Inlong-aided skulls, along with their origins, are undoubtedly one of the most heavily debated areas within modern archeology. Many independently funded researchers who have explored and subsequently exposed vast arrays of unusual and as yet inexplicable features surrounding a particularly few examples of these intriguing and incredibly puzzling artifacts. For regardless of known head-binding practices, a well-studied and historically an extremely common practice, thus one which modern science has an extensive understanding of, including the effect this had on the shape of the skull, makes any skull which endured these traditions are easily to identify post-mortem. The most commonly found incorporated wooden boards pressed upon the head, creating large flat areas along the frontal lobes. Pressing the brow area of the skull upward, this malformation creates a crease or bulge near the normal napping areas of the skull, as seen in these photos of remains currently claimed as a suspected alien found in Croatia. Yet due to this knowledge of malformation, we can easily identify that it is indeed of a Homo sapien. This so-called crease is easily identifiable upon bone structure. However, as previously mentioned, there exists a particular few whose remains not only have an elongated cranium, but the individuals in which they belong not only possess said craniums undeniably formed via natural processes, but are identical in appearance to millions of witness testimonies describing what we all now know as the Greys. With huge eyes, long wide craniums, frames of a tiny stature, and micro-thin pelvis, remains of tiny humanoids, possibly visitors to our planet, who may have crashed here, subsequently marooned upon our planet, is an account which has been told before. We have in the past explored the compelling story surrounding the Dropa disks, an ancient upark that, according to a number of individuals who have examined and tested them, tell this exact tale. Long barrows, granges, earthworks, and hinges found across the United Kingdom all have rumors surrounding long-headed skulls being covered up after having been found at the sites. Passionately protected from trespassers, a vast number of the largest barrows have never been opened. 5 tons stones blocking the entrances, clearly suggesting they are buildings of tremendous importance, but without enormous multi-million-pound machinery, permits, and most importantly permission from the landowners, conveniently all these incredible undug sites are set on private lands. We will probably never find what's inside, but many rumors abound, like those which circle Bella's nap, tales which tell of more elongated skulls exhumed from the surrounding earth during a normal archaeological exploration. Yet regardless of this seemingly meticulous suppression in the UK, an incredible find has nonetheless been unearthed in Crimea. Many of the intriguing features of the remains are the same characteristics which gave rise to the elongated skulls of Peru's popularity. But this skull still possesses its tiny complete skeleton. The eye sockets which once housed the creature's eyes were enormous, and although the entire frame of the creature is of a small size, the lack of a pronounced pelvis would have made them very slender and would have emphasized the size of the cranium. It is a strong candidate for the only complete elongated skull remains in existence. We find the elongated skull highly compelling. The ancient ruins of Giza, perhaps the most incredible of them all, and possibly the clearest displays of academic conspiracy, with much of the most puzzling of areas, all but closed off, away from public view, an attempt to stifle controversial questions which inevitably arise from such baffling ancient wonders. However, this attempt to obscure the greatest aspects of ancient Giza just fans the flames of curiosity. For when one realizes that much of ancient Egypt is being actively covered up, so-called officials avoid any obligation to explain the methodology. Behind many constructions found on the plateau, structures and relics, which to this day escape any logical explanation. Once one accepts this reality, one begins to wonder what unspoken motivation there could be to ardently hide these sites' true characteristics. We have in the past covered many areas of ancient Giza, which cannot be explained. Many people are aware of the issues surrounding the construction of the pyramids, and the largely exposed void in modern understandings. However, this conundrum is but one among a smorgasbord of highly intriguing, yet no less mystifying features hidden in plain sight all over the plateau. The basalt floor, which still contains volumes of tool marks, evident of high precision, high rotation ancient power tools. The gigantic megalithic blocks, each sunk flat, level with the base of the pyramids, which although walked over by millions, have been largely overlooked by all. Some of these blocks, forming the immediate foundations of the pyramids, are similar in size to the pregnant woman of Balback, which is estimated to weigh some 1,000 tons. Additionally, all of these features, according to mainstream teachings, were created by the ancient Egyptians. A civilization we claim merely re-inhabited the site, like many others around the world. It is a fitting hypothesis, which if indeed the case, then all said tasks were undertaken and masterfully accomplished with nothing more than a set of soft copper tools. A clearly illogical hypothesis, disproven in many ways, one of which is by the main pink Aswan granite relics, still in existence all over Egypt, which were all simply impossible to have created with just copper chisels, and our next artifact of interest is of no exception. This imposing altar was found at the west end of a passage, just outside the northern wall of the temple of King Amenhamhat I. Originally, it is presumed that the altar once stood in the open court of the temple, with its roughly shaped lower part, suggesting that it was sunk into the ground. A rectangular libation basin is carved into the top of the altar, as well as representations in flat relief of an offering mat containing two libation basins and three loaves of bread. The middle one incised with the king's throne, with the name Horus added, with the phrase May he be given life forever, uncannily similar to long live the king, but I digress. At the center of the altar's front side, the incised birth name of the king Amenhamhat, with rows of approaching fertility figures who are designated by inscriptions as Personifications of gnomes, regional governorates of northern and southern Egypt. It is undoubtedly an incredible ancient artifact, one carved with such precision and artistic accuracy and upon some of the hardest stone on earth, to suggest this was achieved with soft chisels is to us absurd. Who made the altar of Amenhamhat? How did they carve it? An exquisite ancient relic, which is, like much of ancient Egypt, highly compelling. There are many ancient monuments found all over the earth, which possess extraordinarily precise solar and lunar alignments. In genius designs, often many thousands of years old, constructed from stones sometimes quarried, cut and transported to the sites from many miles away. This movement of megaliths was accomplished using techniques or technology as yet not understood, and to date, many of these megalithic stone placements are perceived as near-impossible feats of ancient engineering. And although many impressive examples of monuments which track the sun can be found to have originated from many different civilizations, the most notable of antiquity, most famous for a seemingly obsessive level of monuments devoted to the observing of the sun's path was undoubtedly the Neolithic. It has to wonder, why was there such a fixation? Was the motivation for this mass of undertakings of a tragic nature? Was it out of fear, fear created by a memory of a catastrophic event, possibly involving the sun's powerful emittance of radiation? Maybe they experienced the consequences of an ancient warming cycle. We may never know, yet the most important question in our field is not why these volumes of solar-aligned relics were created, but how? How did our ancient ancestors, claimed as having existed over 10,000 years ago, construct such precisely positioned granges, hinges, barrows, and sun daggers? Something we have previously covered, an incredible type of sundial which tracked a sunspot across the wall of an ancient cave with each month, solstice and new year precisely marked out across the walls. The sundials in question in this video are a group of far more familiarly designed dials left by the Neolithic. These sun-tracking dials can be found across the Neolithic sites of Ireland, Scotland, Orkney, and England. First discovered by an American by the name of Martin Brennan, a 39-year-old from New York. Not only did he discover the true function of curb stones located in Noth, codenamed K7, K15, among others. He also cracked the earliest form of writing while studying the Irish Stone Age artwork. Earlier this year, a theory emerged on the internet by writer and journalist Ben Gagna. He suggested that there was an image of a swan on Curbstone 15 at Noth. He claimed that while examining a photo he had taken of K15, he flipped it upside down and saw something no one had ever seen before, the faint but unmistakable image of a swan in profile. The true meaning or purpose of the curb stones had for a long time been heavily debated within certain circles. The intriguing cup and ring marks had been known of for some time. Yet as previously mentioned, though the most popular theory of the design on K15 was the claim that it was the depiction of a swan glyph, this hypothesis was rejected Even before Martin's unarguably accurate translation was discovered, Martin identified the sundial while examining a passage mount in the Boine Valley. And although sundials thousands of years old have been excavated throughout Europe, many specialist individuals reviewing Martin's finds believe that the sundial discovered in County Meath is the oldest and possibly most important ever found. According to Martin, who has been studying megalithic Irish art for the last ten years, Ireland's megalithic tombs are suffering from appalling neglect. Some of the most important passage mounds excavated previously have been ignored or conveniently completely sealed up. Martin's discoveries are undoubtedly remarkable and are of tremendous value to our ongoing deciphering of ancient antiquity and its past civilizations. It is a journey of discovery we find highly compelling. There are many ancient monuments found all over the Earth which possess extraordinarily precise solar and lunar alignments. In genius designs, often many thousands of years old constructed from stones sometimes quarried, cut, and transported to the sites from many miles away. This movement of megaliths was accomplished using techniques or technology as yet not understood, and to date, many of these megalithic stone placements are perceived as near-impossible feats of ancient engineering. And although many impressive examples of monuments which track the sun can be found to have originated from many different civilizations, the most notable of antiquity, most famous for a seemingly obsessive level of monuments devoted to the observing of the sun's path was undoubtedly the Neolithic. One has to wonder, why was there such a fixation? Was the motivation for this mass of undertakings of a tragic nature? Was it out of fear, fear created by a memory of a catastrophic event, possibly involving the sun's powerful emittance of radiation? See they experienced the consequences of an ancient warming cycle. We may never know, yet the most important question in our field is not why these volumes of solar aligned relics were created, but how? How did our ancient ancestors, claimed as having existed over 10,000 years ago, construct such precisely positioned granges, hinges, barrows, and sun daggers? Something we have previously covered, an incredible type of sundial which tracked a sunspot across the wall of an ancient cave with each month, solstice, and new year precisely marked out across the walls. Yet the sundials in question in this video are a group of far more familiarly designed dials left by the Neolithic. These sun-tracking dials can be found across the Neolithic sites of Ireland, Scotland, Orkney, and England. Discovered by an American by the name of Martin Brennan, a 39-year-old from New York, not only did he discover the true function of curb stones located in Noth, codenamed K7, K15, among others. He also cracked the earliest form of writing while studying the Irish Stone Age artwork. Earlier this year, a theory emerged on the Internet by writer and journalist Ben Gagna. He suggested that there was an image of a swan on Curbstone 15 at Noth. He claimed that while examining a photo he had taken of K15, he flipped it upside down and saw something no one had ever seen before, the faint but unmistakable image of a swan in profile. The true meaning or purpose of the curb stones had for a long time been heavily debated within certain circles. The intriguing cup and ring marks had been known of for some time. Yet as previously mentioned, though the most popular theory of the design on K15 was the claim that it was the depiction of a swan glyph, this hypothesis was rejected even before Martin's unarguably accurate translation was discovered. Martin identified the sundial while examining a passage mount in the Boyne Valley, and although sundials thousands of years old have been excavated throughout Europe, many specialist individuals reviewing Martin's finds believe that the sundial discovered in County Meath is the oldest and possibly most important ever found. According to Martin, who has been studying megalithic Irish art for the last ten years, Ireland's megalithic tombs are suffering from appalling neglect. Some of the most important passage mounds excavated previously have been ignored or conveniently completely sealed up. Martin's discoveries are undoubtedly remarkable and are of tremendous value to our ongoing deciphering of ancient antiquity and its past civilizations. It is a journey of discovery we find highly compelling. In our last video, we explored compelling links, connecting the countless megalithic ruins which litter much of the world, long claimed as the work of separate stone age groups who, due to the claimed era of construction, supposedly never made contact. Flint-wielding ancestors attributed with inexplicable trilithons many tons in weight, incredibly precise alignments and an impressive, intimate knowledge of some of the most complex of solar orbits known to man. We posited that regardless of the claimed isolation of these separate groups, the similarity found among many megalithic buildings is unarguable evidence, suggesting that Neolithic man either didn't create these structures or they were not the primitive nomad they have long been claimed as, but were instead a world-going, world-dominating superpower who built the same enigmatic barrows and henges the world over, the Harhoog. These mystifying Neolithic structures are conveniently rarely explored, this may be due to their existence being a difficult task to explain. And as that of tombs, it is the sheer number of them, however, which makes their existence a baffling thing to explain. As mentioned previously, many of the building types dating from the Neolithic age turn up on more than one continent, yet the Harhoog and its once enormous collection of over 600 individual so-called tombs are unique in their shape and style, currently claimed as having belonged to the ancient settlements of the funnel beaker culture who lived around 3000 BC, and although, as mentioned, there were once approximately 600 of them, the Harhoog have been getting actively destroyed since their rediscovery in the modern age, with over half of them now having been destroyed to date. The megalithic tombs are built with large, rough stone slabs, each arranged into different random patterns. Ernst Sprakhoff, who created the six-category classification for Neolithic dolmens, classified them as extended dolmens. The other five types are simple dolmen, great dolmen, assaged grave, longbarrow, and cyst. Discovered in 1925 during excavations of earth, for the construction of the Hindenburg Dam, they were regardless, largely ignored, and have been little investigated since, with a brief archaeological inspection having took place in 1936. The Nurhag, a stone structure with a similar enigmatic, yet unique and once in equally numerous ruin, is a stone age dwelling we have previously covered. Found on the island of Sardinia, they are the main type of ancient megalithic edifice found in Sardinia, yet rather differently to the lack of attention given to the mysterious Harhoogs, the Nurhag have come to be the symbol of Sardinia, and indeed its distinctive culture. And dwarfing the 60 Harhoogs, more than 7000 Nurhags have been found to date, though archaeologists believe that originally there were more than 10,000. And this could quite possibly be the case with the Harhoogs as well, for in reality, no one can say for sure who built them, why they built them, or perhaps most importantly, when in human history this took place. Although little is known regarding the Harhoogs, they are undoubtedly an incredible collection of stone age relics, ones which we find highly compelling. Over the past few weeks, the channel has been focusing on the many neolithic ruins which can still be found littering our planet, enigmatic earthworks built in a bygone age supposedly by our primitive, flint-wielding ancestors. Enormous ancient undertakings, like that of the long barrows or solstice-aligned mounds such as Newgrange. We also explored dolmens, found the world over along with many other recurring neolithic features. However, there still remains many as yet unexplained, yet clearly excellently executed ruins that due to the capabilities of their past constructor, fortunately still exist to this day. Ancient supposed neolithic ruins, such as that of the effigy mounds. It seems, regardless of the gigantic effort these would have once been for currently claimed architects, these effigy mounds, such as that of the great serpent mound of Ohio, the largest surviving mound of this type, were created merely for entertainment purposes or perhaps as an offering to the gods. We are, in the modern age, fully aware of serpent worship, once undertaken by ancient civilizations across South America, and due to these already understood ancient belief systems, the possibility that these unexplained mounds may have been religiously motivated becomes a logical postulation. The great serpent mound is 1,348 feet long and runs along the landscape continually 3 feet high. It is claimed by some as neolithic, yet no one seems to be able to definitively determine its age. A prehistoric effigy, located upon a plateau aptly named Serpent Mound Crater in Adams County, Ohio. Now maintained by the Ohio history connection, it has been designated as a national historic landmark by the United States Department of Interior. The Serpent Mound of Ohio was first reported from surveys by Ephraim Squire and Edwin Davis in their historic volume, Ancient Monuments of the Mississippi Valley, published in 1848 by the newly founded Smithsonian Origin. We feel, due to its inexplicable nature, archaeologists will continue to find these incredible relics difficult to explain. As such, the origins of the mound are still heavily debated. The mound, like many other ruins we've covered, we posit were in fact left by a civilization far older than currently conceived, and as such, like the many similar sites and ruins we have explored, contains no archaeological artifacts, no burials, and no dating material, leaving academics with no later inhabitants to pin the site's construction on. As such, they remain incapable of establishing a permitted claim as to the age of the mound. The two main funded theories are that it was either created by the Edina culture around 320 BC or the Fort Ancient around 1070 AD. However, these claims are both light in regards to any compelling lines of deference to argue said hypothesis. Archaeologists began attributing the mound to the Fort Ancient culture within the publication of Serpent Mound, a Fort Ancient icon, in 1996. A 2017 article, Radio Carbon Dates Reveal Serpent Mound is More Than 2000 Years Old, argues for a construction by the Edina culture, circa 320 BC, yet any solid data to confirm said claims remain elusive. The academic debate regularly experiences rebuttals, with each published in the Mid-Continental Journal of Archaeology. Who built the Great Serpent Mound, or indeed the effigy mounds as a whole? Were they, as we claim, the work of a now lost, serpent-worshiping civilization? Just like that of South America's inexplicable ruins, we find the evidence to suggest such highly compelling. Among the beautiful Greek islands, there is one in particular, Uboa, which hides a secret, one of the most enigmatic mysteries to be found anywhere within the Mediterranean. Built into the landscape of the island, 25 ancient yet masterfully built and geologically camouflaged structures, which are known as Dracospita, or the Dragon Houses, still found dotting the island's landscape. Often built using enormous, multi-ton limestone blocks, thus making their explanation very difficult to explain, and also quite possibly multiple remnants of a now lost but once technologically and capably advanced civilization, one which far predated that of our own well-known, well-studied ancestors. The true age, origin, or indeed past function of these mysteriously, curiously named Dragon Houses, remains a complete mystery. Now found in varying degrees of decay, yet the substantial erosion present in some areas of some of the Dragon Houses is indicative of a civilization far predating any known or more specifically academically permitted groups as having once been responsible. Researchers working for Ancient Code have posited that many of the surviving Dragon Houses were built using quote, Cyclopean masonry, and after exploring the curious structures ourselves, we seem to concur with this opinion. Just the mystery as to why these buildings were made in the first place, the motivation for their curious creation still remains. According to said research, the locals dubbed the structures Dragon Houses, this because local legend telling of attributes in which their creators possessed they were supposedly bestowed with superhuman powers. This conclusion however is disagreed with, and rather ironically, using the exact same feature which proved these buildings are inexplicable. Others now argued as having been inspired by later rediscoverers due to the size of the stone blocks used in the building process, something modern academia due to a lack of an ability to explain said anomaly would simply ignore this aspect during their own explorations of the site. It seems that although those funded to provide the answers, when found lacking, are more than happy to continue to provide a status quo, often in blatant denial of facts in front of us all. A tale of events which does not ruffle the feathers of those who fund said research, thus such practices can be looked upon as job security, displays of allegiance to those who pull the strings of said institution. Thus, although capable, funded individuals have a reoccurring habit of overlooking the same said features over and over again. However, those with other often self-funded motivations, or indeed a set of sturdy foundational ethics, then those with a keen eye for facts can always expose that which is ignored by others with an agenda. These valiant pioneers, these modern-day Indiana Jones, have an opportunity to approach that which has not yet been explained with curiosity and a hunger for the truth, which could make them the person who alters the world around them, and ultimately makes a real difference to the world around you. Wikipedia states, �Dragons can not only mean a reptilian fire-breathing giant lizard, but also man, those who possess superhuman powers.� Furthermore, according to Wikipedia, there is no accepted theory about the identity of the builders, nor an agreed estimation on their dating. No mention is identified in classical texts, and the first account so far known to have been cited dates from the 18th century, done by the British geologist-traveller writer John Hawkins. The first detailed account after Hawkins was by German archaeologist H. N. Ulrichs, written in 1842. The French classical scholar Jules Girard visited Uboa and described the Ochi Dragon houses in detail. In 2010, Swiss archaeologist Carl Reber successfully tracked down all to-date reported buildings, subsequently published a report upon the completion of his research. Yet, alas, any explanation as to their original purpose, or indeed true age, was predictably lacking from the report. Thus, the site is currently crying. Capable antiquarians are desperately needed to explore and unravel the mysterious Dragon houses of Greece, houses we find highly compelling.


So, yeah, welcome box office if you assume anything related to popcorn. This is not the right Presentation, I'm sorry. What I'll talk about is putting LibreOffice into a sandboxed XDG app Bundle, if you happen to be at Guarek this year, then most of it will sound familiar I gave Pretty much the same talk back then This time I'll concentrate more on the part that we as LibreOffice will have to do to make this wonderfully working reality So Maybe some of you even haven't heard yet about what XDG app actually is It is an initiative that The year started a while back It's hosted in the GNOME or rooted in the GNOME and free desktop as the name Communities and tries to address two Goals or reach to goals One thing is to make it easier for developers to produce binaries that will run On arbitrary Linux distros so that you just build it once And then run it everywhere and not have this problem of having to deliver it for various Various Linux distros The other aspect is There's so much software out there From people some of you might you might know them others you have no idea about Who they are what they wrote why they wrote that actually if there's anything bad in there On the way to you maybe somebody put something bad in there so you want to have some some security and in downloading something from the internet and running it and How to do that of course is to run that app in some kind of sandbox that Shields the rest of your system From whatever that app does so the app is limited in what it can do For us of course that means if we are limited in what we can do We need to Find ways to still let the user do what he wants to do with our app So I'll come back to that later So that's xdg app the broth as you'll know to first concentrate on this part of building Just once Run everywhere So what is our matrix of pain there? most of you know we have Hundreds of configure switches more or less obscure ones we have Close to a hundred external sub modules that we depend on that need to be there in some way on the Platform that we later run on either we bring them with us or we depend on them being available already on the platform We have about a hundred localizations That's also the thing to consider if you want to package some software you just package it for the US market for the globalized Everybody speaks English market or do you go into the individual? Locals and Please actually face your users there So we're famous for being able to Break whatever the same is out there and whatever frame work is out there and Montage created this lovely t-shirt some people even wear it and Yeah, that's this is one more One more a framework where we can see if we can Stretch its limits. So yeah do that As a send for us or for any application that wants to go out into the world be available Publish the source compile yourself as one option, but most of your engines want to have some binary This is especially as we as with our TF heads on now No, we do Mac builds we do Windows builds that's Plain business because there's one target to target. You just need to make sure that Whatever is your base version of Windows or Mac that you want to target when it comes to Linux? It's rather fractured because the Linux world Is not one stable one common API but a lot of different Individual libraries that have their IP eyes and each distril bundles a different set and Use different ways to to deliver software be it our PM lead that Libraries having different still names to link against and stuff like that So what we as TDF do for example is to to produce That and our PM packages for it's 86 and it's 86 64 builds all the distros do that themselves of course anyway for for their versions of LibreOffice But sometimes users do want to use A version that is not yet available. Maybe the distro if only for testing for example So they demand to also have Bills done by TDF of the latest For example So our TDF build is this somewhat crippled or used to be somewhat crippled for example It's been a pain to to update to GTK 3 or to get rid of this old You know VFS, which is a method of Excessing non file system data like HTTP or FTP or whatever some but Centralized common way There's an old implementation a new one and we were stuck with the old implementation Because that was the only thing we could Expect from a baseline that we want to run on which is a very old Linux so Hope is that we'll Reach a point where we can just build once and Be done with it another Thing that my benefit from this is our buy-by-sect repose Which you're also Done by somebody with a fat machine to keep us How's warm in the winter? These people just More or less randomly pick from this matrix of 100 or 300 configure switches So it might happen that by accident They pick one switch to build against the system that on their machine Which then when you download that huge by my second repo then that one Little library has a different name on your machine. So that was one Famous case where you need to with at least one of the repos you need to If you run it on the fedora, you need to rename or sibling one system library into a different name so that then the The library office app will find it and then be happy again But that's unfortunate things that you've done with a huge buy-by-sect report. I want to use it and then find out there's one little Issue that keeps me from from using it if we would use xg app Binary bundles for that and that will be a thing that could have happened by definition so actually try to To stuff the graphers into this framework. How does that look like? xg app as I said is a standardized interface into which to in which the standardized environment Applications run so they do define this very precise API of what is available That's the one point the other when you do want to build such a Application into this framework, then there's of course some sort of SDK Which is all the headers or the libraries that you need that match the runtime environment That is somewhat unfortunately build of some not some But the the next is true about some yokto distro that is mostly aimed at Embedded and has as we then found out with a break every tool chain approach and has some slide obscurities like it's the first Instance where I found a distro that lacks one of the obscure pearl Pearl archived for modules that we need still need during the build because we have this legacy part of the install set creation that is still based on some 15 year old pulse grips help us to Eventually fix that by by removing that Part of our system anyway, what I do from now is just from the outside copy that one Perl module the system both copy that into the the yokto SDK now the point for example that there was no glue library there for the OpenGL that is a Kind of wrapper library to simplify things Good news what that there was Anyway, always the only two places I think in our code base that used it and that could both be removed so we drop one of our hundred external dependencies By doing that anyway one other thing That took a while to debug is that one of our externals that we do include Because it is not available on the on the base that we run on One of them ran in XML config script, which is like package config just especially for lipxml and should give you the command line arguments to link against XML config but in this yokto base for whatever reason that XML config batch script just come is reduced to one line which says exit one So we turn failure so the configuration of our external module I think it was red land that use of that kept failing very strange error statement for now went into the our internal red land module and Patched that to no longer call XML config So with that out of the way Configure and building Does work smoothly so it is able lots of stuff that is not available in Base there and some of it doesn't make even make sense yet For example cups. There's no printing yet from from inside of the sandbox come to that in the moment There's no Java in there so it is able Java so Solution probably if you want to keep Java available for the extensions in LibreOffice you need to bundle a JDK that a JDM into our app Most of the things we depend on from the system we can use the actual system once there is about 30 cases where things are not available in the in the runtime platform but where we have These external libraries bundled and so we use those This is still x11 based Moving forward to our wayland For now it's 11. What falls out of all that then is Not that small bundle of about 350 megabytes. So that's what users will then need to download I'll talk how many languages That's just one Maybe I'll interlude here with a little Demoing of it before I come to the explanation of how the sandboxing actually works So to You then have that Then have that bundle the application bundle can download that you can push that up to application repositories in the internet from where you can download it I've done all that Just too much bandwidth here, and then there's a little Application that is for example already Available in Fedora latest Fedora releases already have this xdg app thing And if you want to run an application Inside it you do this xdg app run and then there's a name for the Application and I was all in colors Surprisingly the process and you can even pass parameters and What you see is that Your average another standard the brothels sandboxed You don't know as much of it from the first view But if you for example want to open a file then There is a file dialogue opening up and you have a home directory Yeah, that's that's the sandbox part home directory is empty We are running as a fake in an environment where you don't have your Normal home directory so this app if it were malicious couldn't modify your data or you can read your data There's nothing much here that we could open we do have And in the root there's an app directory where our app there our installation actually is so if you Know how in the process installation tree looks like this looks familiar. It's just the tree So we might try to Open the license file that's included there and that will work. So Read only because the installation trees is read only So that's not that much Fun for for for actually using a Leero as you could draw your drawings in there for fun And then throw them away because I've been safe to outside the sandbox You can't say inside the sandbox. So when you reopen the office your wonderful drawing that did it last time would reappear But you can't get it out there. So That needs to be changed and there is hope there is change available there's a Feature and I fake that into this Leero office, but that's a otherwise vanilla one. I I Took the feature that we do have two different file dialogues anyway we have the system one and we have the The Leero office internal one which has a different feature set and look the same across all systems I took that out and replace that with one that is the sandbox specific file open dialogue and when I use that one and Now the file open the file open no dialogue looks very different So I have different. This is Kind of mock-up state for how it will look like in the future So this is still all work in progress how to the ECGF framework will look like in the end and So for now you can Navigate into your your true home directory. So here's my documents folder. There's some test ODT I can't see like that And war there it opens I have some debug code in there so What it actually does open inside the sandbox is not nothing in the home directory, but there is a Fuse file system behind the scenes so that maps that file from outside the sandbox into some run user Whatever plays And that's the file URL that I'm using inside the sandbox, but it By a fuse from outside the sandbox is actually the same file as the one in my in my whole dear So Key, this is the same box one. This is bright one Yeah Can you open the same file it sure if it will be Still where there is the test there's a test yeah, it even works for this version. This is a Slightly outdated version. So things are moving quite fast They're at the moment but It's persistent. Yeah So running out of time hurry up a bit the interesting part about the sandboxing For for our bill as I said in the beginning People are not sure about what they download from the internet That's probably not the most the biggest motivation to run the liberal first sandbox But another very real and very important use case for actually sandboxing the brothels is that we do have Bugs some of them still in our code and some of them might be security The risks so if you do have a document from somewhere on the on the internet And you don't trust its author then it might happen that if you open that It could compromise your system.  So that's that's the very real use case for for sandboxing the brothels So how does this you go full screen again So that's how does this? file accessing work so the idea behind all this Getting out of the sandbox or reaching resources from outside the sandbox The philosophy behind how to do that as always There needs to be some code which runs outside the sandbox in the trusted system So it's from your trusted fedora distro That is actually executing some code on your behalf. So you initiate While you're running inside the sandbox you initiate some activity outside the sandbox That can access resources outside the sandbox and because you as a user and not your program behind your back because you as a user in UI initiate that the Sandboxing framework will then open a small little hole That allows that resource to be accessed from within the sandbox. So the the magic point about is The code that actually does the allowing and opening of the channel into the sandbox runs outside the sandbox so that the application can't temple with it and The request to actually do something needs to come from the user and not from the automatically from from the application itself So what's done with this file dialogue that I presented that's a debas in the face from The sandbox to the outside world. You can request to open the dialogue that dialogue goes up in the outside world It's the dialogue that the the application itself can't control because it's a real GUI dialogue that the user has to operate You select a file there. You have the full access to all the files They're just that one file that you select is that made available as a set by a fuse to inside The the the sandbox application That's the the simple idea The way to work Comes the office with all its Ideas of what it wants to know about its environment So simple apps Will be happy with just having that one file We for example want to know About whether some other instance of LibreOffice locked that file Or there's also a feature in Calc to have multiple users work on the same file And then there's some some additional file next to the original to the file itself That records all that information. So we don't want to only have this one file We want to create another file next to that and that's where things start to get interesting and And Way, you need to make sure that your sent boxing Features Make that available. So you saw that the the test document that I opened that opened up and read only mode Because we can't create this lock file next to it There's also The way these files are made available Now it's why a fuse and in a previous instance It was done by a GIO and a special document URL scheme That would have had for us the benefit that When we open some document by a GIO, we know it's from remote So we don't try to create this lock file anyway, so our code paths would already have Taking care of some of the things that we need to now take care of to make it for example available Possible to do to save files. This is for now only file open file safe will be the next thing Printing is a thing that needs to be addressed both in the sandboxing API as probably as well then in our code base So they'll be a number of small Tweaks and fixes that will be needed in our code to make it actually Have you work inside a sandbox? Well, it like a show with that dialogue that was just some some ten lines of code to to swap in Using this special file open dialogue I think in all these cases won't be much work. It'll be little little tweaks here and there another thing That will come up is how to handle these 100 localizations whether to build a hundred different Apps each with one localization or to bundle all the localizations and have a have a app that is even larger than 350 max for the windows for example the windows Install that you download that includes all the languages and then at installation time You just use or choose the ones that you want to put on your artist So that's a precedent for people Downloading that much data anyway and not complaining too much about it So it might be feasible to to to include all of them or majority of them Some other minor issues is like we try to only have I have one instance of the broth is running Why are some protocol of our own listening on some you mix the main socket? This of course is something that is also Forbidden in the sandbox to create arbitrary sockets To listen on them. So but there's also a divas Service to do pretty much the same thing so we can can use that So it's one of the things that just needs a little tweaking and that's It for For me, so if you have any questions, I think it's time for coffee


That it just, you know, comes down to the little things. The team that executes the best in the fourth quarter usually win. And got the tip of our heads to the bills because they did that. You guys have been kind of fighting and calling to stay in this for so long. To have that point of possibility, just all out of your grasp. Is that a difficult thing or how do you think that this team needs to respond to that? It's very difficult, I mean, because that's why we played a game. So I said at this point in my career, I know it's getting closer to the end, but, you know, you come back and play to play a meaningful game, to get to the playoffs, to get the chance, you know, to win championships and play for championships, and we fell short. So it's tough, but we're a young team and this would be a feeling that hopefully everybody in this locker room remembers leaving the field, the bills clenching to play off-berth, and hopefully use it as some type of motivation to get back to this point where we're playing meaningful football in late December, early January, and we'll be the ones, we'll be clenching to play off-berth. You guys have done a really good job over a stretch of games of generating turnover. Why do you think that's the case that you guys have been getting canceled from the ball? I think it's just a combination of good rush, good instinct by players, playing zone, everybody having eyes on the quarterback and just having some really good football players on our defense. That's all it is. Josh was scrambling. He always had a good job with just trying to keep the play alive. He got to the sideline. He just wanted to make a play, and Foe did a good job with just getting the hand on it. Got a hand on it, popped it up. I just wanted to make sure I caught this one, had the opportunity early in the game to catch one, but I didn't. But great play by Foe to put me in a position to create a turnover. Without a doubt, I mean you just think about it, most teams playing in the playoffs and meaningful football, I mean cold cities, cold cities everywhere. I don't know if it's half and half, but you know you got to be able to win games in any type of situation. Range, snow, under storm, whatever it is.  We came out here and we fought. We played hard. We played to the end, but just came up short. We kind of knew what they were going to do. We knew they were going to move the ball, but we knew we had to make them kick three. We just didn't do that enough. As you're out there, you try not to think about it, but it's human nature, because we got them in a couple of third downs. We got them some third and tens, and they were just able to convert. We talked about that. We wanted to get them behind the sticks, and we were able to do that, but just certain situations we weren't able to finish, and it just prolonged the drive. How does it have to be effective in the second half? I want to say clog it up, because like I said earlier, he's a phenomenal player. I mean the growth that he has shown from his rookie year to what I first played him to now is amazing. I just think they did a great job of just going to what was working. The run game was working, the quarterback runs was working, and that's what good football teams do. So hats off to Dayball for just figuring out what they had to do to win the game, and they did that.  At the end of the day, I mean we got the best job in my opinion in the world. We get to play a childlike game for a lot of money, and we have a lot of people cheering for us, and we're a role model to a lot of people. So it's our job to go out there and in the season, the right way, the best way we know how, and that's where to win. And just look to continue to build. I'm really, really just thankful to be a part of this team, because I mean we got a lot of young guys, but we got a lot of young guys that want to do it the right way, that want to fight, that want to get better, and just thankful, truly thankful that Terry and Coach Smith seem to fit, that I come here and help lead, and turn this place into a franchise that wants football games, and plays meaningful football in December and January. Just what you think it said, and this team's been fighting for a couple weeks now, and it's pretty nuts the effort out there. It's just, you touched on it earlier, the lessons you can learn, but you know, there's no moral boundaries, but what lessons do you think you know the team has been fighting for this past year? I just think, you know, kind of what I said earlier, you know, the team that makes the least amount of mistakes is going to be the winners. And I just think, you know, we play well, we play hard, but the bills, when it counted the most, they made the least amount of stakes, and they were ever to be victorious.  All right, thank you. All right, guys. Happy New Year, everybody.


Now the Lagos State Government says it has reached a consensus with the Nigerian port authority NPA, in streamlining checkpoints along the corridors and feeder routes to eliminate gridlock and curb illegal extortion along Apapa-Tin Canaxis. The Special Advisor to the Government Transportation, Oluwa Tony Fainca, said this at a stakeholders meeting or transport unions in Lagos on Monday. Nafayinka said that the State Government would enforce zero-tolerance on illegal extortion and activities of miscreants along the corridor through special mobile courts created to address the challenges. He explained that in streamlining the corridor, illegal extortion points would be sucked as the agencies charged with the role of managing traffic flow along the axes have been clearly defined.


On this beautiful platform of YouTube, we have a whole niche of commentary channels. And basically, in a little nutshell, commentary channels are here to keep other YouTubers accountable. But who is keeping commentary channels accountable? What is up everybody? This is Chris from the Rewired Soul, where we talk about the problem, but focus on the solution. And if you're new to my channel, what I like to do is take a look at what's happening in the YouTube community and try to see what lessons we can learn from them. So if you're into that stuff, make sure you subscribe and ring that notification bell. And while you're at it, make sure you follow me on social media at the Rewired Soul on Instagram and Twitter. I just recorded episode seven of the brand new podcast and I'll be announcing that when it's live over on Twitter and Instagram and all that kind of stuff. But anyways, I was talking about the subject of ignorance versus lying on the podcast and it made me think of the body language expert, Derek Van Schaik, all right? Basically I remembered that Derek Van Schaik's most recent video was reading the body language of James Charles in his apology video to Tati Westbrook and calling him a liar. Now before I get started, I just want to make it clear, I find the technique of body language reading very, very fascinating. I read like the number one book on body language called What Everybody is Saying is from a former FBI agent who was like legit when it came to interrogating people and reading their body language. It's very interesting to me, but at the end of the day it is kind of a pseudo science. If I'm being honest, I do prefer Reagan Wolf and I'll explain why pretty soon, but I think the point of this video will kind of let you know.  Oh my God, James Charles clear of all charges. But it had me thinking. It had me thinking. So as I was talking about Derek Van Schaik and accusing people of lying, I went and I checked out his YouTube channel because I was like, wait a second. His last video was using body language to accuse James Charles of lying. But since he made that video, it came out that James Charles was telling the truth. So my question was, did Derek Van Schaik do one of a few things? Did he take that video down? Did he release another video correcting that video? Like did he do anything to say like, yo, I was wrong about this, right? And I looked and there's nothing. So one of the first things that I'll just say, like, I'm just going to use one example to talk about one of my issues with body language. And it comes from this clip right here. I owe everybody an explanation. What you'll notice is that James has this smirky grin on his face through most of his apology video, which indicates he's not as sincerely sorry as he says. A sincere person shouldn't be smiling. Why would a person be smiling if they truly believe they hurt their close friends? All right, like that for me is a terrible example. Like when you read the book on body language, it talks about how body language is something where like you usually have to have multiple encounters with a person to understand their tells, right?  This is an indicator that he's lying. Like I think that is a little bit rough because so many people have so many different reactions when they're nervous or when they're afraid.  All right. Like this is common. So it is very difficult to say, okay, there's a smirk. You're automatically lying. Like that is not a very obvious tell, but his videos are kind of littered with things like that. So like I said, it came out that James Charles was telling the truth. And this is where I think it's important to realize that we as YouTubers, anybody who's doing commentary, anybody who's judging a situation, we have to have our own accountability. We have to have a certain amount of integrity for what we are doing. The problem I have, and I've brought this up in another video that I made about the difference between news channels, commentary channels, drama channels and the like is like different levels of integrity. Okay. So when I talk about integrity, what I mean is doing the right thing, doing the right thing, especially when nobody's looking, just do, do the right thing. All right. And something that YouTubers can get caught up in and I won't accuse Derek Vanshake of this because I don't know him. I don't know what's going in his mind. But the problem that some of us YouTubers can struggle with is chasing views and chasing narratives, right? And it's very important for you as the viewer to understand this and to watch when you're watching YouTubers, watch it with a certain level of skepticism because we are all human. We can all create our own biases and just based on the information we're taking in. So for example, when it comes to commentary channels or when it comes to somebody like myself or Derek Vanshake or anybody else who's doing commentary and like kind of looking at what's going on in the YouTube community, we can start to create a bias based on the information that's coming in. Here's what I mean by that. The videos that we're watching on the subject, right? The people talking on Twitter and what they're saying. James Charles is a prime example because it was originally thought that James Charles was a terrible, awful human being. So everybody was making videos saying James Charles is a terrible, awful human being. So then one possibility is we create a video and perpetuate that narrative. We throw out facts, reasoning, logic, evidence out the window. We're like, okay, there's a narrative going on. I can play into the audiences confirmation bias by making a video agreeing with what everybody's saying. And this is dangerous. This is why we as YouTubers have to have a certain level of accountability. But who's there to do that? Nobody. There's nobody policing, you know, the commentary channels, right? And I'm not, I'm not here to attack Derek specifically, but I hope to open up a larger conversation. Now, again, although, you know, a lot of us commentary channels, we talk on trending topics and things like that.  Because like I said, we are receiving a lot of information, right? And that's why we all need to take a step back. And something I try to teach you as the audience is be, be very, very careful about mob mentality or it's talked about a lot in crowd psychology. When you keep hearing the same narrative over and over and over again, you start to believe it and then you get into a situation of groupthink. You are no longer being an independent thinker. And I feel that we as creators, we have an even bigger responsibility to be self-aware when that's happening to us. Now, again, the reason I'm making this video is because, you know, I went back and I checked it Derek van shakes video calling James Charles a liar based on body language has almost one million views, almost one million views. It is touched almost a million people. I don't know how many of those are unique views, but I don't know how many of you watch the same video over and over. But imagine all the likes, the shares and everything like that. Right? So this is a massive, a massive accusation going out there to almost a million people. And then there has been no attraction, no follow up statement on that end. And this gets to my final point. This is why I respect Reagan Wolf and what she's doing, because Reagan Wolf was probably the first body language channel that I found. And I agree and disagree with her in certain instances. Like I've watched some of her videos where I can tell like, like a great example is her own videos. I'm like, OK, you don't like Onision, so your mind might create, you know, additional, you know, negative things about him, even though Onision isn't a great guy by any stretch of the imagination.  But the point I'm getting at is Reagan Wolf has come out and she's talked about and corrected herself. I can't remember which video it was. It might have been something to do with Melanie, the musician, and, you know, the accusations against her with her old friend, Timothy. But it was on Edwin's generation in his video. He brought Reagan Wolf on there for a guest segment and she talked about how she, you know, she was newer at it and everything like that. And she she wanted to correct those things. Right. And that's that's awesome. That is so awesome. I have given props to Einaber for doing the same thing. He removed one of his first James Charles videos for a similar situation. So all this is very, very important. So again, I just want you to think about and just be very mindful of the content you're consuming and don't believe everything a person says just because they're on YouTube. They are human. They are going to have biases and things like this are going to happen. All right. But anyways, that's all I got for this video. If you like this video, be sure to give it a thumbs up. And if you're new, make sure you subscribe and ring that notification bell because I make a ton of videos. And while you're at it, don't forget to follow me on Instagram and Twitter at the rewired soul. So you get updates on all the cool new stuff I'm doing. And before I leave, I want to give a huge, huge thank you to everybody supporting the channel over on Patreon. You are all amazing. All right. So thank you so, so much for watching. Be sure to watch out for your own confirmation bias. And I'll see you next time.


Everybody forced here up in 2023 bowman chrome baseball choice 12 box case number 16 at random divisions Let's go ahead and random now and then we'll get ripping seven seven on our random One two three four five six and seven Harper down a Christopher P and seven times on the divisions one two three four five six and Seven and at least on the AL central Harper with the NLE East in the NL West way how with the AL West Jeffrey H. AL East Michael Y. NL Central Christopher P with the AL Central just got the results posted to the site dropping you a link right now They could be found anytime at late in sports cards Dot com results quick link at the bottom of the website search bar also a good way to Look up some results Viviana with a spot in the mixer. We are almost a single digits on Sunday Funday you heard that right 11 to go once on Sunday fund a well-passed halfway eight on spectra 17 on luminance 25 on plates and patches Just the Colts left on Panini one football Six divisions up in the encased case and 12 teams on NT football. Let's rip Sam's live at 10 a.m. All fanatics tomorrow everybody we got PYT's and auction styles Um flawless is Wednesday. I mean not more needs to be said about that break your list it for Wednesday I think rich was getting Thursday listed also But yeah, Wednesday all Flawless little bit of finest little bit of finest you a foe a little bit a little bit Manors about the ice this game. I think Manners of the gigantic second half Puka Anybody gonna be buying puka cards First auto nice one for the Giants here gonna be Rainer Arias Sean's got it ready tonight to Shane It's been made already. Oh Yeah, it's ready. I know I'm not on it got first auto is Hans Montero for the Yankees I think Steve isn't on it probably not even Anthony Yeah, they've all been really Yeah, they've just they've honestly been pretty stand-up fellas in the chat recently sure Atomic first auto Yonatan Enriquez 100 of 100 Mets Brian Robinson jr. A touchdown I might have a chance to be done. I Have him I'll have to go check the score after in between breaks here For Sean's he's on me right now first auto base. You'll see go on for the Rangers AL West Rangers Choice first auto AL central you and your Marine the 150 99% Who crapped the bed for Donny he had a big rejection earlier look at his defense Hey, thanks. Oh, he started the Jets D Refractor first auto Javier Osorio to 499 for the AL central. Yeah, we're not first auto for the NLE's Carlos de la Cruz Got first auto Ben Metzinger for the NL central Garrett Wilson got hurt. That's not good. And it looks like green. Yeah true green first Paul Macintosh auto 1099 for the NLE legal sounds pretty jealous right now Nebraska I Am glad they won last night though. Yeah, it's a hell with that Colorado state First auto is shim for the NL central next up first bowman auto Luke Berryhill AL West and we got some gold here First oh, it's the Reds. It's gonna be Duno, isn't it? It is Alfredo Duno to 50 NL central great hit 38 of 50 NL central seems to be doing pretty well here Yeah Yeah, I don't know This one feels Colorado state as well. I mean, they just got short of the field every win now First auto is Jonathan Enriquez for the NLE Security better step it up there, man. First auto is Gordon Graceffo for the NL central Did you watch though? He told him in the pepper. I'll let him get off the field then come on Because of his foot, you know, he was like guys gonna let me get off for you guys come right on there They did that is pretty funny. They stopped waiting for him and then they all came on the that is pretty damn funny Actually, he's like do it, but wait respect.  Yeah, I run it all You got gold first auto junior cornel or one cornel to 50 said you junior That's one cornel to 50 for the NL West They are very new to this one's the last time Colorado was good like once in the early 2000s like one year and before that it was like No Stewart Stewart they were like all right back then. Yeah Now I was gonna say they're they're very new to this We got the hype. We got the swag You got my a a first auto for the AL East He's going on Keith Best pull from this break so far probably a gold Alfredo. Do no auto. This my a is very nice too though Go AL East God first woman base auto y'all on the Rivera for the NL East and atomic first woman auto Camilo Diaz the 100 for the AL West Long time Yeah, do we think Dion leaves after one season? I think it'll be more than one season. I think he's there play two or three Kitten gets drafted to stay for the kids. I mean about the kids First auto is y'all the boy for the AL West. I'm sure he's making a ton of money off those glasses, dude Everything he touches it's gonna be getting endorsements and stuff. It's gonna be on like a And we're like on a half-act commercial or something one day green lava first Auto is uh, john sock shim to 99 for the NL central Ready to give me some deons on glasses First refractor auto out of 499 AL West Christian Monroe to 499 Rams gave up a pretty pretty good game of the Niners Come back. Cowboys winning the Denver's trying but washington had a washington monster second half.  I guess first auto is pinto for the AL East Base auto here first bowman NL central daniel guillart day and refractor first bowman auto Can he Gomez the 499 for the AL west? Jerry jones hires deon next year for sure He'll be he'll be a call right for at least two seasons. I would think The pats deon What are the pats? Yes, I highly doubt it but Although I am ready for uh For bill to check the step down first auto ever Cooper the third for the NL east There are deacons approach so First autograph here paint williams AL east and first refractor auto is christian man. That's a 499 AL central Come on last three boxes.  Come on Let's see a johnny bench Sam was in chat earlier saying joe burrow and two Darn foam was pinched. It's really stuck All right, do you have some gold coming up though got oxy l plas first base auto for the nl central Gold shimmer first auto nl central javier revas 47 to 50 Has he been really that bad illegal you think so and refractor first woman auto al east is anderson delas Santos the 499 that was a solid box there First auto omari daniel twins AL central green lava on the first woman auto torrent montgomery nl east of 99 Refractor first woman auto jack panetta 499 Going to the AL central. Give me one second. We will recap everybody Put any one sold out Kurt grabbing some spectra tim with your grabbers of spectra spectra is at six to go now The link is in chat for you Put any one sold out now spectra's at five to go actually Beautiful loving that 16 on luminance as well luminance is almost halfway full Oh rich is talking trash Rich is talking trash by fantasy Is he he went from worse last week to scoring the most this week So now he's yeah, now. We'll never hear it. It was like week one never happened now. He's chirping. He's chirping now Okay Recap this one guys. That's an okay case nothing crazy. I mean the gulduno is very nice just some other nice hits, too But nothing Outrageous uh base autos of daniel plus Peroso delgado Peyton williams ever cooper the third daniel guillart a adrian pinto Yaniela boy. You're you on the revero brand of my a nice one there According uh, Gordon graceffo yonatan and riquez berry hill shim med zinger gala cruise Galan montero arias is nice for the nl west refractors the 499 we have javier osorio christin munro Kenny gomez christin manna marco vargas anderson de los santos jack veneta to 150 we had uh junior marron To 100 of enriquez and diaz to 99 of macintosh Torian montgomery Shim to 50 we had cornell and the revas And gold to 50 was an alfredo duno That'll do it. Thanks again everybody moving on now to hockey


So what we have? We have a given matrix for an ensemble of matrices. In this case, it would be n times n symmetric real matrices. Suppose that we do not like lambda vector a, the spectrum of a. And what we did was to define the empirical spectral density given a matrix a, like rho sub pi of lambda is equal 1 over n, the sum i from 1 to n of the direct delta of lambda i. And the exercise was to try to express this thing as something related to a problem in a stack mech. Did you manage to do this? More or less? You don't know how to do it, what? Yeah, yeah. Very good. So shall we do it together? So the idea is the following. So first, let me recall here the tricks I'm going to use. The first one is that 1 minus the limit for eta going to 0 plus 1 divided by x minus i eta is equal to the principal cosine of 1 divided by x plus i pi delta, direct delta of x. Let me to simplify the notion of eta, not to write too much. For the time being, I'm going to assume that every time there is an eta, the limit of eta going to 0 plus is implicit. OK? So what I notice is that the imaginary part of this is equal to pi direct delta. Therefore, direct delta is equal to 1 over pi, the imaginary part of 1 divided by x minus i eta. Right? Now let us focus on this part here. I have in the sum, direct delta of lambda minus lambda ai. So using this, I can write this thing as 1 divided by pi, the imaginary part of 1 divided by lambda minus lambda i a minus i eta. Right? And then I put you see, I do the derivation from the definition step by step now to the sum. So then I have that rho sub pi of lambda is equal to 1 divided by pi n of the imaginary part of the sum of i from 1 to n of 1 divided by lambda minus lambda ai minus i eta. Right? That's why I get rid of the annoying principle Cauchy part, taking the imaginary part. And now what can I do? I can do the following. I can write this thing as 1 divided by pi n, the imaginary part of the derivative with respect to set of the sum i from 1 to n of the logarithm of set minus lambda i a when set is equal to lambda minus i eta. But this is equal to 1 divided by pi n, the imaginary part of the derivative with respect to theta of the logarithm of the product of 5 from 1 to n of set minus lambda i a, or set equal to lambda minus i eta. Right? Are you with me? But the logarithm, I'm going to do this part here, the logarithm of the product i from 1 to n of theta minus lambda ai is equal to the logarithm of the determinant of theta times the identity matrix n times n minus a. Because if I do an analysis, this is asymmetric matrix, can be diagonalized by orthogonal transformation, the logarithm of the determinant of this is equal to this. Good. And this, I can write the task now as follows. Second, I can do minus 2, the logarithm of 1 over the square root of the determinant of this part. By the way, this map, you can do it in different ways, OK? To get to the final result. But this is just one of the three or four ways to get there. So what have I achieved? I've achieved to write, to express this in terms of the logarithm of the determinant. The determinant has a Gaussian expression. And that Gaussian integral expression is going to be our partition function, right? So let me put all the pieces together. So we end up having the following. Now that rho sub pi of lambda is equal to 1 divided by pi n, the imaginary part of the derivative with respect to set. I have here minus 2 of the logarithm of 1 over 1 second, the logarithm of 1 over the square root of the determinant of a set times the identity matrix minus a. That is equal to lambda minus i. So far, so good. I have not done anything fancy at all, OK? Now remember that now I can write 1 over the square root of the determinant of what is a symmetric matrix as follows. I can write this thing as an integral for the product of i from 1 to n dx i divided by 2 pi of exponential of minus 1 half the sum for i and j from 1 to n of xi set identity matrix a entries ij xj. Call this object my partition function, although it's not really a partition function because set is complex, right? But morally speaking, it looks like a partition function. Let's call this thing set of set. So what we find is that the gross pay of lambda and I guess this depends on a is equal to minus 2 divided by pi n the imaginary part of the derivative with respect to set of the logarithm of set questions. But it's symmetric. No, it's symmetric. It has a small imaginary part. It's not an issue. If you think it is an issue, what you can do is to use what is called a bisonic representation for the determinant. So what you will do instead of using this trick, you will do this logarithm of 1 divided by the determinant. And then you can use the other formula we discussed, the one for a general complex matrix. But you can use this one. So you see a problem or an object related to a problem in random matrices, or for a matrix, still this matrix is a given matrix, can be related to an observable related to some sort of a spin glass problem, right? Well, in this case, the identical variables are continuous spins. And the interactions between these variables are given by the matrix entries of the matrix you are interested in calculating the empirical spectral density. So for somebody that was asking yesterday, well, but if I know the acting values, I should worry about this. So the question, if you see what happens here, is that I express the spectral density directly in terms of the matrix entries. For some reason, I'm interested in calculating the expectation of this object with respect to an ensemble of random matrices. I don't need to diagonalize to calculate this object. The only thing I need to worry about is to do the expectation value with respect to the matrix entries. So I overcome the problem of diagonalizing matrices. All right? There is a minus here, yes.  Now in the context of this stachmic problem, the logarithm of a partition function is normally, and the logarithm of the partition function is a free energy. And the derivatives with respect to the logarithm of the partition function generates observables of interest. So here, you see, if I were to do here, I have to put when set is equal to lambda minus eta. So if I were to do the derivative with respect to set of this expression, what I obtain is the following. I obtain the expectation value of something. So I can relate directly the spectral density to the expectation, the thermal expectation value of a local quantity. So the derivative with a minus 2, just look like this, the derivative minus 2, the partial derivative of the logarithm of this object. It's going to be what? It's going to be 1 over set A. And then I'll have the internal, let's put this integral in this way, d and x. Let us call this exponential of minus a Hamiltonian. With the sum, when I do the derivative with respect set, I have the sum i from 1 to n of xi squared. So let me introduce the equivalent of what would be the Gibbs measure, p of x, is equal to 1 over set A set of the exponential of this minus h of x, where h of x is equal to 1 half of the sum for i and j from 1 to n of xi, set 1 minus a i a xj. I'm just using the vocabulary of StackMaker. So then this means that this guy here minus 2 times the partial derivative with respect to set of the logarithm of the partition function is equal to the expectation value of, sorry, the sum for i from 1 to n of the expectation value of xi squared. So therefore, in this mapping, the spectral, the empirical spectral density associated to a matrix A is equal to 1 divided by pi n, the imaginary part of the sum of i from 1 to n of the expectation value of xi squared, when set is equal to lambda minus i eta. So you see, again, I'm relating the spectral density of a matrix to the expectation value of a local observable related to a Hamiltonian. Can you speak up? Sorry? You didn't get this part. The only thing I'm doing is using the analogy with the statistical mechanics. So I define a Hamiltonian, which is what is inside the argument of the exponential. And since this is the partition function, the exponential of the Hamiltonian divided by the partition function is equivalent to the Gibbs measure that appears in a stack map. Now I notice that if I do the derivative of the logarithm of the partition function with respect to set, in this vocabulary, this is equivalent of calculating the expectation value of these variables that appear in the Hamiltonian. Ah, because the. So sorry. Yeah, because, sorry, this is the identity matrix. So I'm taking the elements i and j. So what this thing means? Sorry, maybe I didn't explain this part. So this set times the identity matrix minus the matrix a. So the entry ij is set Kronecker delta ij minus aij. So in this sum, the first one, only the diagonal term remains. That's why you have here xi square. Thanks, Gaussian. Which Gaussian? There are several Gaussians here. A square root of, yeah, thank you. Thank you very much, a square root. Yeah? Thank you very much. Actually, it doesn't matter in the end, because since you have the logarithm, and this is expressed with respect to an expectation value, this factor, it will cancel. But it's important to be precise. Thank you. More questions? Here? So after the derivative of the logarithm of the partition function, this would be 1 over the partition function, the derivative of the integral, right? The set is in the integral. You apply what is called the derivative of an integral. You don't get the, sorry, what? Yeah, no, it's to just be a bit more picky with the notation. Just to remind that this set is lambda minus i eta. It's just that, OK? So this expectation value depends on the gives of Boltzmann measure, that depends on the Hamiltonian. The Hamiltonian depends on this set. This set must be lambda minus i epsilon. It's not for any set. It's just that. I was trying to be a bit more explicit, OK? And remember that also eta has to be taken in the limit when eta goes to 0 plus. More questions? Sorry, what? So it's what I said that this spectral density is related to the expectation values of local observables. Well, because this observable, right? It depends on a given node, right? It depends locally of something on the graph or something in the matrix, which is just node. So it's a local quantity. So you don't have, for instance, a function that depends on a collection of variables that takes into account, for instance, an extensive part of the matrix. That's why I say it's a local observable. Sorry, can you speak up? Why I don't? Yeah, I do keep them. Yeah, the only thing I was saying here is this notation means for i and j that this is equal to set the chronicle delta ij and aij. So here is for all i and j. And of course, here you will have a diagonal part. The only thing I put this thing here is a size that when I do the related with a spec set, set is coupled to the chronicle delta, and therefore, only the diagonal part of this sum for this term is what appears here. So that's why you have an xi square. So you see this mapping is exact. There is nothing I put, no assumption for a. So a can be whatever. Well, asymmetric matrix, OK? So the spectrum has to be real, yeah? More questions? Now, so forget about now the rest of the universe. That means, let's forget a second about this problem or this mapping, realize the following. So I have here the spectral density depends on the expectation values of this sort, yeah? So you remember when we discussed cavity method, the way I introduced it, and a simple way to get the expression for the magnetization. So here, in principle, well, for definition, the expectation value would be equal to the integral over all values of x. I join for the distribution for the x's, and then xi square. So since I only know the expectation value for one of the entries, local observable, this means that this is equal to the integral with respect to xi pi xi xi square, yeah? So if I'm only interested in this expectation value, the trick is to find a way to see where I can write close equations for pi xi, right? So can I or can we write down simple close equations pi? Well, let's think about the cavity method, the way we introduce it. So the cavity method, we introduce it for the Hamiltonian of an easy model with pairwise interactions. And in this case, we have a Hamiltonian H of x, which is the sum of i and j. And there is one half, which I missed. For i and j, xi, xi, x, yeah. So this is also pairwise. The only difference between this Hamiltonian and this Hamiltonian of the easy model is that these are real variables. The one in the easy model, they are easy variables. They take values plus minus ones. But if you think about the cavity method, the steps you do have nothing to do with the character, the type of random variable you have, dynamical variable, has more to do with the factorization we discuss. The fact that this Hamiltonian can be written for a given node as something happening to that node, the interaction of that node with the rest of the universe, and what happens with the rest of the graph. So now we're going to do an exercise. I'm going to delete this, where we are going to derive the equivalent of the cavity equations for this Hamiltonian. And the idea is to show, I'm going to give you the final formula, if I can, is to show that the single-side marginal pi xi can be written as follows. It can be written as 1 over i exponential of minus 1. Minus z xi squared divided by 2. And then times an integral that takes into account, give me a second, takes into account the neighbor's i of the distribution when i has been removed of the neighbors of i. And then the following, the sum for the neighbors of i of xi a, i, a, i, l, x, l, or something like this. So this derivation of this relationship is exact. When you derive this relationship, you can assume that maybe you are in a random graph, or you can assume the beta-pals approximation for this young probability. Assuming beta-pals approximation, take that the joint distribution for the neighbor of i can be written as the product for l in the neighbor of i of pi, l, x, l. Finally, assuming this, you close the questions doing the same idea in a graph or in a matrix where you have removed something. And you can find that the single side marginal pi xi, where j has been removed, is equal to 1 divided zone factorization, sorry, normalization factor of exponential of minus z xi squared. And then I have the product for l belonging to the neighbor of pi without j of the integral x, l, of exponential of i, a, i, l, x, l, the right distribution at a node l of x, l, when i has been removed. And now, it's exactly the same blood equations and the gravity method for the decimal, but continuous variables. Because if you look at the derivation mathematically, there is nothing that prohibits you to do exactly the same steps. The only thing that you do is to change discrete sums by integrals, but integrals are sums, right? The same thing. Now, here, the hate is when the different comes and that people thought that it was a major obstacle. Why? Because you see the gravity method applied for easy variables. These marginals can be parameterized by just one real number, right? Because the random variable takes values in the IC model plus minus 1. So in this case, this is annoying, right? Because this is a real variable, so you have a proper distribution, or a proper function. So if you look at this, you might think, OK, this is going to be very difficult to solve numerically. How can I do this? Maybe if I were to parameterize these distributions or these functions, I need an infinite number of parameters, and then I need to close to find a set of closed equations for those parameters, in the same way that in the exercise I left, that we are going to do it for the cavity method in the DC model, you have this closed set of equations for the cavity fields. But here, it was just one parameter. Here, in principle, I need an infinite number of parameters, right?  But here, if you look at this expression, you realize something that there is a special set of functions that are a fixed point of the cavity equations. So that means that if you take a particular form of this set of functions, the form of these functions does not change. It remains, OK? So if you notice this, that means that you can use this set of functions, and this set of equations simplify a lot. So the question is, this would be the equivalent of the cavity equations. Again, the question is to realize that there is a particular family of functions for these guys, for the Pi Jxi. And I say this thing, that function or whose form doesn't change under this iteration. Because suppose that, for instance, I put here a particular function, whatever, I don't know. Whatever you can think of, it doesn't matter, OK? So after doing this integration, the form of this function might change, right? But again, there is a particular type of functions that after this process, the form of the function does not change. It remains the same. No more parameters are introduced or generated, OK? So there is a particular family of functions for which the cavity equations are a fixed point. So the question for you is to find the set of functions. You might think that some sort of the Pi Jxi, that's why functional is speaking, the form of the function does not change, OK? Those functions will depend on a set of parameters. The parameters have to will obey a set of closed equations, OK? But the form of the function does not change. So no more parameters are generated, yeah? Because if you were to generate more parameters, that would change the type of function. It is the same thing. So suppose now that this is the equivalent, or you can understand it as a connectivity matrix, or an adjacency matrix. The only difference now is that if the entry is different from 0, you might think that the nodes i, j are connected, and the link has a given weight, which is the value of that matrix entry, right? But from a graphical point of view, of course what I can have is given a matrix A, I can put the off-sites n times n, I can put n nodes. And then if this is not i and this is not j, the link between the nodes i and j is the matrix entry i, j. Yeah, but you know, up to here, remember that up to here, you don't have to assume any type of sparseness with respect to the matrix. This is exact. When you are going to do, when you do the betapalus approximation, you know that the betapalus approximation would be exact for a particular type of freeze, or in this case for a particular type of matrices, OK? But to get here is for any matrix. To get here is for a particular subset of matrices, which are those that have this kind of tree structure. Once you are here, this has to do with the structure of the cavity equations, this part here. But for another part of matrices, it works very, very well. Questions? Go ahead. You don't get the notation with this one here. It's the same notation as in the cavity method. L belongs to the set of neighbors, which are the neighbors of i, removing the node j. Remember that in the cavity method, we introduce this notation that we have a node i. This would be node i. This node is connected to a set of nodes. And this set of nodes, we call it dj. And then in cavity method, let us say you remove one node. Let us say this one, j. So the corresponding set of neighbors is the neighborhood of i without j. This inverted line is minus notation in set theory. No, we don't have freedom. And that was a major obstacle to solve this problem.  And in principle, this can be any function. But these functions, they have to wait this set of closed equations. And it turns out that for a particular set of functions, when you put them under this operation, the form of the function doesn't change. So that means automatically that that set of functions have to be the solution for this set of equations. Yeah, but you can prove that there are no other solutions. Because if there were other solutions, they would generate different functions. So this set of equations doesn't close. Questions? No, so then first exercise, let us do it again with yesterday, this one. But this is essentially the cavity method. Second one, this one. Third one, find a way to realize that there is a particular set of very simple functions that solve this set of equations. Good? So I'll give you like 50 minutes, 5 minutes, right? 5 minutes. Is that OK? OK, so again, we do it in groups. So you turn around, you look at each other, and you form the group, and then you discuss. And I go around. Clear what you have to know? Yes, but the idea is that we got this method realized only on this very trivial property of the exponential function. That's it. Yeah? So then the second thing, how we did this derivation for the easy model. The way we did it, remember, is that I want to derive the single side marginal at a given node. So what I do, what we were doing in that case, I'm going to use the notation for the easy model. What I did is to rewrite the Hamiltonian in such a way that I put explicitly the dependence on the node i, the interaction between i and the neighbors, and then the rest of the system. Now in this case, and that in that case gave us the following. This was what? Minus h i sigma i minus sigma i, the sum over all the neighbors of i of j i l sigma l plus the Hamiltonian, where I have removed spin i. The reason I can write this thing in this way is due to the structure of the Hamiltonian, which is a two-body interaction. Right? Now in our case, the Hamiltonian that we have, which again is not really a Hamiltonian, right? I call it Hamiltonian because I'm abusing of this vocabulary from a stack map, is the following. So h of x, it is minus z divided by 2, the sum for i from 1 to n of x i squared. And then you have plus 1 half, the sum for i and j from 1 to n of x i a i j x j. So take this Hamiltonian and apply the same idea, right? So from this Hamiltonian, I want to derive the single set marginal pi x i. So I need to isolate from here what is the node, the variable x i, how the x i is connected to the rest of the neighbors and then the rest of the graph. And then you remember that the definition of this marginal is that this is equal to the integral over the whole system, but removing the node i of the original Gibbs distribution. That's it. Good? Better? So I give you 10 more minutes. And again, listen, I'm doing everything by heart, so maybe there is a sign which is dancing around. So don't believe what I write down. Just do the derivation. Come on. Yeah, what I'm trying to say is, if you look at derivation of the cavity method in this derivation, this derivation depends on the fact that the derivation that depends on is that you are using the property that the exponential of a sum of objects is the product of exponential of those objects. That's it. So if you have the exponential of a1 plus a2 plus a3, this is equal to the product of a1, a2, a3. That's the most important property in this derivation. Any other thing is not important. It's not important that you don't have a probability distribution. It's not important the character of the variables. They can be discrete. They can be continuous. This is not important. The reason that is important is you have the exponential of the sum of objects. That's it. Thank you. So I'm trying to say, when I think of the case, when you do, in this case, for any derivation, focus on the properties which are the most important ones to do derivation, not thinking about the context in the derivation, in the context you are working, right? For instance, because sometimes you might think, ah, since I'm doing this derivation in the context of statistical mechanics, this method only applies to statistical mechanics. Not true. False. It depends. I mean, if these were really the connectivity matrix, then yes. If it's any matrix, then you have to specify that you are summing over those elements of the matrix that connect node i with its neighborhood. Set minus aii multiplying the factor xi square. That's everything that changes. But again, what I wanted you to notice is that in this derivation, the only thing you use is this very simple property of the exponential, right? Very good. Now, this is very simple, once you have here. And the question is, have you thought of functions that when you plug them in the cavity equations, the form of the fashion doesn't change? Gaussian. Why Gaussian? Because, yeah, because Gaussians are stable under convolution, right? So therefore, if this is a Gaussian, this is a convolution of Gaussian. This is a Gaussian which shifted. If this were a Gaussian, after this integration, you get a Gaussian, right? Because this is an integral operation of convolution. That means if I realize that the subset of Gaussian functions is a fixed point in the set of the structure of this set of equations, and I take now the following parameterization. I take the pi xi without j is equal to 1 over the square root of pi without j, or the exponential of minus xi square divided by 2 delta ij. And again, these are not really Gaussians, OK? I call them Gaussians, but this delta in principle is a complex number. What am I doing? What I'm writing is the following. So as the colleague pointed correctly, so this is a subset of functions whose form doesn't change under this integral operation. Those set of functions are Gaussians. That means if I put here a Gaussian, what I get is a Gaussian. So that means that the Gaussian are fully characterized by two parameters, which is the first two cumulants, right? So now I do the same thing I did for the cavity method, but for this model, I parametrized this function, and I write down the cavity equations in terms of those parameters. So if I take this parameterization, I'm not putting the mean value, because you have to prove that the mean value, you have to take it equal to 0. So you only need the variance of the Gaussian.  That delta i without j is equal to 1 divided by set minus a i i minus the sum for l belonging to the number of i without j of a i l squared delta l without i. These are the corresponding cavity equations when you assume that the form of this one is a Gaussian. And the equivalent to this, but for the marginals, would be the following delta i is equal to 1 divided by set minus a i i minus the sum of l in the number of i of a i l squared delta l i. You have to remember, you have to remember the following. In our mapping, the spectral density was related to the expectation value of xi square. So remember that we found out that the spectral density, rho lambda of a, was equal to 1 divided by pi n, the imaginary part of the sum of i from 1 to n of xi square. But if this is the form of the single side marginals, then the expectation value of xi square is precisely delta i. That I'm going to put here that depends on set. Basically, therefore, rho of a sub a of lambda is equal to 1 divided by pi n, the imaginary part of the sum of i from 1 to n of delta sub pi lambda minus i eta. And that's it. That's the problem. And this could be used for very, very, very large matrices. And it's exact when the matrices look graphically like trees. So how it will work, this algorithm, you introduce a set of parameters, these deltas, that are complex. You iterate this. This would be the equivalent of the iteration of the cavity equations, which is the value propagation algorithm. When you have the solutions for these deltas, you put them here. You obtain delta i. You do this thing for all i's. And you get the spectral density for again value of lambda. The same idea that you used to obtain the magnetization for days in model on random graphs. Questions? Ertons or any graphs, right? They look locally like a tree. And the limit of this graph becoming large, the rate approximation is exact. Now you can do the following. I'm going to give you another exercise. Do these derivations as an exercise. Now we are going to consider particular types of matrices, which are related with what they are called as random solar graphs. Suppose we have random regular graphs. These are graphs. These are trees with a fixed connectivity on each node. But they are called random regular graphs, because if you would have a tree, it will start growing. And the boundary would grow exponentially. But at some point, the boundary closed to itself. So then you don't have a boundary. So assume that you have a random regular graph where the connectivity of each node is k. Suppose that the connectivity or the number of neighbors of each node is k. For instance, this means the following. Now suppose that k is 3, the graph would look like this. This is a node. It has three neighbors. And the neighbors, they have three neighbors. And the neighbors, they have three neighbors, et cetera, et cetera. And at some point, it has to close to itself. So suppose that you have a random regular graph with fixed connectivity. And the weights of the nodes are the same, like for instance one. So if you have an homogeneous random regular graph, you have an homogeneous and homogeneous. This means same weights for all links. So for this particular set of graphs, you can solve exactly this set of equations. And you can say that the spectral density is equal to a given formula. Yeah. This, so see, yeah, yeah. So what I'm trying to say that this mapping, this depends on the expectation value of this guy. And according to our parametrization, this expectation value is precisely the variance. Unless, precisely, unless that in some cases, they simplify, and you can solve them exactly, explicitly. So in this case of random regular graphs with which are homogeneous, you can solve this set of equations explicitly. Tell me. Yeah, yeah. So random and regular graphs are graphs which are regular. So that means that all the neighbors have the same, all nodes have the same number of neighbors. Like for instance, in this case, I'm not drawing the whole graph. It's just a small part, right? So in this case, all the neighbors have the same, all the nodes, sorry, have the same number of neighbors, which is 3, yeah? 3, 3, 3, 3, 3, right? So that means regular graph. Random regular graph means that if you, if these were exactly at 3, you see the boundary. If you expand this thing, the boundary of the graph will grow exponentially. And this is sometimes not good. So what you do is to take the boundary, and you close it to itself. And there are many ways to close the boundaries. This gives rise to the randomness of the random regular graph. And the homogeneous part is that the weights of the links is the same for all links. So that means for this matrix, OK, all the elements of the matrix are the same. Sorry? Yeah, you create loops. But if the graph is large enough, those loops are not important. If the graph is large enough, those loops are not important for this equation. It still is exact for very large graphs. Questions? Well, not that one, the previous one. How it is a convolution? Because this is a Gaussian weight, right? I'm missing the diagonal part that I put there. Product with a Gaussian weight, and I'm integrating over a subset of variables, fixing the eyes. So this is the product of two Gaussians and integrating over a subset of Gaussian variables. For general cases, yes, numerically self-consistency, yes. So you start with some initial values for these variances, and then you iterate this set of equations. Questions? More questions? OK, thank you.