How should we plan this, which vessel first.? 73... ym, admitted w/ c/o progressive dyspnea leading to emergency hospitalisation for ADHF No relevant past history, diabetes+, Trop I negative. Echo Global hypokinesia, EF- 20%show more

🚨 EARTH IS SPINNING SLIGHTLY FASTER AND FOR THE... FIRST TIME, SCIENTISTS ARE SERIOUSLY DISCUSSING A “NEGATIVE LEAP SECOND”. For decades, Earth’s rotation has been gradually slowing, which is why we occasionally add a leap second to keep atomic clocks in sync with the planet. But since around 2018–2020, something unusual has happened: Earth has been rotating faster than expected. Several days in recent years (including June 29, 2022) were among the shortest ever recorded by atomic clocks. This acceleration has forced timekeepers to consider something that has never been done before: subtracting a second from official time (a negative leap second) instead of adding one. Why this matters: • A negative leap second would mean clocks skip a second (e.g., jumping from 23:59:58 straight to 00:00:00) • It would be the first time in history this has happened • It could affect GPS, financial systems, telecommunications, and any infrastructure that relies on precise timing • The leading theory links the speedup to changes in Earth’s liquid outer core, though melting ice sheets are partially counteracting the effect The deeper implication: Earth is not a perfect clock. Its rotation speed is influenced by complex interactions between the core, oceans, atmosphere, and even climate change. As we become more dependent on ultra-precise global timing, these small geophysical changes are no longer just scientific curiosities they’re potential infrastructure issues. A 2024 study in Nature suggested a negative leap second might be needed around 2029, though the exact timing remains uncertain and depends on how Earth’s rotation behaves in the coming years. Would you rather we keep adding/subtracting leap seconds forever, or should we eventually decouple our clocks from Earth’s imperfect rotation? Follow for more frontier Earth science and timekeeping realities.show more

this is the moment successfully finished scheduling shifts for... my parent's tea store for the first time. my mom is BLOWN AWAY. this is going to save her hours of every week going back and forth with the team and sorting out this annoying task. the way we set it up: - "CameliaOS", our moltbot, sends her a reminder every morning to ask for inputs from team - team members respond with times - my mom sends screenshots to Camelia - Camelia updates her on any missing inputs - Camelia drafts a plan, adds it to google calendar (color coded, which is the form factor that the team is used to) - my mom gives Camelia feedback - she ships it one interesting learning: as we were teaching Camelia this new skill, my mom sometimes asked me "how should i explain to it that X or Y" I told her - just discuss with her like you would with any human, just share your doubts and concerns.. Opus is so great at making sense from vague inputs and help crystalize a plan. we are making progress, many more workflows to teach CamealiaOS, and I am sure more will surface the deeper we go into it.show more

Corvettes Up to 1,000T Following that analysis and the... idea of decentralized naval power, I must admit I was very surprised by the Finnish corvette Hamina and the Skjold, but especially the defense system of Hamina, which features 8 VLS for a vessel weighing only 250 tons. The Nordic countries understand the concept of decentralization very well. These small, well-armed, fast, and stealthy vessels symbolize much of what we've been discussing over the past few weeks. 🇸🇪🇳🇴🇫🇮 Today, I want to showcase a few corvettes up to 1,000 tons, and in this category, no one beats the Russian Karakurt and Buyan-M in terms of cost and firepower. Particularly the Karakurt, which is equipped with the Pantsir missile defense system covering a 20 km radius and carries 8 Kalibr missiles with a range of 2,500 km for land strikes, or 8 Oniks with a range of 600 km. The Karakurt is unquestionably the best option for corvettes up to 1,000 tons, but I would also like to highlight the Swedish Visby, which also has a defense system with a 20 km radius using Umkhonto-IR and features advanced stealth technology. Although the Visby is more modern, the cost of the Karakurt is highly relevant, along with its combat range. In a war, the cost of equipment replenishment should always be considered a top priority.show more

Dear Hunters, It has come to the development team's... notice that some illegally gained material "leaks" are spreading on multiple platforms. We are sorry for this situation. We are sorry if this illegal leak undermines the ceremonial first meeting between you and Sylus. Every love interest's first meeting with the hunter is a precious memory that cannot be repeated. For a long time in the past, planning content, promoting development, optimization and modification... We have been trying our best to prepare for this surprising "first meet." However, this incident disrupted the plan and undermined the experience for all players. Meanwhile, we also believe that the first glimpse may not be everything, because you and Sylus will have countless days of surprise that are worth looking forward to. Rather than let malicious leaks disrupt the pace, it is better to go forward bravely—debut of Sylus's Preview. The development team will continue to prepare for your formal first meeting. We sincerely hope that after he comes to your side, you two will gradually get to know each other and get along well. If the future ahead is good enough, the regret caused by this incident will be soothed. To whom behind this illegal and vicious incident, Obtaining and maliciously leaking business secrets through illegal means may give you a certain sense of accomplishment, but these acts will not escape the law. The investigation of this incident has been fully launched, and we will take all necessary rights protection measures, including but not limited to civil and criminal rights protection, according to the results of the investigation, to pursue to the end, and severely investigate the legal responsibility of the infringer. We sincerely call on Deepspace Hunters to join us in stopping the spread of this leak. The special mailbox for collecting information and clues about vicious access and leaks related to confidential content has been opened. If you encounter related behaviors or clues that are suspected of malicious leaking, stealing, and spreading undisclosed game content, you are welcome to send relevant information to the following email address: [[email protected]], the relevant departments will follow up the first time. Thank you again for your understanding and support through all this time. I hope we can work together to maintain a healthy and harmonious community environment and protect Linkon City for every player. Love and Deepspace Global Teamshow more

its me, blank - i'm starting a new company... called S7RX and im going to do what i've never done before - sharing it all here you probably know me as the founder of openpurpose but in short - i'm a designer turned founder - i started my studio 17 years ago called 3drops in stockholm which i rebranded to openpurpose a couple of years ago and grew it to over 70 members globally working with leading tech companies in us besides running the agency, over the past decade i took on a few personal projects that meant something to me - like leading the digitization of the global visa system for over 65 countries and working with a few enterprise founders to launch daring projects to future proof their organizations along the way i experimented with dozens of ideas which some turned into ventures and a few became companies with their own dedicated teams but for as long as i can remember i only had one dream - to launch a brand that earns like a tech company but feels like a lifestyle brand so now at the age of 36, i'm doing just that and calling it S7RX my first product is launching next week and with that we are officially starting this new journey so follow on IG to see the stories and say hi : ) this will be differentshow more

I am very happy to report we have scanned... the last page of the Howard W. Sams Photofact books for AI training. Here is the video of the final page of 1000s. No, not to repair TVs and Radios. But why? Many reasons. One is to capture the logic and thinking processes of an ancient epoch. This book series alone will align ANY AI platform to higher abilities because of the thinking used. Another is to understand what analog technology really is in a modern concept as it informs many functions completely unrelated to electronics. Thus I now am going to plan on a preservation process for these books that should allow them to be available for the next few 100 years or perhaps 1000 years. They are a masterpiece of very high protein data. In fact the highest protein data I have discovered, each square inch is valuable. I will write a series of articles on some landmark discoveries Ai have made in these books. More soon. And once again thank you for this donation. Thank you for thinking of our future through our past. Many say they will “help me out” some very smart and very wealthy, this guy came through. Gratitude.show more

Vitaliks mandarin fluency is a super bullish signal for... Ethereum 🐂 He had an open town hall at HK where community members asked him all sorts of questions, from the easy to the difficult The hard questions were all in Mandarin so i couldn't follow those 😅 At the town hall he laid out the guiding principle for Ethereum: cooperation without domination It's especially important in today's world where a powerful person dictates terms and others have to follow, or we have no cooperation & there's chaos What this means at a technical level is that Ethereums the world computer & we need to build enough trust that developers feel comfortable building apps on top of it. Solo staking, a conservative approach to changing the protocol etc are all part of this He also spoke on how new technology is a reset & creates a level playing field where the game starts again from zero with bringing a lot more people right to the frontier We are seeing this with AI (and zk too), where a noob developer can still catch up to a veteran with good prompt engineering. He shared his own experience of building an android app for the first time using AI despite having no prior experience in it Before people would say that EF needs to write more documentation. Now it's more relevant to show how deep seek integrations with solidity and Java can help easily create new Ethereum apps He sees AI as making it much easier for newcomers to build web3 apps & is making a push in this directionshow more

Universities and High Schools have not moved rapidly enough... to guide students to have skills for the next decade. THEY HAVE FAILED. It is a massive crisis that can be averted by understanding what AI and Robotics will bring about. Solutions are knowing how to use these tools and new industries that will rise. But this situation is also on ALL OF US. No “job” is safe from founder to entry level in most industries. You and I, by what we do, will be “replaced” ultimately. What to do? AI and Robotics are tools, the next decade is owned by those who know how to use them expertly, but this is also temporary. We have to understand that what we do for “work” will change giving ultimately a greater value to those that are: Creative Flexible Always learning Willing to be wrong Love being human Love being alive Know history Covet wisdom Knowing all tech has downsides Building strong family and friends Realize many institutions have failed The first four are required for you to be able to live through this period with your sanity intact. The rest will allow you to thrive. There are no true careers at this point anymore. There are advocation and vocations which will either earn you money or give life meaning. We will learn that we are not “what we do”, just like we knew for 99% of human existence. Let that sink in. — You and I are far, far ahead of knowing this and we can do two things: 1) Laugh at the “clueless” 2) Help people understand with grace Go to Reddit if you are 1, in fact don’t follow me because you will not like this next decade and what I post. You are 2 and thank you. Even if you and I have not solved this issue, we can help people understand what is ahead and with determination and creativity bound together to solve it locally. Or human family has done this millions of times. The evidence is: you are here. The Neo Luddite movement has not even begun and it will potentially rip apart society even more than all the fashionable moment in the recent past has. These Luddites will have a good point with the wrong answers cooked up by dying academics that cling to labels, “virtues” and victim hood. It will be readymade for some governments to enter in as “big daddy” to “help us”. You will not like what they do, but you will only know when it is too late. It will include YOU “volunteering” to “leave” by 60, to “help out” CanadaPod style. “Brian, I’m 24 what do I do?”. I hope to do much more here to help. But I do know this: 1) Learn a trade or vocation because it’s valuable. It may also be free to low cost if you do it right. 2) Learn everything you can about USING AI and TRAINING YOUR AI. Your expertise will be in the top 1% for a decade. But not forever. 3) Understand Bitcoin and how it will rise while other things sink. This is a short list for now. We will know more moving forward. When you see videos like this posted below, know one thing: Many of these folks had no real family of mental and physical support. Maybe no parent or one parent. Maybe only a broke system to prepare them for—nothing. This was not their doing. Now it is not your “job” to help them, it is your survival to help them if that is what you need. See some day after the dust settles these 20 year olds will be 40 year olds and running YOUR world. And at some point you may need them more than you think you do. You will need them, as they need you now. THIS IS WHAT PAST WISDOM KNEW. The elders of the past never found the need to piss on the youth and hope for the best. THE YOUTH ARE OUR BEST, let us all find ways to change it, even if every aspect of “the system” wants us to berate them into the ground.show more

Officially moving on from Tech game after I get... this thought off my chest. I more than welcome anyone smarter than me in regards to the football to chime in. I truly, truly, truly cannot wrap my head around the thought process here. These two plays I'm sure anyone with brain can agree officially sealed KU's slim chances in having a chance to win this game. The play calling to me seems like completely flipped in logic at best? First one, you are down 4, on your own 30 so you are not going to go for this. Ignoring that we were getting dominated in the trenches in this game and that the 'obvious' play is a run, I don't get why we make the decision in a must get spot to take the ball out of our QB's (who at the time was rolling) hands. Jalon Daniels is our best player. In an absolute must get/need, we should be relying on him to make a play. Then the second one. I obviously don't know the answer here, but I feel somewhat confident that the reason we didn't run here was because of how the earlier 3rd & 1 run went. While I don't necessarily agree with the premise of decision making on this alone, I can appreciate the recognition that we are going to struggle to gain a yard in an obvious run situation. But the thing is, we are in go for it range so the one thing you absolutely cannot have is a massive negative play. Literally anything else is okay (obviously not a turnover). I truly don't think there's a good chance we run the ball on this attempt and get a yard. But THIS situation gives you a free shot at it if you want to take it. I think this play call would have worked if we didn't let their best player run at our qb freely but I'd just argue this play had a ton of potential risk that wasn't necessary. Hell even a play action pass out of out shot gun or something rolling JD out to the left would have given us a good shot at first down with an escape route to bail out on the play if something went wrong. I'm once again for the millionth time saying I know and understand that this entire staff knows more about football in their pinky than I do. But I do think the game has evolved and game + clock management doesn't really require football knowledge/have a direct correlation to one's football knowledge. It's not as simple as ESPN's graphic says GO so you should go etc, there are variables and human behavior etc to deal with and I understand that. But we are just getting these situations downright wrong. We are flipping a coin that has a 20 pound weight attached to the heads side and calling tails almost every single time. S/O anyone who read all this but would just love some insight if there's anyone who disagrees and is a lot smarter than I!show more

Candace will be doing an exposé on Erika Kirk’s... past much like her “Becoming Brigitte” hit piece. I’m going to give her the same courtesy. At least there’s no glaring conflict of interest. It wont be pretty but there are a lot of lies that need debunking. I started doing a deep dive into her history a year ago. I still cannot see the bottom on her life’s shenanigans. It must be important to understanding who Candace is, if Candace believes it’s important to understanding who Erika is. Candace’s history is relevant because Candace herself says that it’s relevant. I find it really interesting Candy was a Young Steff groupie & tried to break into the hip-hop industry but failed. Something awful happened on that set. I don’t know what she did to get cut out of the video, all but .8 seconds. The artist hits her in the head while dancing & it looked intentional. Editing this in is a real insult. In a video on YouTube Candace tells us that an apology, from the boy who called her a racist name in high school, would have solved all of her problems and prevented her from making very destructive decisions, which led to her dropping out of college and starting a doxxing site called “social autopsy”. I imagine the embarrassment from this experience in the music industry was deeply scarring to her. Candace likely believes a young woman’s past is worthy of sifting through because her past is very checkered—going all the way back to high school. This video alone doesn’t prove as such but it does represent her abject hypocrisy and celebrity complex. It might explain why she latched onto Kanye and attacks celebrities. Obviously, I understand a lot more about her rejection from leftists politics than black culture. Media corruption & Politics is more my wheelhouse. She railed against “black culture” & “Marxism” only after being ejected from it. She was literally hating from outside of the club. Tree of Logic 🇺🇸 (a former police officer & black conservative YouTuber) was the first to call her out for being a nasty bully in 2017. Candace seems to run from other black women who call her out. 🧐 Tree was doxxed and harassed for months after calling out Candace Owens for doxxing and harassing people. Unfortunately, not many were willing to share arrows back then and it was just memory holed. Tree of Logic should have been platformed over Candace Owens and I will die on that hill. I’d love to hear what other SINCERE women think about the racial dynamics at play here. I have a limited perspective, clearly. She seems to be afraid of some women and just hates the rest. I don’t think there’s much in between. 🤷‍♀️ Just raising questions.show more

THE DREW PAVLOU ORIGIN STORY: My haters only know... me from my past year of tweeting. You have no idea how funny my actual origin story is. This is the story of how I accidentally caused an international political incident between China and Australia at the age of 20. I recorded that video of my Dad yelling at me the night before my first ever anti-CCP protest back in 2019. My Dad had just learned dozens of Chinese guys on Facebook were promising to kill me if I held a pro-Hong Kong protest at my university. So my Dad was yelling: “DREW, KEEP A FARKING LOW PROFILE!!!” I am a great son but I admit I am one of the most annoying people in the world today (top 0.0001 percentile). So the next day my Dad opened Facebook to find me giving interviews to international press as police helicopters flew over my university campus in midst of major standoff between our group of 30 anti-CCP activists and 500 pro-CCP thugs. This was June 2019. My 20th birthday marked the 30th anniversary of Tiananmen. Hong Kong was kicking off. I’d been reading about the persecution of Uyghurs and Tibetans. I became obsessed. I didn’t even know a single Uyghur or Hong Konger at first, I was just having orientalist white boy/autistic political fixation moment. I would read articles about it every day for hours and ultimately decided I had to do something. I had completely pure, noble intentions. No money, no CIA/State Department backing, just extremely enthusiastic white boy political autism. Like, I had taught myself 20 words in Cantonese so I could sing the Hong Kong protest songs. I even called it the “FREE HONG KONG FREE XINJIANG RALLY” because at this time I didn’t know Uyghurs hate the term “Xinjiang” (it means “New Territories” in Chinese) 😂 I had no experience with media, no experience protesting. I just knew how to be annoying. So I organised 20 of my friends and planned campus protest for Market Day, the busiest day of the year at the University of Queensland (UQ), the biggest uni in our state. I picked the busiest walkway at UQ and decided we would hold 30 minute sit-in chanting protest slogans against Xi Jinping. We didn’t know this at the time but UQ had perhaps the deepest economic and political ties with China out of any university in the English speaking world. 20 per cent of UQ’s budget came from Chinese international students. 9000 Chinese international students paying approximately $300 million a year. The Chinese government directly funded courses on campus through the UQ Confucius Institute and these courses taught that Hong Konger protesters and Uyghurs were terrorists. We had Chinese academics affiliated with the UQ Confucius Institute studying high tech weapons technologies, we had research institutes on campus helping to develop engines for PLA fighter jets. The Chinese government gave a medal to our university president Peter Høj for promoting Confucius Institutes worldwide and we later found out he was receiving a secret $200K bonus each year for deepening ties with China. And this wasn’t even scratching the surface. The youngest guy ever appointed professor at UQ was a bloke called Heng Tao Shen and he used Australian government research funding to develop AI technology that he then took to China to be deployed against Uyghurs in surveillance. So this was the combustible environment we were unwittingly stepping into. Chinese ultra-nationalists found our protest event on Facebook a couple nights before and started bombarding us with hundreds of death threats. They said they would rape my mother and kill me. I am Greek Australian man with hot Mediterranean blood, I couldn’t take this lying down. I searched “insults in Mandarin” on Google, I sent back the Chinese characters for “Fuck your ancestors to the 18th generation.” I think this was the point at which my Dad started yelling at me. The next day 500 Chinese ultranationalist counter-protesters rocked up. You can watch what happenedshow more

Whether you are a random person on X or... Elon Musk, I urge you all to please read this post and stop using videos like this one to claim that Biden has an "open border policy": #1) The people in this video are already on American soil. The agents have a few options here. Detain them behind the razor wire or detain them in front of it, let the children cut themselves on razor wire or make sure they don't get cut. #2) In May President Biden issued an "asylum ban" which barred migrants from applying for humanitarian protection if they cross the border against the law or fail to first apply for safe harbor while crossing through another country on the way to the U.S. The US COURTS OVERTURNED IT. Biden also requested $3.5B for more border patrol agents and judges and lawyers. Republicans refused. #3) Let me explain to you all why the people in this video can't simply be put on a truck and driven back into Mexico and dropped off: a - They have a right to due process according to our Constitution. b - There are international laws indicating that we can't just drop people off from Honduras or Cuba or any other nation into Mexico. What if one of these people claimed they were from Canada? Should we drop them in Canada? c - How do we immediately prove that a person is not an American, or an Italian, or a Brazilian if they claim they are? Stop pretending that Biden isn't doing anything. Stop pretending that the immigration problem is simple. Stop pretending that this has not been a problem for decades. Understand that the surge of migrants isn't the fault of Biden but actually global geopolitical upheaval in Cuba, Nicaragua, Venezuela and other nations. Instead of pointing fingers and claiming that "Biden has an open border policy," when his policy is not much different than those we have had for the last 40 years, how about working together on comprehensive reform? So before you make another Tweet claiming Biden has an Open Border Policy, how about instead you provide actual solutions that are LEGAL, that should be implemented.show more

On the leg between Guam (PGUM) and Kalaeloa (PHJR)... we experienced a fault with one of our 2 AC packs. This left us a single point of failure away from de-pressurization, which would require a descent to an altitude where we could breathe without supplemental O2. Keep in mind, a lower altitude drastically increases fuel consumption. Of course a single pack can maintain cabin pressure all the way up to the aircraft’s service ceiling, but if that pack fails, the aircraft cannot be pressurized. The situation required that Bob Allen & I make a plan as to how to handle the potential loss of our remaining pack. This plan would be dynamic, as the action taken would depend where we were at the time of de-pressurization. Past the ETP (Equal Time Point) turning back to GUM was not an option; and continuing to JRF at a low cabin altitude was ALSO not an option - as we’d be short on fuel. PKMJ was a bit too far south to be of use, but PWAK (Wake Island) and PMDY (Midway) were valid alternates that we could use for diversion and still land with the engines turning. Even though we did have ETOPS planning info on our flight plan, we can’t always rely on it 100% because ferry flying creates some unique challenges due to the fact that we don’t operate the same aircraft all the time, and we have no operational history to set the burn bias. We need to be proactive in the cockpit so on the secondary FPL page of the MCDU, Bob and I played out a few scenarios at different points and compared fuel burns. We decided on a boundary where once crossed, the diversion alternate switched from WAK to MDY. In either case - we’d land with fuel, but it would be pretty minimal. Passing 170W would be the most critical point. The options would be MDY or LIH from there and both would land with under 800 KG of fuel. Because that didn’t inspire much confidence, we took some additional measures and brought 2 POBs (portable O2 bottles) up to the flight deck. This way, we’d have both the crew O2 from the pressure demand bottle (about 30-40 mins estimated) plus the O2 from POBs available to remain a bit higher longer in the event of a depress. Staying higher meant saving fuel and having more options - always a good thing. Anyway, the operational pack remained working, and we were able to get the aircraft to JRF before getting the bad pack back online for the next leg - so crisis averted, but the moral of the story is: you always need to have a plan! Especially when flying over remote areas of the planet..show more

Today we're launching Chipped 💅 [link in second tweet]... 6 months ago we approached Shahanaj Akter with an idea. I wanted to turn my NFC chipped manicure into a set of press-ons so that I didn't have to spend hours doing it myself. Simple idea. Yeah not really, even though this idea has been around for a few years and so many great artists have been manually doing this, no one had worked out how to manufacture it. 6 weeks and 30 prototypes later we had it, she was a little rough around the edges but she worked, you could program it to anything with a URL. But linking to socials wasn’t enough, so we teamed with disco to build proof of irl schemas, so that when you tap it, it creates a decentralised friends list, stored privately, offchain but secured by your private key. During EF events we chipped over 200 crypto natives and the response was incredible with over 1000 data points being created in the first few days and 1 million impressions on twitter over the duration of the campaign. So, today is a fun day. We've released pre-sale. The colour drop is the result of governance and a community vote, but this is just the beginning for the colours and designs we plan on creating. For $49, the set of 22 press-ons comes in an aluminium matchbox with 2 NFC chip nails, and nail glue, so you can set your nails up in a few minutes literally anywhere [my salon of choice tends to be the airport lounge between conferences.] The nails come set up to your profile, which is kind of like a linktree [but cuter], where you’re able to add the socials you want it to link to, whether that's just your socials with the choice to add proof of irl credentials. It’s literally the memorable way to network. For guys who think this is ‘not for me’, consider it the easiest way to onboard your mother, your sisters and your girlfriend into web3. I wanted to create a product that eclipses the need to understand blockchain and makes it fun to use. I've dropped the link below and thank you to everyone who has been on this journey with us. xoxoshow more

My DMs and notifications are blowing up from this... slide situation. Here are my final thoughts. In every quarterback room I was in, we were taught to slide early (like way too early) and if you don’t, then you have to dive. Diving is the only way to protect yourself unless you decide to slide way before a defender is near you. Watch how Brock Purdy plays if you have questions about this. When he scrambles, he does a great job of deciphering slide versus dive situations. Niners fans see it every week. I’m not taking away from the fact that Trevor’s head injury is terrible, but we see this every other week with late hits on QB’s and when you have a guy running 18+ mph at you that has trucked defenders before, that’s a weird situation to be in. I’m not saying that Al-Shaiir was innocent, because he wasn’t, but I am saying that quarterbacks should be responsible with making it no doubt for defenders in split second situations. Trevor was clearly trying to get the first down and then slide. And we’ve also seen him people in the past. So I’m not buying the narrative that Trevor is a non-scrambling quarterback that slides all the time and that defenders should treat him that way. Happy to have a discussion leaving big feelings out of it :)show more

[Discrete Fourier Transform] by Hand ✍️ In signal processing,... the Discrete Fourier Transform (DFT) is no doubt the most important method. But the math involved is extremely complex, literally, involving a summation over a complex number term e^(-iwt). I developed this exercise to demonstrate that underneath such complexity, DFT is just a series of matrix multiplications you can calculate by hand. ✍️ Once you see that, it should not surprise you that a deep neural network, which is also a series of matrix multiplications, with activation functions in-between, can learn to perform DFT to process and analyze signals so effectively. How does DFT work? [1] Given ↳ Signals A, B, and C in the 🟧 frequency domain: ◦ A = cos(w) + 2cos(2w) ◦ B = cos(w) + cos(3w) + cos(4w) ◦ C = -cos(2w) + cos(3w) ◦ Each signal is a weighed sum of four cosine waves at frequencies 1w, 2w, 3w, and 4w. ◦ We will apply Inverse DFT to convert the signals to time domain representations, and then demonstrate DFT can convert back to their original frequency domain representations. ↳ Signal X in the 🟩 time domain. X is sampled at 10 time points 1t, 2t, …, 10t: ◦ X = [-2.5, -1.8, 3, -0.7, -1.0, -0.7, 3, -1.8, -2.5, 5] ◦ Suppose X is also a weighted sum of the same four cosine waves, but we don’t already know their weights. We will apply DFT to discover them. [2] 🟧 Frequency Matrix (F) ↳ Write the coefficients of A, B, C as a matrix F. Each signal is a row. Each frequency is a column. ↳ A → [1, 2, 0, 0] ↳ B → [1, 0, 1, 1] ↳ C → [0, 1-, 1, 0] [3] Cosine → Discrete ↳ Sample from the continuous cosine waves at discrete time points 1t, 2t, 3t, to 10t. [4] Cosine Matrix (W) ↳ Write the samples as a matrix, Each frequency is a row. Each time point is a column. [5] Inverse DFT: 🟧 Frequency → 🟩 Time ↳ Multiply the frequency matrix F and the cosine matrix W. ↳ The meaning of this multiplication is to linearly combine the four cosine waves (rows in W) into time-domain signals (rows in T) using the weights specified in F. ↳ The result is matrix T, which are signals A, B, C converted to the time domain. Each signal is a row. Each time point is a column. [6] Transpose ↳ Transpose T, converting each signal’s time domain representation from a row to a column. [7] DFT: 🟩 Time → 🟧 Frequency ↳ Multiply the cosine matrix W with the transpose of matrix T. ↳ The purpose of this multiplication is to take a dot-product between each time-domain signal (columns in the transpose of T) and each cosine wave (rows in W), which has the effect of projecting the signal onto a cosine wave to determine how much they are correlated. Zero means not correlated at all. ↳ The result is an intermediate version of the “recovered” frequency matrix where each column corresponds to a signal and each row corresponds to a frequency. ↳ Compared to the original frequency matrix F, this intermediate matrix has non-zero weights in the correct places, but scaled up by a factor of 5 (n/2, n=10). For example, signal A, originally [1,2,0,0], is recovered at [5,10,0,0]. [8] Scale ↳ Multiply each value by 2/n = 1/5 to scale down the intermediate matrix to match the magnitude of the original frequency matrix F. [9] Transpose ↳ Transpose the recovered frequency matrix back to the same orientation of the original frequency matrix F. ↳ Like magic 🪄, the result is identical to the original F, which means DFT successfully recovered the frequency components of signals A, B, C. [10] Apply DFT to X: 🟩 Time → 🟧 Frequency ↳ Now that we have some confidence in DFT’s ability to recover frequency components, we apply DFT to X’s time-domain representation by multiplying W with X. ↳ The result is the an intermediate matrix. [11] Scale ↳ Similarly, we scale down by a factor of 5 to obtain the recovered frequency components of X (a column). [12] Transpose ↳ Similarly, we transpose the recovered column to row to match the orientation of the frequency matrix. ↳ Using the coefficients [0,0,3,2], we can write the equation of X as 3cos(3w) + 2cos(4w). Notes: I hope this by hand exercise helps you understand the essence of DFT. But there is more technical details, such as: • Sine: The complete DFT math also includes sine waves that follow a similar calculation process. • Phase: Here, we assume all the cosine waves are aligned at the origin, namely, phase is 0. If a phase p is added, for example, cos(w+p), we will need to calculate the sine component and use their ratio to figure out what p is. • Magnitude: If phase is not zero, the magnitude will need to be calculated by combining both cosine and sine terms.show more

Naturally, Ralph Alvarado’s Ralph Alvarado MD political profile grew... in Kentucky following his GOP convention speech. This created a very interesting dynamic during the 2019 Kentucky Governor’s race when then-Kentucky Governor Matt Bevin Matt Bevin switched out his Lt. Gov. choice Jenean Hampton with Alvarado. Following this move, former Hampton aides claimed Mitch McConnell U.S. Senator Mitch McConnell was behind the last minute surprise switcharoo. This was reported in numerous Kentucky media outlets despite McConnell denying it. Matt Bevin went on to lose his reelection to Andy Beshear Governor Andy Beshear, which handed a red state like Kentucky to a Democrat governor. Beshear has gone on to hold power, leading to liberal policies in a Republican state. While on The View in February, Beshear called for ICE to leave Kentucky: “Well, every ICE agent should be withdrawn from every city and every community that they’re in.” Sources tell Loomer Unleashed that Beshear is also preparing for a Presidential run in 2028 on the Democrat ticket and he has been consulted on how to teach other Democrat candidates in red states how to publicly appear as a “moderate Democrat” while having radical Left, progressive policies. Elections have consequences, and no one understands this better than Team McConnell U.S. Senator Mitch McConnell… Perhaps Mitch knew Alvarado would be unpopular, which would lead to Bevin's defeat and, in turn, cause embarrassment for President Trump and the Republican Party, while also leading to a Democrat controlling the state. Now, we are facing a similar situation again. Alvarado is running for Congress in what’s supposed to be a safe red seat, while at the same time, he’s lying to voters by claiming to be a Trump supporter. Alvarado’s record proves he has NEVER been a Trump guy. Hmmm, it’s almost like the Paul, Massie, McConnell “sabotage Trump” political machine is working overtime in Kentucky to ensure Democrats win the midterms as a way to undermine President Trump’s legacy and the remainder of his time in office. Remember this information as the Kentucky GOP Primary approaches next month on May 19th, 2026! RECEIPTS 👇🏻show more

This is the second of two posts I’m making... about the teaching of Andy Stanley because I have a burden to warn people to be like the Bereans "examining the Scriptures daily to see if these things were so." (Acts 17:11). I have attached a short video clip where Stanley says we don’t know Jesus rose from the dead because the bible tells us so. He says it’s the other way around. Now how do we know Jesus bodily rose from the dead? Did any of us see it happen? No, it happened 2000 years ago. But haven’t people researched the resurrection and found all sorts of evidence consistent with Him rising from the dead. Yes, but such evidence, though powerful, and we can certainly use in our witnessing, does not ultimately prove He rose from the dead. In fact, no matter what evidence we point to in geology, biology, astronomy etc., none of this proves in an ultimate sense the bible is true. Now it is certainly true such evidence properly interpreted does confirm the bible’s history. For instance, the molecule of heredity DNA is a complex information system and language system. No one has seen matter produce information or a language from matter by natural processes. Our observations and experience show information and language have to come from an intelligence. Such evidence confirms an intelligence behind life. This certainly confirms the first verse of the bible, “In the beginning God created… .” But nonetheless, it’s not absolute proof. Think about it. We are finite beings living in the present. We don’t know everything. We don’t know how much we don’t know or do know in relation to whatever there is to know! When we try to interpret evidence of the present in relation to the past, how do we know we have all the relevant information to make the correct interpretation. Some information we don’t have could totally change our interpretation. That has certainly happened with scientists solving crimes using circumstantial evidence. When new evidence comes along, some of the interpretations change and certain people thought to be guilty were found they were innocent after-all. We need to have all the information needed. But we can’t know everything. However we have a book that claims over three thousand times to be the Word of God. This book claims that God moved people by His spirit to write His Word, what He wants revealed to us about life, the universe and history. This book, the bible, tells us that God knows everything, He is infinite in knowledge and wisdom. He has all information. “In whom are hidden all the treasures of wisdom and knowledge” (Colossians 2:3). If God’s Word is what it claims to be (and it is), then the infinite Creator God has revealed to us the key information we need to know to have the ability to correctly interpret this world in relation to the past, present and its purpose and meaning. “Therefore, we never stop thanking God that when you received his message from us, you didn’t think of our words as mere human ideas. You accepted what we said as the very word of God—which, of course, it is. And this word continues to work in you who believe” (1 Thessalonians 2:13). This means if we build our thinking on God’s Word, we build a Christian worldview to enable us to look at the world through “biblical glasses” and have the ability to correctly interpret and understand it. And Genesis 1-11 is the history that is foundational to the rest of the bible and thus our worldview. So, when we start with God’s Word we learn that the God revealed to us in the bible is the One Who created all things. Now by just looking at the world, for instance at DNA, we might deduce that there’s an intelligence behind life. But we would not know who that intelligence is unless revealed to us. The bible reveals who that intelligence is, God the father, Son, and Holy Spirit. But, if we just looked at the world with all its death, suffering and disease, we could assume that the intelligence behind life must be an ogre to make such a violent disease ridden suffering world. But when we start from God’s Word, we understand there was no death or disease to start with, but these entered the world because of sin. We also find man has a problem called sin which alienated him from God. We even find in Genesis that God promised someone would come to save us from our sin and restore our relationship with God (Genesis 3:15; 3:21). We learn later on that “someone” is Jesus--the one who became flesh for us, the babe in a manger 2000 years ago. It's important to understand we can’t know anything absolutely unless an absolute authority has revealed to us what we need to know. Now Andy Stanley claims we don’t know Jesus rose from the dead because the bible tells us so, but claims it’s the other way round, that because Jesus rose from the dead, we can believe what is says about this in the bible. In reality, Andy Stanley is actually claiming he knows all information about the resurrection to know it’s true so then he can proclaim what the bible says about the resurrection is true. This is not so. And remember from the previous post, Andy Stanley accepts man’s view of evolution and millions of years as true to declare what Genesis records about creation is not all true. So why shouldn't people take the word of others who claim Jesus didn't rise from the dead to then declare the account of the resurrection in the gospels can't be true. Stanley, as a finite fallen human being with very limited knowledge, starts outside the bible to go to the bible to make pronouncements over God’s written Word. No wonder he rejects a literal Genesis. Sadly, this is the case for the majority of our church leaders and Christian academics, particularly when it comes to Genesis. Think about it. Really Stanley is acting in accord with our sin nature because of what happened in Genesis 3. Part of our sin nature concerns us wanting to be our own god. Consider Genesis 3:1 and Genesis 3:5, the temptation by the devil. Satan tempted Adam and Eve to question God’s Word, and be want to be like God to decide good and evil, truth, etc., for themselves. In actuality, the statements Andy Stanley is making about Christianity and God’s Word are reflecting this sin problem we have. He is letting his sin nature master over him in this instance instead of letting God’s Word tell us clearly what we should believe. And I would say that about all Christians who reinterpret parts of the bible (like Genesis) because of beliefs from outside the bible. Now the whole bible is actually about Jesus, from the very first verse, that Jesus is the Creator (Colossians 1:16 “For by him all things were created,”), & and he is the Savior (Revelation 5:9), to the very last verse, “He who testifies to these things says, “Surely I am coming soon.” Amen. Come, Lord Jesus! The grace of the Lord Jesus be with all. Amen” (Revelation 22:20–21) God reveals all we need to know about Jesus in His Word. We know Jesus rose from the dead because the bible tells us so! We know we are sinners because the bible tells us so. We know we can be saved through faith in Christ because the bible tells us so. We know we need to repent of sin because the bible tells us so. As Christians we know we will spend eternity in Heaven because the bible tells us so. “So faith comes from hearing, and hearing through the word of God” (Romans 10:17). I still remember singing the chorus as a child Jesus loves me this I know, for the bible tells me so. Yes, the bible tells me so – that’s how know who Jesus is, that He is the Creator, that he died and rose from the dead, and that He is our Savior.show more