one of those. So linearly polarized one is the first one that's written up here and I'm showing you what the real-valued field would do inside. It would just oscillate up and down. The vector would just oscillate up and down everywhere. So it's pointing this way and just going up and down. For a circularly polarized one, at each point the vector field will be moving in a circle. So these are two possible polarized solitons which are only possible because of the vector nature of the field. For a scalar, there is no such quantity. There is no polarization to talk about. Yes, please. Is the polarization not a dynamical variable? No. I mean, dynamical in what sense? Sorry? Chalk, man. Chalk. So the question was is polarization a dynamical variable? Maybe I should answer more carefully. Here, epsilon being a constant provides a solution. And all solitons that we know of come with epsilon being a constant. All solitons in this, they don't depend on time. There could be higher energy states or some other configurations where this epsilon would also vary with time. So general solutions could of course vary. But for solitonic configurations that I'm talking about it's a constant in space. And time. Okay. Can I ask a question? Yes, from the nebulous internet. Yes, sorry. I'll turn on my camera. I don't know if you can see me. So these objects are stationary and the other hand I guess we want to identify its constituent particles with some kind of very realized velocity. My question is can I still interpret different polarization vectors as transverse versus longitudinal? I would not do it at the level of individual particles. I would do it at the level of the field itself. It's not, I think we've already taken the non relativistic limit where I can't, I've integrated in some sense I've dropped all scales relevant for the individual particles at the Compton scale. The other reason I wouldn't think of this as transverse and this is transverse with respect to what? This is not a massless particle. There's no sort of fundamental direction I can talk about. So here when I say transverse is longitudinal polarization and transverse polarization in that sense but with respect to what? With respect to some axis that I pick. It's an arbitrary axis that I picked. It's not something inherent to the particle that I can pick. Hopefully that answers the question. Sorry but so if a particle has a small velocity at the level of the particle if it has a small velocity I think it still makes sense to think about transverse as longitudinal. But this is a massive particle right? What is the unique how are you going to split it uniquely? You can talk about it if you want. So the longitudinal polarization would be the one which is in parallel to the three momentum and the transverse would be short. I think if you want to do it at the level of the particles that's perfectly, I'm not saying it's not impossible but I don't see a big benefit to doing that at least in what I'm going to say. I'm not saying it's not possible. It's also I don't think about it this way. It's just because you're when so many particles are sitting on top of each other forming this field I find it almost becomes confusing to think of each one of them having an independent identity. The other question you asked which I did not answer which was about realization and so on the velocity dispersion for this is roughly the inverse of the length scale of the object here. Okay. There is also a question in the Zoom asking how the scalar and vector dark matter are getting related to the scalar and vector soliton. So scalar dark matter is being organized itself into scalar solitons. Vector dark matter can organize itself into vector solitons. So they are not, it's not that solitons are all of dark matter. It's just these are configurations possible within specific classes of dark matter. Okay. Let me move on. One of the important things that comes out of these solitons, vector solitons is that they can have spin angular momentum. You can calculate the spin by taking a cross product of the polarization vectors and for the linearly polarized one it has zero spin for a circularly polarized one it has a spin equal to h bar times a particle number. Again particle number you can just get by integrating the mass over the mass of the soliton getting the total mass of the soliton if you want. So this can be because the mass of the soliton is big and mass of the boson is small this ratio can be macroscopically large or really big. It's just a number of particles. So that's why these things I got really fascinated by this, that this has an object with a gigantic macroscopic spin. Not big enough to make it elliptical. Not big enough to make it elliptical because in the non-relativistic limit gravity knows nothing about spin. It's just a collection of three scalars so it doesn't know that there is an angular momentum that gravity cares about. So it doesn't in a full GR case it will care. In the non-relativistic limit no. Yes. By the way these are two examples of these solitons. You could take because both of these end up having the same total energy for fixed particle number that means I can take linear super positions of these guys and create a fractionally polarized object. So I can take I can put this basis solitons together in appropriate coefficients and create a fractionally polarized object which will have a spin between zero and this maximum value. And all of these configurations have the same total energy. Yes. If you are only using Newtonian gravity none. Okay. If Newtonian gravity is your only probe far away you cannot tell the difference. It's the same. It's exactly the same as it is for scalars and it's the same for each polarization. So the question was that from the point of view of a distant observer is do different spins have some implications. Thank you. See if I was taking an exam I would fail. Many times over. Okay. Yes. Yeah. You can take think of it that way. Projection. Projection along the Z. I mean here I've taken them to be along the Z axis. Okay. One thing I want to make sure I mentioned right is that this so these solitons are new. The ones I've talked about essentially this we found them in the last year you would think this is such a simple thing why hasn't been this has been just in literature these polarized solitons with macroscopic spin. I suspect and I don't know for sure of course is that we were misled perhaps by symmetry. So the simplest configuration you could think of perhaps at the vector field which would be spherically symmetric not just in the mass density but also in the field configuration. You would think that the field should also point radially outwards or inwards. That is a simplest symmetric situation you could think of. But if you think about it a little bit if it's a vector field and it's either pointing in or out then it has to go to zero at the origin. How will it choose which direction to go in? It cannot be multi-valued. That means that the profile of the soliton if it was a vector that was pointing radially outwards has to have a node at the origin. You perhaps know from quantum mechanics that solutions with nodes usually cost more energy than solutions without nodes. So this gives you some intuition for why even though this is a perfectly good solution it might be a higher energy state than the ones I've been discussing whose profile doesn't go to zero at the origin. It's a nice Gaussian profile. So these the hedgehog ones the ones that are all pointing outwards porcupine one they've been known in the literature. They're often called pro-castiles. Those are fine. They seem to be higher energy than the ones we are discussing here. In simulations the ones we have done we have only seen these objects forming the lower energy states not the hedgehogs very easily. It doesn't mean they don't exist. It's harder. I should also mention a caveat that everything I'm talking about is a non-relativistic limit. If I do a full GR case where I'm getting close to compactness of neutron stars and so on we haven't done that yet. So there are some questions in the chat. Do you take them now? One is that why do you assume or do you assume that the spins are aligned in this solid or is there a reason for them to be aligned? The other one is why doesn't this boson star collapse because of gravitation and form a black hole? Let me answer both of them. They are very relevant questions. The reason it doesn't collapse is because there is a gradient pressure. The field wants to disperse off because of gradients. You can think of this as gradient energy or gradient pressure. Sometimes people call it quantum pressure. I don't like the word, but it's just gradients wanting to move outwards. Gravity is trying to pull you in. There is a balance between them if you want. It's a static solution between the two. This is the usual case of why stars exist. Something is pushing out. Gravity is usually pulling in. The same reason stars exist. These boson stars also exist. It's a pressure associated with gradients. The other question was about what do I assume the spins are aligned? No, I don't assume they are aligned in the sense that for a soliton solution what I mean actually this polarization vector that you see on the top for a minimum energy solution the polarization vector is a constant in space which means the cross product of it will also be a constant in space at every point in space. In that sense the spin density at each point is pointing in the same direction. It doesn't matter whether it's linearly polarized, circularly polarized or a combination of them and you will see that there's nothing deep about there being a constant spin density. You take a collection of three fields put them together in a configuration with having the same profile unless they're perfectly in phase you will end up generating a spin density. Let me just tell you what we have said so far. I've told you that there are solitons in scalars. There could be solitons with higher spin so it's extending a new axis in this plot. How much time have I taken? I have already taken it? Wow, okay. I will speed up a little bit so and we'll take a break maybe after 10 minutes from here so that we we recover a bit and then we'll start over for the next 15 minutes if that's okay. So let me give you some phenomenology for these. Sorry, the numerical phenomenology that will be connected to what I've just said. This is I think perhaps the most fun part. So notice that I've got two panels on here. The first part is the first row is a simulation of vector dark matter. The bottom row is a simulation of scalar dark matter. The colors are the mass density, projected mass density. I start both simulations with the same initial conditions in terms of their density. There are some idealized halos, in this case they're solitons themselves. And I let this go. There's a full 3 plus 1 dimensional simulation. You and some of the first ones that have been done on this so you start this you move this forward and you notice at the end of it the time is running towards me at the end of the simulation you see some very similar structure. There's some dense region in the center with some fuzzy stuff around. I don't know if the screen is allowing it but hopefully you can see some differences between the two. Slight differences. Anybody want to take a guess what the differences are? Let's not look at the boundaries too much. Let's look doesn't have to be in the center. Yes, go ahead. Exactly, interference patterns. Here we see more interference in the scalar one. Look, there are more dark and bright spots here compared to the one on top. This is what we should expect. This is exactly what we see. There's also detailed information about the soliton but you can't see it on the screen. So let me tell you about the detail difference in the central regions. So the scalers here I'm looking at the final result of this merger process of the polarizations. By the way, I should tell you that you might have a question about what are the what do I choose for the polarization of the vectors and all of these things because vectors have so much freedom. We do lots of things meaning we choose random polarization vectors, we choose unpolarized cases, we do basically do 100 simulations with all different initial conditions. And we will compare when I present you the results it's either an average of them or all of the simulations together. And then I plot the average, yes. These are two simulations for the same mass of the particle itself. But if I change the mass I would imagine that the interference pattern would be affected because of the variety of elements. Does that make sense? If I give me a few moments we'll exactly get to this point. I'm just worried that when you say that this is vector the scalar and the scalar are more interference. Could it just be that I could see a different scalar with a different mass with less interference and mistake it for a vector? I will try to argue that there is a degeneracy that can be broken. But certainly it's a very valid question. But we are just getting in a couple of sites we'll get to this. I did not repeat the question. The question was whether there is a degeneracy between scalar and vector interference patterns depending upon if I am allowed to choose different masses. Okay. So here I'm showing this for the same mass of the particle same total initial mass. Everything is the same. As much as I can make it. And you notice that in this simulation the profile, the density profile this is angularly averaged is different for the two cases. The vector case is in red. The scalar case is in blue. The vector case is as you can see is shallower in the center compared to the scalar case. The scalar is allowed to get more dense in the center. Another important thing hopefully you notice is that far away from the core they start looking similar. It doesn't really matter whether it's a vector or scalar. You might be worried that I won't know what the initial mass of this is. Here I it's very idealized simulations where I know the initial conditions perfectly. What if I didn't know the central core? Well if you normalize by the central core density done over many different masses you notice that there is a difference in shape as well. The difference in shape is that the transition from the inner region to the outer region for vectors is smoother than that for scalars. I cannot give you a full analytic argument for this but it's very it's basically because of interference again. There are three components that don't allow you to have a very distinct region between the two. Just some confirmation about interference here is a density pdf or a histogram of densities in my box you notice that the scalar case which is in can go all the way to zero densities but the vector case doesn't it can't have that much interference. Similarly the excursion at the high density regions is more for scalars compared to vectors this is again coming from coming from interference or it's basically dominated by a central soliton. By the way I should have mentioned that the central if you can fit the shape of these profiles very well in the center to help by taking a soliton profile that's why I'm saying that there's a soliton in the middle. So there's a central soliton profile that fits very well and then the outer core. Sorry to butt in from the sky why do you have solitons as initial conditions? Very good question because it was easy to do I will talk about because I know the solution it's easy to start with I will talk about formation mechanisms and I'll tell you what other people have done where they don't sort with solitons as well the whole idea here for us was to do a control simulation where we could tell the difference very exactly when we start with identical conditions and this was the easiest thing we could do but we don't have So ideally would you want to start with some Gaussian distribution? I'll get to it I'm not sure if I will but I might not get to it but I will at least you can look at the slides and I talk a lot about formation in the second half of the talk which will not happen Okay here is a picture of the correlation length of these interference patterns so just a two point correlation function in density and what you find is basically normalized by the central density you find that it's the two point correlation function sits exactly on top of each other which means that they have the same de Broglie length whether it's scalars or vectors so this Asim is going towards answering a bit of your question they have the same de Broglie scale here why? because this de Broglie scale is just a gravitational thing it's 1 over mv for the same mass they will have the same de Broglie scale it doesn't matter whether it's a vector or a scalar it's just a smooth potential that determines the scale however because of interference the amplitude of the interference pattern or the amplitude of the fluctuations is going to be lower for vectors compared to scalars the same de Broglie scale but different amplitude for scalars versus vectors that's how you can tell the difference so one example that I really like which is very recent and we'll change the mass I think the delta rho over rho has to be the same regardless of the delta rho over rho it typically is of order unity this is just an interference pattern on top of a smooth smooth thing it's just a difference between vectors and scalars will be 1 over square root of 3 that's to say it's not a statement about the nature of the field or anything right it's just okay I will skip this in view of time if you don't mind let's take a I'll take a 5 minute break because we've been going on for quite some time and I cannot imagine anybody's attention given that I'm giving the talk and I'm bored I'm sure you are as well so let's take a 5 minute break and then we can continue if that's okay