Item Number – SCP-432 Object Class – Safe Special Containment Procedures SCP-432 is kept in a standard storage area at Sector 25, is to be kept locked at all times, and the key to the lock kept in the adjacent security station, under guard by 3 Level 3 personnel. No other special containment required. Description – SCP-432 is a two-door steel storage cabinet, measuring 2 meters tall by 1.2 meters wide by 1 meter deep. The exterior of the cabinet is painted matte green, and bears no remarkable features, except small areas of corrosion and light scratching commensurate with being left exposed to the elements for a long period of time. The doors of the cabinet are fitted with a basic slide bolt and a hasp for a padlock, allowing the door to be secured from outside. The interior dimensions of SCP-432 display significant disparity with the exterior. The doors open into an apparently extra-dimensional space, containing a large labyrinth complex comprised of an as yet uncharted series of corridors. The walls, floor and ceiling of the corridors are constructed from heavily-rusted steel and adhere to the same height and width scales as the exterior of SCP-432, 2 meters high by 1.2 meters wide. The corridors within SCP-432 are lit at irregular intervals by what appear to be regular household light bulbs, secured to the walls and wire mesh fittings. Many of the bulbs are observed to flicker, and numerous others are burned out or broken. In places, several large-gauge steel pipes have been found bolted to the walls of the tunnels. These pipes are notably cold to the touch and contain flowing water, although the source and destination of the pipes in water are unknown. Many of the pipes observed are in obvious need of repair and leak cold, average of 3 degrees Celsius, water. The thickness of this water has revealed a low-oxygen content and trace amounts of iron oxide, but the water is otherwise potable. The exact size of the labyrinth complex to which SCP-432 connects cannot be accurately measured as each time the doors of the cabinet are closed and then reopened, the entrance created by the cabinet apparently moves to a different section of the maze. The fate of personnel within the maze when the door is closed is unknown, although remains discovered within the maze suggest starvation is a likely outcome. Other remains, coupled with additional evidence gathered during exploration, suggests that the labyrinth contains a large predatory inhabitant of indeterminate species, hereafter known as SCP-432-1. GPS units used within SCP-432 are rendered useless, as are cellular phones. Remote-controlled devices sent into SCP-432 are similarly impaired and cease to function after traveling an average of 20 meters into the maze, rendering remote mapping of the internal layout impossible. High-gain radio transmissions can be used to keep in contact with the personnel within the labyrinth, although significant interference occurs deeper into the maze. If the doors of the cabinet are closed, then all forms of contact with personnel within SCP-432 are severed. Additional Notes SCP-432 was discovered in an abandoned industrial complex in U.K. It came to the attention of the Foundation after Dr. T. Small heard reports of several homeless persons in the area disappearing after staying in the complex. Upon investigation, Dr. Small discovered the cabinet at the center of an abandoned steel mill, surrounded by a number of sleeping bags, bags of clothing, and other personal effects, suggesting a number of homeless persons had recently made camp there. SCP-432 was unlocked, but the door closed upon discovery. After exploring the immediate area beyond the entrance, Dr. Small exited SCP-432 and summoned Foundation personnel to transport the cabinet to Sector 25 for analysis. Currently, the expeditions have been sent into SCP-432 to attempt to chart its internal geography. To date, several D-Class personnel have been lost within the maze. No further expeditions may be made without express permission of at least two Level 4 personnel. Test samples, metal fatigue, and construction techniques date SCP-432 to having been constructed in the early 1950s. However, artifacts recovered from within SCP-432 have been accurately dated to much earlier periods. Expeditions Below are the expeditions within SCP-432 to date. The standard-agreed mission equipment pack, agreed by Dr. T. Small and Dr. W... is One hand torch, flashlight, with a three-hour lifespan, and additional power sources providing up to six additional hours. One headset microphone linked to control. One shoulder-mounted video unit set for wireless transmission. Two 0.5-liter bottles of water. Two high-calorie energy bars. Eight sticks of luminous marker chalk. SCP-432 Expedition 1 Date Expunged Expedition Supervisor Dr. T. S. Subject is D-6402, male, average physique. Subject's background shows history of aggravated assault and burglary. Subject is equipped with standard mission equipment pack and sent into SCP-432. Camera is activated, and subject enters SCP-432. The door is held open by a three-kilogram weight placed inside the doorway, with technicians on hand to remove the weight and close the door, if required. Camera activates, showing a short corridor constructed from the same rusted corroded metal as the exterior of SCP-432. The floor is formed from ridged safety steel, as might be found on industrial walkways or gantries. The corridor makes a 90-degree turn to the right, approximately five meters ahead of the subject. Control asks the subject to move around the corner. Subject moves forward as requested, turning the corner into a longer tunnel, the exact length of which cannot be judged due to lack of lighting. A conventional electric bulb on the wall lights the immediate area, but the light fails to illuminate much beyond three meters. Further lights can be observed ahead, though they only illuminate patches of the tunnel. Control instructs the subject to turn on his torch, and the lighting is notably improved to the limit of the torch's beam, approximately twenty meters. Control asks the subject to proceed down the tunnel. After approximately forty-two meters, a crossroads appears in the tunnel. D64502 asks Control which way to go, and Control tells the subject to pick a tunnel. The subject chooses to go left, and, before entering the new tunnel, produces a stick of marker chalk from the equipment pack and draws a large arrow on the wall, indicating the direction of the exit. As subject moves into new tunnel, Control notes that video quality has begun to degrade, with visible interference appearing on the monitors. Control does not inform the subject of this. Subject proceeds down new tunnel for eleven meters before tunnel T-junctions left and right. Subject takes the left tunnel, again marking the direction back to the exit with chalk, and continues onwards. Subject walks approximately five meters down the tunnel then stops, and asks Control if they heard anything. Control replies they did not, and asks what D64502 heard. Subject is quiet, as if listening, then replies in muted tones that he can hear someone banging on the wall in the distance, and shouting. Subject becomes agitated, and tells Control the person sounds f***ing scared. Control boosts audio gain on the subject's camera and pick up sounds similar to the subject's description, repetitive, distant banging, consistent with someone striking a metal surface with their arm or hand. A voice can be detected, but audio quality is not sufficient to discern words. Subject is becoming increasingly agitated by the sounds. Control informs the subject to move in the direction of the shouts. The subject objects, but after a short discussion with Control about the nature of his employment, he moves forward. After approximately 14 meters, the tunnel turns 90 degrees right, and angles downwards in a gentle slope. Video interference is now noticeably increased, and slight audio interference is now audible. Subject has begun breathing heavily, and muttering under his breath. Subject continues down the tunnel for approximately 27 meters until the floor levels out again. The subject abruptly stops, crouches, and swears. Control asks why he has stopped. The subject remains silent, but breathing has become louder and heavier. Control asks again why the subject has stopped, and D64502 replies. He heard a scream, and that the banging and shouting has suddenly stopped. Control informs the subject to stand and move forward, but the subject becomes agitated, and demands to be allowed to leave. After several minutes of arguing, the subject stands, takes a long drink from one of the bottles of water, and moves forward again, although slowly. Ahead the tunnel, T-junctions left and right, and Control tells the subject to go right. Subject marks the way back to the exit with chalk, and goes right. The tunnel ends in a dead end after 6 meters. Control informs the subject to go back to the junction, and take the left tunnel. This too ends in a dead end after only 4 meters. Subject seems to have calmed slightly, and suggests returning to the previous T-junction and trying the other tunnel. Control confers with Dr. W. who decides to recall the subject and analyze the data collected so far. The subject has been within SCP-432 for exactly 37 minutes at this point. Control informs the subject to return. The subject moves back through the tunnels, following his chalk marks towards the exit. At crossroads, the subject freezes again, and asks Control if they heard a noise. Control confirms that they are detecting a sound, but requests D-64502 explain what he is hearing. Subject identifies the noise as wind. At this point, the camera captures a small drift of what appears to be dead leaves blown from the right hand unexplored tunnel. Subject remarks that the breeze smells stale. Control informs the subject to collect several leaves for analysis, and then proceed down the right hand tunnel to locate their source. Subject collects leaves and complains about orders to remain in SCP-432, but moves towards the tunnel mouth. As subject nears the tunnel entrance, a loud echoing roar is heard over the audio, similar to a large animal such as a bear or lion. Subject panics, screams, and runs for the exit, ignoring Control's demands to investigate the sound. Subject sprints to the exit and collapses in the storage area. Expedition is aborted. The door closed and locked, and subject removed for debriefing. SCP-432 Expedition 2 Date Expunged Expedition Supervisor Dr. T.S. Subject is D-6411, female, 32, average physique. Subject's background shows an incident of attempted murder. Subject is equipped with standard mission equipment pack, and sent into SCP-432. Camera is activated, and subject enters SCP-432. The door is held open by a 3-kilogram weight placed inside the doorway, with technicians on hand to remove the weight and close the door if required. Camera activates, showing subject is in a long corridor constructed from the same corroded metal as the exterior of SCP-432. Light from the open door behind the subject, coupled with the illumination provided by the bulbs located at irregular intervals on the walls of the structure, lights the tunnel for approximately 20 meters. More lights are visible further down the tunnel, but are very dim. Control requests subject turn on her torch and move into the structure. Subject complies. The passage continues for approximately 100 meters from the entrance until it ends in a T-junction, leading left and right. Subject asks control which way to go, and is told to go right. D-6411 marks the route back to the exit with marker chalk, and proceeds down the tunnel for 50 meters, until a crossroads is reached. Control informs subject to take the left-hand branch, and subject marks the tunnel wall and enters the indicated passageway, which is followed for 47 meters until another crossroads is reached. Control notes interference to both the video and audio feeds has begun to appear, but is currently negligible. Subject pauses to drink from one of her bottles of water, and marks her route back before selecting, without permission from control, the right-hand branch. Control admonishes D-6411, but allows her to continue. The passageway makes a 90 degree turn left after 18 meters, then continues straight for approximately 73 meters. Ahead of the subject appears another crossroads, but as the subject nears it, she freezes, and reports that she can hear a rhythmic banging coming through the walls. Control boosts audio gain on camera, and the sound is picked up. The banging lasts for 73 seconds before it stops. Subject has remained still while listening, attempting to breathe quietly. Control prompts the subject to mark the tunnel wall, and proceed left. The subject remains motionless, and makes several inquiries into the nature of SCP-432 and the source of the banging. Control firmly reiterates their commands, and subject resumes walking, taking the left tunnel as indicated. Subject has traveled for almost 150 meters when she stops, and aims the camera at the left wall of the tunnel. She observes that all of the light fittings in this stretch of the structure have been broken. Shards of broken bulb are visible scattered across the floor. Subject continues forward, remarking that she has begun to detect a faint, unpleasant odor. When asked to describe said odor, D-6411 replies, something dead. After a further 24 meters, the subject notices an object in the tunnel ahead, and moves towards it. Video quality is now beginning to severely degrade. Camera angle tilts as subject kneels to examine the object, and Control asks subject to explain what she has found. Subject explains the object is a left sports shoe. The camera zooms in on the object, while the subject illuminates it with her light source. Our view tilts again as subject suddenly looks down at the floor of the tunnel, and emits a loud expletive. The floor of the tunnel is covered with a large quantity of dried brown residue that crackles and flakes as the subject moves her feet. Sprays of the residue are observed dried onto the walls. The subject remarks that the substance is apparently the source of the odor, and she surmises it is dried blood. The camera tracks several large smears of the substance leading away from the pool up the corridor. Subject's breathing is becoming slightly panicked. Control requests the subject collect a shoe and a sample of the substance for analysis. Subject does so, although complains continuously about the smell, and expresses wishes to exit SCP-432. Her requests are denied, and Control orders the subject to continue onwards. Subject continues down the corridor at a much decreased walking speed, and is becoming agitated. Camera view changes repeatedly as subject begins looking over her shoulder at erratic intervals. Video and audio feed are beginning to become severe, and Control asks subject to halt while they confer with Dr. W. Dr. W decides to recall the subject, who is now becoming extremely panicked, complaining of hearing footsteps behind the wall to her right. Control boosts audio, but interference prevents confirmation of subject observations. Dr. W confirms the expedition is over, and Control recalls the subject, who begins moving back towards the exit at increasing speed. Subject's egress from SCP-432 is unremarkable, except for subject's increasing speed as she nears the exit. Once out of SCP-432, the door is closed and locked, and subject sent for debrief. SCP-432 Expedition 3. File locked. SCP-432 Expedition 4. Date. Expunged. Expedition supervisor. Dr. T.S. Team is made up of three members. D-5891, male 27, D-8321, female 32, and technical assistant K. Equipment pack for this expedition differs from norm. Each member carries one hand torch with a three hour lifespan and additional power sources providing up to six additional hours. One headset microphone linked to Control. Two 0.5 liter bottles of water. Two high calorie energy bars. Subject D-5891 is equipped with 10 sticks of luminous marker chalk. One 250mm steel pry bar. Subject D-8321 is equipped with one shoulder mounted video unit sent for wireless transmission. Technical assistant K. is equipped with one standard issue Beretta 9mm firearm with 20 rounds of ammunition. One back mounted Oxyacetylene cutting torch. Subjects have been briefed that they are to enter SCP-432, move a short distance into the structure, and then attempt to cut through the interior walls with the Oxyacetylene torch. Camera is activated and team enters SCP-432. The door is held open by a three kilogram weight placed inside the doorway, with technicians on hand to remove the weight and close the door if required. Camera activates, showing team is in a long corridor constructed from the same corroded metal as the exterior of SCP-432. Light from the team's torches illuminates the tunnel for approximately 30 meters. The team moves into the structure, with D-5891 marking their progress every few meters with luminous chalk. After several turnings, chosen by control at random, the team arrives at a crossroads. Attached to the wall of the northern passageway are two large steel pipes. The team is asked by control to examine these pipes. K. places a hand on one pipe and remarks that it is very cold to the touch, and that there is a sensation of liquid moving within the pipe. K. requests to cut into the pipe, but control denies the request, directing the team to follow the pipes instead. Team moves north from the crossroads, following the pipes for almost 300 meters, taking several turnings in the process until the pipes continue through the wall of a dead end. Control informs the team that they should ignite the Oxyacetylene torch and cut through the dead end. At this point, K. moves to the fore and lights the torch. D-5891 takes up position behind him with the pry bar ready, and D-8321 moves back to cover the other two with the camera. K. cuts into the wall, attempting to excise the hole large enough to step through. As he begins cutting, D-8321 remarks that she believes she heard a noise behind them. The camera angle changes as she looks over her shoulder, revealing the corridor behind the team to be empty. Control requests she turned back and filmed the cutting. K. has made an approximately one meter high cut into the wall when D-8321 remarks again that she can hear something moving close by, and begins looking around. D-5891 and K. appear not to hear her over the sound of the Oxyacetylene torch.  As D-5891 steps forward and inserts the pry bar into the cut, a loud roar is heard, apparently coming from behind the wall. D-8321 screams and begins to back away, at which point the cut section of wall is seen to bend outwards, pushed by something from behind. At this point the video feed becomes confused, as D-8321 attempts to flee and the camera is unable to compensate for her rapid movements. Audio transmission is unreliable due to the interference and screams of the team. It appears that a large indigenous life form came through the hole cut out by K and assaults the team. Gunfire can be heard, presumably from K's sidearm. Along with screams from D-8321 and D-5891, the audio logs also record a loud bellowing, which is currently unidentified, but presumed to be made by the life form. Video stills reveal that data expunged. Subject D-8321 manages to return to the entrance of SCP-432, injured and in a state of extreme mental distress. She exits SCP-432 and, before technical staff can stop her, pulls out the weight holding the door open and shuts SCP-432. When the door is reopened, the internal layout has changed and D-5891 and technical assistant K are assumed lost. Subject D-8321 is removed for debrief, after which she is terminated. During debrief, it is discovered that a large tuft of animal hair is caught in the harness of D-8321's equipment pack. The hair is removed for analysis. SCP-432, Expedition 5, Date, Expunged, Expedition Supervisor, Dr. TS, Subject D-8887, Mail, 19, Athletic Physique. Subject's background shows a history of gang violence and murder. Subject is equipped with standard mission equipment pack and sent into SCP-432. Camera is activated and Subject enters SCP-432. The door is held open by a three kilogram weight placed inside the doorway, with technicians on hand to remove the weight and close the door if required. Camera activates, showing Subject is in a short corridor constructed from the same corroded metal as the exterior of SCP-432, which terminates in a T-junction after approximately 10 meters. Tunnel is notable to previous expeditions in that there are no lit bulbs on the walls. As Subject moves forward, he remarks that there is a large quantity of broken glass on the floor of the tunnel. Subject switches on his torch and proceeds forward to T-junction, then proceeds left as instructed by Control after marking his route. Subject moves through SCP-432, taking turns as indicated by Control. During this time, the Subject is careful to mark his route using marker chalk and makes routine reports to Control, describing any visual or audio impressions of the structure. Subject reports that he can hear occasional distant machine noises through the walls, in that the interior of SCP-432 is quite cold. After 45 minutes, Subject has traveled approximately 2,500 meters through the structure. Video and audio interference is minimal, and Subject has carefully marked his route through SCP-432 with marker chalk. So far, all the wall-mounted light bulbs observed in this section of the structure have been broken. Subject stops to take a drink from a bottle of water and consume a ration bar. After resting for a few minutes, Subject continues and, after taking a turning to the right, encounters three objects on the floor of the tunnel. Subject stops and illuminates the objects with his torch, revealing them to be two crumpled food cans and one bent tin fork. The cans are partially corroded and seem to be quite old. The labels are of a familiar brand of canned beans. Control asks the Subject to place the items in his equipment pack for analysis. Subject continues onwards, but after 40 meters stops and informs Control he can hear something. Control requests clarification, and D-8887 remarks that he can hear a faint sobbing or crying emanating from somewhere nearby. Control asks if the crying is male or female, and Subject responds that it sounds male. Audio pickup fails to register the sound clearly. Subject is currently stood at a T-junction, and Control instructs D-8887 to move in the direction of the crying. Subject takes the left-hand passageway, moves 30 meters down the connected corridor, takes a right turn, and follows the corridor another 22 meters, proceeds straight ahead at a crossroads, and continues for 37 meters. Video interference has begun to increase, and Control cautions the Subject not to proceed too quickly. Subject complains the darkness within SCP-432 is hampering his efforts, then shouts, Hello? Can you hear me? I'm coming! Control admonishes D-8887 for shouting, informing him he may attract attention to himself. Subject asks, What else is in here then? But Control informs the Subject to continue along his current route, and locate the source of the crying. Subject stops at the next junction and pauses to listen. Control picks up a drawn-out moan or scream, apparently human in origin, after which the crying ceases. Subject swears and asks if they heard the scream, stating it sounded very close. Control asks Subject to proceed forward, and Subject complies although slowly, attempting to move with as much stealth as possible. After 20 meters, the passageway turns right. Subject moves around the corner cautiously. The camera reveals the passageway ends in a dead end. Subject approaches the wall and places an ear against the metal. Subject backs away from the wall hurriedly, hissing expletives. Control asks what he heard, and Subject whispers, There's something behind the wall. I can hear it crunching on something. Subject makes repeated whispered requests to exit SCP-432 immediately. Control confers with Dr. S, who agrees to recover the subject. Control confirms the subject may begin retracting his route, which he does so at an increased pace. Subject's egress from the structure is uneventful, although Subject keeps looking over his shoulder and requires repeated verbal encouragement from Control to prevent the onset of panic. Subject returns from SCP-432 after a total expedition time of one hour and 47 minutes and is sent for debriefing. SCP-432 materials recovered. All documents contained in this file are Class 2 clearance, requiring two signed approvals to access. All of the following items have been recovered from within SCP-432 during the expedition to date. Leaves. Discovered on Expedition 1, 12 leaves in total, 3 oak, 4 ash, 2 rowan, and 3 maple leaves. All leaves are dry and crumbling and exhibit signs of extreme age. Footwear. Recovered on Expedition 2, a single left sports shoe made from rubber and canvas with the red logo on the ankle. The branding and manufacturing style dates the shoe to 1982. The shoe shows signs of heavy use. Frayed laces, worn soles and scuffed toes, and is caked in a fine layer of earthen rust. Dried blood. Recovered on Expedition 2, scrapings from a large dried bloodstain. Tests have confirmed the blood is human, male, type O positive. The blood is too old and degraded for DNA reconstruction. Animal hair. Recovered on Expedition 4, a large tuft of matted brown animal fur with a large clump of skin cells attached to the roots. The hairs are approximately 13 cm long, stiff in course, and smell extremely unpleasant. DNA analysis has placed the creature in the order of family, although noticeable irregularities in the DNA profile exist, suggesting data expunged. Food tins and fork. Recovered on Expedition 5, two crushed and empty cans of baked beans with meatballs and one tin fork. The cans have apparently been opened with a church key type can opener, and the contents consumed. Dried residue confirms the contents of the cans to have been baked beans with meatballs. One can contains traces of human blood mixed with the food sauce, as well as small traces of human tissue. The blood and tissue is mixed with the food sauce in a manner to suggest it was added to the food prior to consumption. The fork is stamped from tin, and of a manufacturer in style consistent with 1940s army issue mess kits. It is bent and scratched in places as commensurate with extended use. The tines of the fork are covered with dried food sauce, consistent with baked beans with meatballs, as well as traces of human blood and tissue. Lesson complete. If you missed the previous orientation, go watch SCP-431, Dr. Gideon, right now. Or for the complete course, watch this playlist.


trying to be you know aggressive in my zone and you know swing at good pitches I think you know so many times you know guys take themselves out of a bats not swing at the right pitches not being ready to hit so it's really I'm just trying to keep things simple at the plate swing at the right pitches and you know I've been able to have some a little bit of success. The outfield was extremely impactful not only did you Homer Frazier and Judge as well does that add to the excitement when you guys represent like that in the outfield. Yeah I mean you know when everybody is you know clicking on offense like that's those are the games that are really fun when it's just you know next man up you know kind of just passing baton you know from top to the bottom of the lineup so yeah it's awesome you know home runs are really fun. Aaron Judge exited with a left oblique injury if he's lost for any amount of time what does that do to this team? You know obviously he's you know a key part of the team you know obviously the performance in the field and as well as his leadership skills you know as a team though we just gotta you know bear down kind of you know dig our feet in the sand and keep keep keep playing baseball the way we know how you know I think you know whatever nine is out there is is a is a dangerous team and we just have to play that way. Thanks for the time.


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Welcome to this session, so in today's class we shall be focusing on basics as well as we shall try to cover a few problems to understand the concepts in a better manner. You know I always like to compare this to listening to your favorite song, you know.  And automatically the lines and verses become imprinted in your mind. So similarly the aim of today's lecture is that we shall be revisiting few of the concepts that we discussed earlier. Consider this as a quick recap so that it will be easier for you to solve numericals. So we are going to discuss quickly about real aperture radar and synthetic aperture radar. Remember when we discussed about real aperture radar we mentioned that the resolution of a real aperture radar is primarily dependent on the length of antenna. The larger the antenna, better is the spatial resolution but in the case of real aperture radar it is not practically possible for us to have a very long antenna. Now shown here is the flight direction. By now I assume that you are familiar with these terminologies that is the nadir direction, perpendicular to the platform, the azimuth direction is shown here, the ground range direction is shown here and swath is shown here. So in real aperture radar or side looking airborne radar the amplitude of each return echo is measured and processed amplitude. Shown here are also the expressions for azimuth resolution which we have covered as part of earlier lecture. It is nothing but lambda into R by D where lambda is the wavelength, R is the range and D is the length of antenna and over here we have range resolution in brackets I have written slant range to differentiate it from ground range resolution. So here it is range resolution which is nothing but C tau P by 2, C is the speed of flight. I will give it a moment to sink in. Now remember in the case of real aperture radar there are other determining factors also such as the antenna beam width and the pulse duration that affect the spatial resolution. Now moving on to synthetic aperture radar or SAR. See when it comes to synthetic aperture radar it is exploiting the history of echoes, exploiting the history of echoes. To be more specific it exploits the Doppler history of echoes that are caused by the forward movement of the antenna to synthesize a large antenna. And we also discussed about chirped pulses, isn't it? Chirped pulses are used in the range direction and motion of platform is inducing frequency modulation in the azimuth direction. Once again let me re-iterate. So in the case of synthetic aperture radar chirped pulses are used in the range direction we know what is range direction. This is the movement of flight we know what is range direction. Chirped pulses are used in the range direction and the motion of platform induces frequency modulation in the azimuth direction. So what is the net effect? Net effect is that in both the directions that is in the azimuth as well as the range direction the signals are getting frequency modulated. And it is this frequency modulation which is sensed in the Doppler shift. So shown here are the relationships for azimuthal spatial resolution which is nothing but length of antenna by 2 and given here is the range resolution. The ground range resolution is given as c tau p by 2 into sin theta i where theta i is the incidence angle theta i. Again let us re-iterate the radar equation which gives the fundamental relationship between the power transmitted and power received which is nothing but P r equal to P t into G square into lambda square into sigma that is radar cross section by 4 pi cube into r raised to 4. I am repeating it because it is the fundamental relationship of transmitting power and received power transmitted power by radar received power by radar how they are related the fundamental relationship is given by a radar equation. Now remember SAR we are understanding it as an instrument that is both transmitting and receiving. There is no separate transmitter, there is no separate receiver we till now we are understanding SAR as a transmitting and receiving instrument. At this point it is worthwhile for us to recollect the chirped pulses where chirp it stands for compressed high intensity radar pulse that is chirped pulse. So just to re-iterate the radar engineers use a long pulse with a linearly modulated frequency called a chirp and with this technique it is possible to increase the range resolution. Once again the aim of a chirped pulse is to increase the range resolution. So given here in front of you is the expression for range resolution which is nothing but C by 2B where C is nothing but speed of light and B is the bandwidth. We have seen the relationship as part of earlier lectures is not it? So this was a quick recap of the concepts which we have been covering as part of module 2. Of course this is not giving us a complete summary moving on. Now remember that in one of the earlier lectures we were trying to understand about different formats of synthetic aperture radar data and that is when we discussed that the very first type of data is called as raw data. And in SAR data by now we know what is range direction and what is azimuth direction. SAR system is moving in the azimuth direction or along track direction and the SAR system is collecting data in the range direction or across track direction along track across track azimuth range. Now please note that radar system can receive even 4000 to 5000 responses for one individual target which means in the first type of data that is the raw data the energy scattered from a target will be spread in both the azimuth as well as the range direction. Let me repeat the energy appear to be scattered let me put it that way. In raw data the energy can appear to be scattered in both directions that is azimuth direction as well as range direction which means if we have a point target its echo will be distributed in both the azimuth direction as well as the range direction. So to explain this let me show you a small schematic on the x axis we have samples within echoes on the y axis assume we have individual pulses and whatever shaded area in red that you see assume it is a field within the SAR raw data that contains power reflected from a ground cell R1A1 range azimuth instead of using x y I am using R1A1. So this is one ground cell which is having scattered power in both the azimuth as well as the range direction which means there is a requirement of SAR data focusing. Now by focusing we mean we want to collect all the energy into one single pixel of the output image because right now in the raw data the it is getting scattered in both the direction azimuth direction as well as range direction. So we need to use SAR data focusing and briefly I will try to explain what is meant by SAR data focusing that is there are many arithmetic computations which are involved in SAR data focusing and it typically involves something known as data compression okay data compression in both the range direction as well as the azimuth direction and data compression in range as the name suggests the transmitted pulse is being compressed in one range bin while the echoes are spread along the azimuth direction okay. Let me try to explain with a schematic. So now what you see in front of you is towards the left side you have the raw SAR data that we already discussed and in the middle assume it is the same image but after range compression okay data compression in range direction as the name suggests here the transmitted pulse is being compressed in one range bin while their echoes are spread along the azimuth direction okay that is why you see the red shaded region compressed in range but with information from a single azimuth spread over many pulses. Now which means we need to go for azimuth compression as well okay which means once we complete the data compression in the range direction the data set is now distributed in the azimuth direction which means we need to perform data compression in the azimuth direction as well which is when you get resolution cell represented like this R1A1. So this is the final representation of a synthetic aperture radar image. So you have the range cells as the x axis the azimuth cells as the y axis okay. Now when you go in detail into the mathematics fast Fourier transforms or FFT is used for data compression in both range and azimuth directions while we may not be going into the mathematical details right now I wanted you to be aware that to convert a raw SAR data we need to compress it in both the range as well as azimuth direction so that we have the information correctly represented okay without echoes distributed in both the directions alright. So with this background let us now try to solve a few numericals. We will try to focus on the radar equation and the Doppler effect. I hope you can recollect it as part of the previous lectures alright. Now moving on to the first question.  It reads an airborne radar is operating in the X band at 10 gigahertz the wavelength lambda is given as 3 centimeters and is traveling at 700 miles per hour. It is tracking a target ahead which is moving at 800 miles per hour in the same direction. So there are two parts of the question. First question is what is the differential speed okay given 700 miles per hour and it is trying to track the target which is moving at 800 miles per hour. The first part of the question is what is the differential speed. Let us write it down differential speed is nothing but 700 minus 800 is the straightforward isn't it minus 100 miles per hour but then we are more familiar with meter per second isn't it. One mile per hour is 0.44 meter per second. So I can as well write it as minus 44.704 meter per second okay differential speed. Now the second question reads what is the Doppler shift of the target. Second part of the question what is the Doppler shift of the target. Now for that let us try to recollect the expression we had come across to quantify the first target Doppler shift. Let us write it down first target Doppler shift is nothing but f Doppler if you remember the notation which was covered in class which is nothing but 2 into relative velocity by lambda which means it is nothing but 2 into 44.704 wavelength is given as 3 centimeter 0.03 meter. So the answer comes to 2.9 kilohertz first target Doppler shift okay easy. Now go to the second question now okay here the question reads that for a single look complex image that is SLC image the value of one single pixel is given as 5 plus 2.7i and the value of amplitude and phase information is asked okay some sort of a fill in the blanks what is the value of amplitude and phase information if the value of a single pixel is 5 plus 2.7i. Now remember we discussed that SAR image can be considered as composed of complex numbers. So here the value of a single pixel is given as 5 plus 2.7i where we know that i is nothing but root of minus 1 isn't it. Now the SAR amplitude image can be computed on a pixel by pixel basis using the expression amplitude equals root of a square plus b square while the phase can be computed by the expression tan inverse plus a by b. Let us try to solve the simple problem. So here the complex number is given as 5 plus 2.7i okay which means I can compute amplitude using the expression which was shown earlier which will come out to be root of 5 square plus 2.7 square it will come out to be 5.68 amplitude. Now phase value for the same pixel it can be computed as tan inverse of 2.7 by 5 you will get the value as 28.3 degrees remember I have given you just one pixel value and when we are discussing about a single look complex image SLC image there are multiple pixels in a SAR image which means there are we are dealing with complex numbers matrix of complex numbers. This question dealt with just one single pixel value alright. So let us move forward to the third question. So this question reads an X band side looking airborne radar that is SLAR system with a 2 meter antenna has an azimuth antenna beam width of what okay? X band which means wavelength is given what else is given? 2 meter antenna is given. So we know that for an X band SLAR side looking airborne radar system with a 2 meter antenna it is going to have an azimuth antenna beam width of lambda by d 0.03 meters by 2 okay. What is 2? Length of antenna. So you will get the value as 0.015 radian okay 0.015 radian. This question what have we done? We have written down the given details that is lambda equal to 0.03 meters. We know that for an X band SLAR system that a side looking airborne system with a 2 meter antenna it is going to have an azimuth antenna beam width of we can write it as theta A equal to 0.03 by 2. What is 2? It is the antenna length which will come out to be 0.015 radian okay. Straight forward questions what you need to do is you just need to understand what is given and relate it to the relationships that we have been learning over the course of lectures okay. So moving forward the next question reads a radar system is having an unambiguous range of 300 kilometers and a bandwidth of 0.5 megahertz. It has two parts. The first part reads what is its range resolution and the second part reads calculate the pulse width okay. So first part of the question what is the range resolution? We can use the expression delta R is C by 2B which is nothing but C we know speed of light by 2 into bandwidth B is given 0.5 into 10 power 6 to make the units consistent. You can get the values 300 meters range resolution okay. So moving on the second part of the question is calculate the pulse width okay. We know the expression for pulse width which is nothing but by C have just rearranged the expression okay. So we can write it as 2 into 300 by 3 into 10 to the power 8. You will get the value as 2 new seconds pulse width you know simple questions simple numericals to help us understand the concepts that we have been covering so far. So let me hope that you understood this part of the lecture and I will meet you again in the next class. Thank you.


Hi, this talk is about two-round Oblivious Linear Evaluation from Learning with Errors. I'm Pedro and this is joint work with Nick Woodotling and Paul Mateusz. Oblivious Linear Evaluation, or OLE, is a protocol between a sender and the receiver. The sender holds two values, A and B, from a finite field, and the receiver holds a value, X, also from the finite field. In the end, the receiver should learn A plus XB. In terms of security, we require that the receiver learns nothing about A and B, and that the sender learns nothing about X. OLE is usually seen as the arithmetic analog of the well-known Oblivious Transfer Primitive, and it is well known that the minimal number of rounds to perform it is two. OLE has found numerous applications throughout the years. The most natural one being, it allows us to securely realize computation of arithmetic circuits, just as OT realizes secure computation of Boolean circuits. It has also been used to realize efficient two-party secure computation schemes in a variety of different settings. OLE has also been used to realize specific tasks such as private-set intersection and machine-learning related tasks. Many OLE protocols have been proposed over the years. Some of these proposals are presented in this table. As you can see, current OLE protocols either require more than two rounds, or a trusted setup, or are based on non-post-quantum assumptions. This raises the question of whether we can build an OLE protocol, which is maliciously secure. It takes two rounds, and it's based on presumed post-quantum hardness assumptions. In this work, we provide an affirmative answer to this question by presenting two protocols for OLE from LWB. Recall that LWB is an assumption which is presumably post-quantum. Our first construction is a construction for an OLE protocol from LWB, which is secure against malicious receivers where security holds statistically and semi-honest senders assuming LWB. The main technical tool that we use in this construction is a new extraction mechanism that allows the simulator to extract the receiver's input and generalizes the PVW extraction mechanism for super polynomial modulus. Then we extend this construction into a fully malicious OLE protocol, and the resulting scheme is secure against malicious receivers, again where statistical security is maintained, and malicious senders. This protocol uses an additional OT protocol. Let us first recall the learning with errors assumption. The LWB assumption states that for a random matrix A, a random vector S, and a vector E, which is sampled from an error distribution, the distributions of S, A plus E, and is computationally indistinguishable from a random vector. Let us take a look at the structure of this talk. We will start by presenting the PVW OT protocol from LWB, and why its extraction mechanism in the security proof of malicious receiver only works for polynomial modulus. Then we generalize the PVW scheme into an OLE protocol and devise a new extraction mechanism that works for any modular skew, even super polynomial. Then we extend this result, this protocol into a maliciously secure OLE protocol, and at the cost of an additional OT scheme. Let us first recall how the PVW scheme works. In this scheme, the CRS is composed by a matrix A and a vector W. The receiver with input B starts by sampling uniformly at random a vector S and an error vector E, and it sends the value S times A plus E minus BW. The sender with input V0 and V1 will essentially encrypt V0 under the public key AZ and V1 under the public key AW, using the same randomness. That is, it will sample a vector R with the low norm and compute A times R, and the value C0, which is Z times R plus an encoding of V0, and C1, which is W times R plus an encoding of V1. The receiver can now compute the value B times C1 plus C0 minus S times C and round the result modulo 2. It is easy to see that the value obtained by the receiver will be equal to B times V1 plus V0. Security against semi-honest senders follows easily from the LWB assumption. Let us focus on the more interesting case of malicious receivers. The problem here is that the value Z chosen by the adversary can be chosen arbitrarily. However, independently of the choice of Z, it can be argued that one of these matrices, A0 or A1, does not have short vectors in its rock span. Thus, we can use the smoothing lemma, which guarantees that essentially one of the ciphertexts will be statistically coaxed with uniform. This means that one of the plaintexts will be statistically eaten. So the problem now is how the reduction knows which case holds. Let's see how the extraction works in PVW. The trick here is that the reduction will choose the matrix A, together with the lattice tractor. Now, given Z, the reduction can check if there is an alpha in ZQ, such that alpha times Z is close to the row span of A. If there exists such alpha, then Z plus W times R is statistically close to uniform and the reduction can set B equal to 0. On the other hand, if there is no alpha, then Z times R is the value which is statistically close to uniform and the reduction can set B equal to 0. However, there's a drawback. In the proof, Q must be of polynomial size, because the reduction needs to go through over all values of Q. This is not good for OLE, because this would restrict the functionality to fields of polynomial size. Instead, we want to perform OLE over any field, even with super polynomial size. Let's see how we can recast the PVW OT scheme as an OLE scheme. Again, the CRS is composed by a matrix A and a vector W over a ring ZQ. Here, Q is a modulus such that Q can be written as Q1 times Q2. The OLE is going to be performed over ZQ1. The receiver will compute the vector Z as before using X as the input. The sender will encrypt again V0 and V1 under the different public keys and send this ciphertext to the receiver. The receiver will compute the value X times C1 plus C0 minus S times C and reduce it modulo Q1. As we've seen in the PVW case, the value obtained by the receiver is a linear combination of V0 and V1. Again, security against a semi-on-sender can be trivially established from the LWB assumption. For the malicious receiver case, we're going to write Z as S times A minus XW plus alpha D for a D of minimal length. Using the partial smoothing lemma, we can actually simulate the receiver's sender's message given only the output of the functionality X times V1 plus V0. So, it remains to show how the reduction can extract X from the receiver's message. To extract S from Z, we're going to choose a matrix A' together with the lattice trapdoor. But now, contrary to PVW, we're going to set the CRS as a matrix A, which is the matrix A' except the last row, and W, which is the last row of A'. Here, T is a square matrix with no norm such that A' times T is equal to 0. So, how can we recover all the components of the vector Z? Well, if we compute F, which is Z times the trapdoor T, then since A' times T is equal to 0, this will be equal to alpha D times T. If D is short, then the product D times T is also short because T is a low-norm matrix. So, we have to solve the equation alpha times D' where D' is the product D times T equal to F, where only F is known. Let's see how we can solve this equation. Let's write F as the vector F as F1 to Fm, and the vector D' as D'1 to D'n. Then, we can construct the following system of equations where each Fi is equal to alpha times D'i. Now, we can eliminate alpha from the equations and obtain the system of equations where each equation is of the form minus Fi times D'1 plus F1 times D'i equal to 0. We can see that it's enough to find the first coordinate D'1 in order to obtain all the other ones. Essentially, the main observation here is that each one of these equations will define a lattice of dimension 2. Our main observation now is that finding the shortest vector in a two-dimensional lattice is actually an easy problem. More precisely, consider the lattice lambda j, which is the orthogonal q-ary lattice defined by the vector Bj. Bj is a vector whose first coordinate is minus Fj over F1 and the second one is 1. Each lambda j corresponds to the lattice defined by the equations on the previous slide. We can now apply an SVP solver to lambda j and obtain the shortest vector Gj. We now observe that D'1 must be a multiple of the first coordinates of each of the vectors Gj. We can now set D'1 to be the least common multiple of these values. Now, given D' we can recover D via linear algebra and given Z and D we can find the solution S' to the equation. Finally, given S' we can extract the receiver's input X. This concludes the proof against a malicious receiver. To conclude, we'd like to mention two additional results that we obtain in this work. The first one is that we can extend the OLE protocol into a batch OLE where the receiver can commit to a batch of inputs and that achieves better communication complexity. The second one is that we can extend the OLE protocol to allow for malicious senders using current choose techniques at the cost of an additional OT protocol. That's all. Thanks.


My name is Hanine, a woman and a mother from Palestine, Gaza. I work now in Portugal, but my babies are still in Gaza. On this Mother's Day 2019, let us promise to protect all our children and our important planet.  Let every mother stand against war. Let every mother call for peace. Let every mother's cry be heard. Instead of flowers give us peace.  Give us instead the abolition of war, the promotion of peace, the care of people and planet. Each day the cruelties of war demand the blood sacrifices of mothers, children, young and old, civilian and soldier, foreign and domestic. It is time to say no more. To put down our foot, each and every one, and reject military's demand for blood sacrifices in all their many forms. Neither the flesh of our flesh nor the children of other mothers nor the prosperity of our labors, nor the earth's vitality should be sacrificed to false idols of war. We, the mothers and the children of mothers, demand respect for common mother, the earth, and for the end of the military's violations of her being. To commemorate Mother's Day without demanding these changes rings flat. For every mother appreciating the beauty of the spring, there is another mother screaming under the terror of bombs and bullets. For every mother savoring breakfast and bed, there is another mother hungry and unhoused, stateless and fleeing from war. We, the mothers and the children of mothers stand united against war and united for the well-being of people and planet. On this Mother's Day, 2019, let us promise to protect all children and our imperiled planet.  Let every mother stand against war. Let every mother call for peace. Let every mother's cry be heard. This Mother's Day, instead of flowers, give us peace, instead of brunch in all wars.


K Kwa vibrant towards Diu b As we try to see what are the rights of domestic workers in the UAE and what are the stipulations, what are the outline in the new labor law of 2022 that is coming into effect in the world Hi guys, welcome back to this channel and if it's your first time to come across this channel please consider subscribing, support this channel by subscribing Let us try to share the information Let us try to share ourselves in opportunities and let us try to share ourselves to grow The returning subscribers Thank you so much for watching videos to this channel and thank you so much for subscribing For the new subscribers Thank you so much Consider subscribing By the way, don't forget to press the notification bell or the notification not It will be the first to let you know when we upload a new video Remember, we are looking at the new labor law in the UAE coming 2022 in February Rights of domestic workers regarding the new labor law that is coming into effect February 2022 In this video we are going to look at the new labor law regarding domestic workers and we shall look at gratitude, leave, working hours and the rest what a domestic worker is supposed to have By the way, when we are talking about a domestic worker we may not look at someone who is actually only working as a nani but it is just a big profession that is classified under different departments especially when you go to look at the professionals in the UAE Remember, when we are talking about the UAE we are talking about the 7 emirates that make up the UAE and including of the 7 emirates the main fabricate these nations we look at Dubai and Abu Dhabi and other emirates that we may not talk about like Syriza and other emirates Remember, a new law is coming into effect in February 2022 and under this new law a lot of stipulations, a lot of articles have been summarized to know your rights as a domestic worker or any other worker in a different department but remember when we are talking about the rights of domestic workers domestic workers law in the UAE contains 41 articles that try to protect their rights and is enclosed within the domestic workers law which would include how much gratitude you are going to get at the end of your contract how much working hours you are supposed to have what is your rest time in case of dismissal by your employer what are you supposed to do all those are stipulated under what we call the domestic workers law I say it contains 41 articles Remember, the domestic labor or the domestic labor law in the UAE ensures to protect the safety of workers in any form of discrimination regarding age, regarding sex, regarding color regarding employment opportunities meaning that ensures that everyone is safe and feels at home when he is in the UAE therefore in this video when we are trying to look at the domestic workers law in the UAE in relation to what is coming the new labor law in 2022 feb 1 I want us to go through what are some of the summarized forms what are summarized out of the law that I need to share with you in this video I am going to read you out the summary of what is what is we expect to come in the new labor law if you are a domestic worker working in the UAE what you need to know what you need to know with gratitude what you need to know with your annual leave your medical leave what you need to know with your rest time even including the mails so let us go just straight into the summary of what I have and maybe by the end of the video you can try to pick up something Domestic workers law in the UAE contains 41 add cause to protect them which enclose the rights of domestic labor including working hours daily rest contract terms annual medical leave and gratitude by mails therefore the UAE domestic labor law ensures the safety of workers on work place and it prohibits discrimination among other employers working in the UAE on the basis of race color, gender, profession and religion in order to protect the domestic workers the following are shortly said details of such rules as patelepa law for the domestic workers in the UAE 1. payment of wages or salary within 10 days of each month 2. domestic workers should constitute a rest of 12 hours of rest every day depending on how long 1 day paid rest every week that you should have 1 day that is paid and this should be your rest day every week paid vacation of 30 days per year and after your contract of 2 years a 2-way ticket to and from your own country medical insurance by your employer if one fold seek a 30 days medical leave per year that is what the law says that is part of the spillation of the law I want you to understand the problem most of you might have not known this that exists but this is part of your rights return air ticket after completing a 2 years contract we say remember when we talk about gratitude and its avenge a worker who completes 1 year is entitled to gratitude depending on the terms and conditions comfortable accommodation to live that is what the law a healthy meal on the employer's expense keep passport and other identity papers with the workers the law spiopilates that the worker should have custody of his passport and the contract papers and other papers that are supposed not to the employer to keep those papers for you then in case of disappearance workers can complain to the minister of human resource and immobilization and in case not solved the worker and the employer will be referred to the court which will dissolve the matter and give the final ruling also domestic workers are exempt from court fees at all stages so for anyone who has any grievance or who has any complaint with the employer and you threaten in any way or you discriminated in any way you have the right to go to court but remember per the new law it says that any domestic worker will be exempt from what you call the court fees also remember there are also legal prohibitions of domestic workers up as per the draft of domestic workers law remember discrimination on the basis of race, religion and profession is prohibited in the domestic workers law the employment of young workers under the age of 18 is not allowed as per the domestic worker law so if you think you going to go and get a job below the age of 18 is not allowed as per the new labor law sexual harassment physical and verbal is not accepted by your employer or by your company in whatsoever exposure to physical harm by your employer and that is women termites maybe as harassment of any age nature per the new labor law is not allowed is criminal assignments or orders contracts for example you sign a contract to look after a house of 4 but in this case you are looking after a house of 20 is not allowed because it is not mentioned in your contract and as per the new labor law coming into effect one of the outlines in the new labor law coming under domestic workers it is not allowed because it is not mentioned in the contract you doing something that is controlling out of what you sign in the contract hope guys have tried to try to summarize for you the rights of domestic workers under the new labor law and hope have tried to share something so if you are a domestic worker in the UAE we look at Abu Dhabi, Dubai, Syriza and any other part of the Emirates and you feel you want to get clarity you can try to get some of this information and you know your rights thank you so much for coming back to this channel by the way don't forget to support this channel by subscribing and pressing the notification bell makes from the next question see you again in another video as we try to look at more of the domestic workers rights in the UAE regarding gratitude and regarding any other benefits that you supposed to occur see you again in the next video