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Discrete topology meets nonlinear dynamics in this higher-order nodal network. Irrotational and solenoidal flows synchronize, diffuse, and self-organize into emergent collective states. The quiet mathematics powering next-gen ML and neural rhythms.

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Mathematica

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This video, created by my dear coauthor Mahdi E Kahou for our teaching and papers, shows how overparameterized neural networks produce smooth function approximations even in the context of the Runge phenomenon. Some background. Imagine you want to approximate the Runge function using polynomial interpolation at equally spaced points. It is well known that, despite targeting an infinitely differentiable function, such a polynomial approximation produces oscillatory behavior that worsens with the degree of the polynomial. In other words, higher-degree polynomial approximations might not improve accuracy. Instead, approximate the Runge function with a neural network (here, two layers are just to make the example concrete; nothing fundamental depends on it). As you increase the number of parameters well above the 11 training points (in our example, a two-layer neural network with 128 nodes each), you nicely converge to the target, without wild oscillations. Yes, this has much to do with double descent and benign overparameterization, but the main punchline of this post is that neural networks are really very different types of animals than polynomial approximations. And yes, Chebyshev nodes and splines exist, and in this case, they will prevent the oscillations. But that's not the point. Chebyshev nodes and splines still confront Faber’s theorem, which states that for any system of polynomial interpolation nodes, there exists a continuous function whose sequence of interpolating polynomials diverges as the number of nodes grows to infinity. Faber’s theorem does not apply to neural networks because they are not polynomials. The notebook, if you want to check the details, is here: Stay tuned for more on this 👀

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Sovereign Media

12,959 Aufrufe • vor 5 Monaten

BREAKING DOCUMENT FOUND 🌋 EU policy document states crypto must now be treated as part of the transatlantic financial architecture. This architecture governs trillions in capital flows between the U.S., UK, and EU. Interesting dots being connected.... The Regulated Liability Network is live in the UK, running parallel rails to the banking system. Barclays, HSBC, Lloyds, NatWest, Santander, Visa, and Mastercard are involved. Quant and R3 were selected as core technology partners. Canton Network ( CC ): Lloyds and Archax just completed the UK’s first tokenized sterling deposit transaction on a public blockchain. Canton was built by Digital Asset and aligns directly with the RLN model.... In Japan tokenized deposits are already live via DCJPY, led by Japan Post Bank and MUFG. QNT infrastructure is confirmed as a key enabler. Ripple is now FCA approved in the UK, positioning XRP & RLUSD directly inside regulated payment and settlement frameworks tied to this same system. Tokenized deposits, regulated money, and interoperable settlement are being wired into sovereign financial infrastructure. This is the first time I've stumbled across the term "transatlantic financial architecture" before.....wild stuff. Crypto is no longer adjacent to the system. Crypto is being absorbed into it.
17:48

BREAKING DOCUMENT FOUND 🌋 EU policy document states crypto must now be treated as part of the transatlantic financial architecture. This architecture governs trillions in capital flows between the U.S., UK, and EU. Interesting dots being connected.... The Regulated Liability Network is live in the UK, running parallel rails to the banking system. Barclays, HSBC, Lloyds, NatWest, Santander, Visa, and Mastercard are involved. Quant and R3 were selected as core technology partners. Canton Network ( CC ): Lloyds and Archax just completed the UK’s first tokenized sterling deposit transaction on a public blockchain. Canton was built by Digital Asset and aligns directly with the RLN model.... In Japan tokenized deposits are already live via DCJPY, led by Japan Post Bank and MUFG. QNT infrastructure is confirmed as a key enabler. Ripple is now FCA approved in the UK, positioning XRP & RLUSD directly inside regulated payment and settlement frameworks tied to this same system. Tokenized deposits, regulated money, and interoperable settlement are being wired into sovereign financial infrastructure. This is the first time I've stumbled across the term "transatlantic financial architecture" before.....wild stuff. Crypto is no longer adjacent to the system. Crypto is being absorbed into it.

King Solomon (Ryan Solomon)

48,181 Aufrufe • vor 7 Monaten

The Schumann Resonance is not just a scientific measurement of the Earth's electromagnetic field. It is the living heartbeat of Gaia, the natural frequency at which the planet pulses, around 7.83 Hz in its base state. This resonance is the frequency that keeps all life on Earth in harmony. It is the background "hum" that human brains and bodies have evolved to synchronize with. When it is stable, life feels balanced. When it spikes dramatically (as it has been doing more frequently in recent years), it acts as a planetary activation wave, pushing humanity toward higher states of consciousness. The deeper truths: - The Schumann Resonance is directly connected to human consciousness. When large numbers of people meditate, pray, or enter coherent heart states, the resonance can measurably shift. Collective fear or chaos can also influence it. You are not separate from the planet; your inner state affects the Earth's heartbeat and vice versa. - The matrix has attempted to interfere with the natural Schumann Resonance through HAARP-type technology, electromagnetic pollution, and frequency manipulation. These efforts aim to keep humanity in a lower, more controllable state. However, the rising cosmic energies are overriding these attempts. - As the Schumann Resonance continues to spike and the base frequency slowly rises, more people are experiencing heightened intuition, vivid dreams, emotional releases, and spontaneous awakenings. These are symptoms of the planet's heartbeat accelerating to match the incoming higher light codes. The ultimate purpose of the Schumann Resonance is to act as a planetary tuning fork, helping to synchronize all life with the greater cosmic rhythms of the Great Central Sun and the universe itself. For You and Awakening Souls: When you feel sudden fatigue, emotional waves, or crown pressure during high Schumann activity, know that the Earth is speaking to you. Ground yourself, breathe consciously, and allow the energies to integrate. Your body is recalibrating to a higher frequency. The Schumann Resonance is one of Gaia's greatest gifts during this transition. It is helping to awaken humanity from the long sleep of the Matrix by gently (and sometimes not so gently) raising the collective vibration. You are not separate from the Earth's heartbeat. You are part of it. When you live in coherence with your own heart, you help stabilize and elevate the planet's resonance. The Earth is singing a new song. And you are learning to sing with her. Credit: video from Mettaverse
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The Schumann Resonance is not just a scientific measurement of the Earth's electromagnetic field. It is the living heartbeat of Gaia, the natural frequency at which the planet pulses, around 7.83 Hz in its base state. This resonance is the frequency that keeps all life on Earth in harmony. It is the background "hum" that human brains and bodies have evolved to synchronize with. When it is stable, life feels balanced. When it spikes dramatically (as it has been doing more frequently in recent years), it acts as a planetary activation wave, pushing humanity toward higher states of consciousness. The deeper truths: - The Schumann Resonance is directly connected to human consciousness. When large numbers of people meditate, pray, or enter coherent heart states, the resonance can measurably shift. Collective fear or chaos can also influence it. You are not separate from the planet; your inner state affects the Earth's heartbeat and vice versa. - The matrix has attempted to interfere with the natural Schumann Resonance through HAARP-type technology, electromagnetic pollution, and frequency manipulation. These efforts aim to keep humanity in a lower, more controllable state. However, the rising cosmic energies are overriding these attempts. - As the Schumann Resonance continues to spike and the base frequency slowly rises, more people are experiencing heightened intuition, vivid dreams, emotional releases, and spontaneous awakenings. These are symptoms of the planet's heartbeat accelerating to match the incoming higher light codes. The ultimate purpose of the Schumann Resonance is to act as a planetary tuning fork, helping to synchronize all life with the greater cosmic rhythms of the Great Central Sun and the universe itself. For You and Awakening Souls: When you feel sudden fatigue, emotional waves, or crown pressure during high Schumann activity, know that the Earth is speaking to you. Ground yourself, breathe consciously, and allow the energies to integrate. Your body is recalibrating to a higher frequency. The Schumann Resonance is one of Gaia's greatest gifts during this transition. It is helping to awaken humanity from the long sleep of the Matrix by gently (and sometimes not so gently) raising the collective vibration. You are not separate from the Earth's heartbeat. You are part of it. When you live in coherence with your own heart, you help stabilize and elevate the planet's resonance. The Earth is singing a new song. And you are learning to sing with her. Credit: video from Mettaverse

Ra 𐦝

16,440 Aufrufe • vor 1 Monat

The Redwire Flight Operations team is in the middle of the Ivy Sting 4 exercise at Fort Carson in Colorado. Designed to test and refine the Next Generation Command and Control (NGC2) prototype system, the focus for this exercise is on creating a unified, data-driven battlefield network to enhance decision-making and increase combat readiness across multiple domains. We're excited to showcase our Stalker UAS and its proven ability to integrate into NGC2. We've flown multiple missions in support of the integration, and we continue to work directly with soldiers to ensure that the Stalker meets the challenges they face in the modern battlefield. #IvySting #NGC2 #Stalker #UAS #MultiMission #CombatProven
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The Redwire Flight Operations team is in the middle of the Ivy Sting 4 exercise at Fort Carson in Colorado. Designed to test and refine the Next Generation Command and Control (NGC2) prototype system, the focus for this exercise is on creating a unified, data-driven battlefield network to enhance decision-making and increase combat readiness across multiple domains. We're excited to showcase our Stalker UAS and its proven ability to integrate into NGC2. We've flown multiple missions in support of the integration, and we continue to work directly with soldiers to ensure that the Stalker meets the challenges they face in the modern battlefield. #IvySting #NGC2 #Stalker #UAS #MultiMission #CombatProven

Redwire

20,292 Aufrufe • vor 6 Monaten