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Nonlinear model reduction to spectral submanifolds is now available even under general (e.g., chaotic) forcing. Asymptotic expansions for generalized steady states of aperiodically forced mechanical systems also follow from these results.

George Haller

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49,120 görüntüleme • 2 yıl önce •via X (Twitter)

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@stevenstrogatz Beautiful.

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@stevenstrogatz Thanks!

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Let x(t) ∈ ℝ^n.The nonlinear diff equ: dx(t)/dt = f(x(t)) f: ℝ^n → ℝ^n. Let z(t) ∈ ℝ^m(m < n). The model dynamics are dz(t)/dt = g(z(t)) g: ℝ^m → ℝ^m. The goal : find g(z(t)) s.t the trajectories of z(t) closely approximate dynamics of the original system x(t).

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What seemed like an intractable problem is now possible: To design proteins with a specified nonlinear mechanical response, capturing complex folding and unfolding mechanisms in singe and few-shot computations. We present ForceGen, an end-to-end algorithm for de novo protein generation based on nonlinear mechanical unfolding responses. Rooted in the physics of protein mechanics, this generative strategy provides a powerful way to design new proteins rapidly, including exquisite and rapid predictions about their dynamical behavior. Proteins, like any other mechanical object, respond to forces in peculiar ways. Think of the different response you'd get from pulling on a steel cable versus pulling on a rubber band, or the difference between honey and glass. Now, we can design proteins with a set of desirable mechanical characteristics, with applications from health to sustainable plastics. The key to solving this problem was to integrate a protein language model with denoising diffusion methods, and using accurate atomistic-level physical simulation data to endow the model a first-principles understanding. ForceGen can solve both forward and inverse tasks: In the forward task, we can predict how stable a protein is, how it will unfold and what the forces involved are, all given just the sequence of amino acids. In the inverse task, we can design new proteins that meet complex nonlinear mechanical signature targets. Read the paper, led by LAMM@MIT postdoc Bo Ni, published in Science Advances: Why do we care about the mechanics of proteins? The mechanics of proteins are critical elements of many living systems - as evidenced in many studies of mechanobiology. Through evolution, nature has presented a set of remarkable protein materials with unique mechanical functions like elastins, silks, keratins or collagens that play crucial roles in biology. However, going beyond natural designs to discover proteins that meet specified mechanical properties remains challenging. So far, the only way to do this was to use existing evolutionary concepts or to manually alter proteins. With our new generative model we can directly design proteins to meet complex nonlinear mechanical property-design objectives. ForceGen leverages deep knowledge on protein sequences from a pretrained protein language model and maps mechanical unfolding responses to create proteins. Via full-atom molecular simulations for direct validation from physical and chemical principles, we demonstrate that the designed proteins are de novo, and fulfill the targeted mechanical properties, including unfolding energy and mechanical strength, and a detailed unfolding force-separation curves. ForceGen offers rapid pathways to explore the enormous mechanobiological protein sequence space unconstrained by biological synthesis, to enable the discovery of new protein materials with superior mechanical properties. B. Ni, D.L. Kaplan, M.J. Buehler, ForceGen: End-to-end de novo protein generation based on nonlinear mechanical unfolding responses using a language diffusion model. Sci. Adv. 10, eadl4000 (2024). DOI: 10.1126/sciadv.adl4000 Codes and model weights available Hugging Face: David Kaplan

What seemed like an intractable problem is now possible: To design proteins with a specified nonlinear mechanical response, capturing complex folding and unfolding mechanisms in singe and few-shot computations. We present ForceGen, an end-to-end algorithm for de novo protein generation based on nonlinear mechanical unfolding responses. Rooted in the physics of protein mechanics, this generative strategy provides a powerful way to design new proteins rapidly, including exquisite and rapid predictions about their dynamical behavior. Proteins, like any other mechanical object, respond to forces in peculiar ways. Think of the different response you'd get from pulling on a steel cable versus pulling on a rubber band, or the difference between honey and glass. Now, we can design proteins with a set of desirable mechanical characteristics, with applications from health to sustainable plastics. The key to solving this problem was to integrate a protein language model with denoising diffusion methods, and using accurate atomistic-level physical simulation data to endow the model a first-principles understanding. ForceGen can solve both forward and inverse tasks: In the forward task, we can predict how stable a protein is, how it will unfold and what the forces involved are, all given just the sequence of amino acids. In the inverse task, we can design new proteins that meet complex nonlinear mechanical signature targets. Read the paper, led by LAMM@MIT postdoc Bo Ni, published in Science Advances: Why do we care about the mechanics of proteins? The mechanics of proteins are critical elements of many living systems - as evidenced in many studies of mechanobiology. Through evolution, nature has presented a set of remarkable protein materials with unique mechanical functions like elastins, silks, keratins or collagens that play crucial roles in biology. However, going beyond natural designs to discover proteins that meet specified mechanical properties remains challenging. So far, the only way to do this was to use existing evolutionary concepts or to manually alter proteins. With our new generative model we can directly design proteins to meet complex nonlinear mechanical property-design objectives. ForceGen leverages deep knowledge on protein sequences from a pretrained protein language model and maps mechanical unfolding responses to create proteins. Via full-atom molecular simulations for direct validation from physical and chemical principles, we demonstrate that the designed proteins are de novo, and fulfill the targeted mechanical properties, including unfolding energy and mechanical strength, and a detailed unfolding force-separation curves. ForceGen offers rapid pathways to explore the enormous mechanobiological protein sequence space unconstrained by biological synthesis, to enable the discovery of new protein materials with superior mechanical properties. B. Ni, D.L. Kaplan, M.J. Buehler, ForceGen: End-to-end de novo protein generation based on nonlinear mechanical unfolding responses using a language diffusion model. Sci. Adv. 10, eadl4000 (2024). DOI: 10.1126/sciadv.adl4000 Codes and model weights available Hugging Face: David Kaplan

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Chancellor Merz: We are trying to procure air defense systems from around the world that will be made available to Ukraine. Much of the procurement is also being handled by Germany and a European consortium. We see that Ukraine itself is now capable of building long-range missile systems that are even better than some of what we in Europe offered and discussed in earlier years.

Chancellor Merz: We are trying to procure air defense systems from around the world that will be made available to Ukraine. Much of the procurement is also being handled by Germany and a European consortium. We see that Ukraine itself is now capable of building long-range missile systems that are even better than some of what we in Europe offered and discussed in earlier years.

Anton Gerashchenko

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.All India Trinamool Congress has destroyed the identity of মাছে ভাতে বাঙালি! Between 2020 to 2026, we imported fish worth 👉30.32 Million USD from Uganda 👉0.16 Million USD from Mauritius Also, 40.9 Crore KG of fish from Andhra Pradesh, Bihar, and Jharkhand between 2022 and 2025. This is not just a setback to our fishermen, but it is also a drain of wealth to other states and countries from West Bengal. We have slipped to number 3 in rice production under Mamata Banerjee , now we even import fish from other states!

.All India Trinamool Congress has destroyed the identity of মাছে ভাতে বাঙালি! Between 2020 to 2026, we imported fish worth 👉30.32 Million USD from Uganda 👉0.16 Million USD from Mauritius Also, 40.9 Crore KG of fish from Andhra Pradesh, Bihar, and Jharkhand between 2022 and 2025. This is not just a setback to our fishermen, but it is also a drain of wealth to other states and countries from West Bengal. We have slipped to number 3 in rice production under Mamata Banerjee , now we even import fish from other states!

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In October, before the 2020 election, Dominion Voting Systems received a $400 MILLION dollar payment from Staple Street Capital, which has ties to China and the CCP. Smartmatic, SGO, and Dominion all allegedly share the same physical address in a small building in Barbados, as a registered headquarters. These companies also share licensing agreements which is also a part of their core software and coding. This connection alone poses a massive national security risk as Smartmatic itself was engineered specifically to alter and manipulate the outcome of elections through backdoors built into the systems, where NO hacking is even required to change election results, it is a feature which was created at the direction of Hugo Chavez to alter election outcomes during Smartmatic's development. The operator's manual itself exposes these backdoor, built-in, features that these systems have that give administrators and operators of these systems full control to alter multiple data points, both on-site and remotely. Testimonies of election workers calling Dominion when problems occurred with Dominion remotely fixing the problems, even after stating under oath that there was no internet connection. Stacy Abrams' website listed numerous vulnerabilities in these systems, Texas rejected using Dominion because they lacked basic security, but swing states and others were allowed to use their systems? These systems seem to have been permitted to use because of their remote and other backdoor capabilities. There were no errors, just sophisticated, intentional, fraud.

In October, before the 2020 election, Dominion Voting Systems received a $400 MILLION dollar payment from Staple Street Capital, which has ties to China and the CCP. Smartmatic, SGO, and Dominion all allegedly share the same physical address in a small building in Barbados, as a registered headquarters. These companies also share licensing agreements which is also a part of their core software and coding. This connection alone poses a massive national security risk as Smartmatic itself was engineered specifically to alter and manipulate the outcome of elections through backdoors built into the systems, where NO hacking is even required to change election results, it is a feature which was created at the direction of Hugo Chavez to alter election outcomes during Smartmatic's development. The operator's manual itself exposes these backdoor, built-in, features that these systems have that give administrators and operators of these systems full control to alter multiple data points, both on-site and remotely. Testimonies of election workers calling Dominion when problems occurred with Dominion remotely fixing the problems, even after stating under oath that there was no internet connection. Stacy Abrams' website listed numerous vulnerabilities in these systems, Texas rejected using Dominion because they lacked basic security, but swing states and others were allowed to use their systems? These systems seem to have been permitted to use because of their remote and other backdoor capabilities. There were no errors, just sophisticated, intentional, fraud.

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Tamil Nadu is showing the way for Maharashtra to follow! - Prof. Deepak Pawar, Marathi Abhyas Kendra Even voices from other states now agree, #NEP is a backdoor #Hindi imposition. It's a cultural & arrogant political overreach by the North Indian cow belt politicians. #TamilNadu under Hon'ble CMOTamilNadu Thiru. M.K.Stalin is standing firm to protect #education, #federalism & linguistic equality. When Tamil Nadu resists, #India listens. 🔗: #DMK4TN

Tamil Nadu is showing the way for Maharashtra to follow! - Prof. Deepak Pawar, Marathi Abhyas Kendra Even voices from other states now agree, #NEP is a backdoor #Hindi imposition. It's a cultural & arrogant political overreach by the North Indian cow belt politicians. #TamilNadu under Hon'ble CMOTamilNadu Thiru. M.K.Stalin is standing firm to protect #education, #federalism & linguistic equality. When Tamil Nadu resists, #India listens. 🔗: #DMK4TN

DMK IT WING

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🪖MilitaryNewsUA🇺🇦

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Sawyer Merritt

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We continue our work in Washington and are soon expecting a decision on F-16s to increase the number of aircraft available to Ukraine. Yesterday, we secured 5 more Patriot systems and dozens of other air defense systems. Today, a decision on aircraft is also expected. We will also finalize two new security agreements, which include support for sanctions against Russia, our accession to the EU and NATO, the protection of our soldiers and people, and reconstruction efforts. There will be at least ten meetings with world leaders. I am grateful to our entire team for their work. Today, we will also have meetings in the U.S. Congress with both parties and both chambers. We appreciate American support and will discuss how to achieve even more positive results in our cooperation with the United States – ideally, long-range and far-reaching.

We continue our work in Washington and are soon expecting a decision on F-16s to increase the number of aircraft available to Ukraine. Yesterday, we secured 5 more Patriot systems and dozens of other air defense systems. Today, a decision on aircraft is also expected. We will also finalize two new security agreements, which include support for sanctions against Russia, our accession to the EU and NATO, the protection of our soldiers and people, and reconstruction efforts. There will be at least ten meetings with world leaders. I am grateful to our entire team for their work. Today, we will also have meetings in the U.S. Congress with both parties and both chambers. We appreciate American support and will discuss how to achieve even more positive results in our cooperation with the United States – ideally, long-range and far-reaching.

Volodymyr Zelenskyy / Володимир Зеленський

489,462 görüntüleme • 2 yıl önce

A great video of Xavi talking about the importance of the ‘4 P’s’ in the Game Model and DNA of Barcelona: Positioning. Pressure. Possession. Perception. Jordi Alba also talking about how it is difficult for players that were not taught these things as children to do them now. That’s why it is so important to implement #KingKnightEd Concepts from an early age.

A great video of Xavi talking about the importance of the ‘4 P’s’ in the Game Model and DNA of Barcelona: Positioning. Pressure. Possession. Perception. Jordi Alba also talking about how it is difficult for players that were not taught these things as children to do them now. That’s why it is so important to implement #KingKnightEd Concepts from an early age.

King Knight Education

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People here can't comprehend the level of poverty among tribals in West Bengal which makes them susceptible to TMC > A Bhumij woman states that TMC workers give them alcohol as incentive on voting day > A mother says her son is being forced to pick rice even after education as there are no jobs > Many state they don't get any benefits from state govt > For these people, even ₹2k per month is a huge amount

People here can't comprehend the level of poverty among tribals in West Bengal which makes them susceptible to TMC > A Bhumij woman states that TMC workers give them alcohol as incentive on voting day > A mother says her son is being forced to pick rice even after education as there are no jobs > Many state they don't get any benefits from state govt > For these people, even ₹2k per month is a huge amount

do'o kappa

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🚨 FLAVIO BOLSONARO: BRAZIL IS NOW TARGETING PRESS FREEDOM Flávio Bolsonaro just told Liz Truss that restrictions on free speech in Brazil have expanded and now threaten the media. “Now that President Bolsonaro is even prevented from running for any public office... these same methods are now also being used to attack freedom of the press.” Source: In The Room

🚨 FLAVIO BOLSONARO: BRAZIL IS NOW TARGETING PRESS FREEDOM Flávio Bolsonaro just told Liz Truss that restrictions on free speech in Brazil have expanded and now threaten the media. “Now that President Bolsonaro is even prevented from running for any public office... these same methods are now also being used to attack freedom of the press.” Source: In The Room

NewsForce

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VIDEO | Hyderabad: On NCRB report, BRS Working President KT Rama Rao (KTR) said, “The NCRB shows that Telangana has recorded the highest reduction in farmer suicides in the country over the past 10 years under KCR’s government, a true example of humane and effective governance. Initiatives like Rythu Bandhu, Rythu Bima, improved irrigation, and 24-hour free power supply have boosted farmer confidence and delivered remarkable results. While neighbouring Maharashtra faces rising farmer suicides, Telangana’s success serves as a model for other states to ensure no farmer suffers due to lack of support.” #NCRB #farmers (Full video available on PTI Videos -

VIDEO | Hyderabad: On NCRB report, BRS Working President KT Rama Rao (KTR) said, “The NCRB shows that Telangana has recorded the highest reduction in farmer suicides in the country over the past 10 years under KCR’s government, a true example of humane and effective governance. Initiatives like Rythu Bandhu, Rythu Bima, improved irrigation, and 24-hour free power supply have boosted farmer confidence and delivered remarkable results. While neighbouring Maharashtra faces rising farmer suicides, Telangana’s success serves as a model for other states to ensure no farmer suffers due to lack of support.” #NCRB #farmers (Full video available on PTI Videos -

Press Trust of India

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I’ve been watching New York real estate for decades. It’s one of the worst places to do business right now. High taxes, broken systems, zero incentive for capital to stay. Now we’ve got politicians promising free everything like it’s a business model. It’s not. Capital doesn’t invest in “free.” It invests in results. If these anti-business policies become reality, money will leave New York fast. You don’t build an economy on fantasy. The American Dream is about opportunity, not handouts. Let’s not forget that.

I’ve been watching New York real estate for decades. It’s one of the worst places to do business right now. High taxes, broken systems, zero incentive for capital to stay. Now we’ve got politicians promising free everything like it’s a business model. It’s not. Capital doesn’t invest in “free.” It invests in results. If these anti-business policies become reality, money will leave New York fast. You don’t build an economy on fantasy. The American Dream is about opportunity, not handouts. Let’s not forget that.

Kevin O'Leary aka Mr. Wonderful

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#WATCH | Chennai | NTK State youth wing Coordinator, Fathima Farhana says, "We want to be a change from these common political parties that are already there... The real freebie would be proper education... and proper access to medicine. These should be of international standards. We see neighbouring states providing good medical facilities and we lag behind that also..." He also says, "Access to roads or pure drinking water is a great question of our right now in Tamil Nadu. I think we should make all these factors accessible to people. And we also promise the people that we will be giving these things as freebies to them instead of actually the materialistic freebies that will only last for a month or 15 days or 20 days because they are not even of good quality..." (19.03)

#WATCH | Chennai | NTK State youth wing Coordinator, Fathima Farhana says, "We want to be a change from these common political parties that are already there... The real freebie would be proper education... and proper access to medicine. These should be of international standards. We see neighbouring states providing good medical facilities and we lag behind that also..." He also says, "Access to roads or pure drinking water is a great question of our right now in Tamil Nadu. I think we should make all these factors accessible to people. And we also promise the people that we will be giving these things as freebies to them instead of actually the materialistic freebies that will only last for a month or 15 days or 20 days because they are not even of good quality..." (19.03)

ANI

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I’m back, with a little something… GPC 1, a new general-purpose classifier enabling: bounding boxes, poses, coordinates, direct mechanical control and so much more, all in milliseconds. Post-trained on millions of datapoints and thousands of unique problem classes learned directly from you guys posting on X, GPC-1 is a great tool for many things. Early user feedback is also good :) A new output class enables precise continuous range numerical outputs, so the model can output coordinates of bounding boxes, exact angles and distances, pose estimations, scores, and more. It goes a lot beyond typical classification which just pick a label. Excited to see where this goes. Available now!

I’m back, with a little something… GPC 1, a new general-purpose classifier enabling: bounding boxes, poses, coordinates, direct mechanical control and so much more, all in milliseconds. Post-trained on millions of datapoints and thousands of unique problem classes learned directly from you guys posting on X, GPC-1 is a great tool for many things. Early user feedback is also good :) A new output class enables precise continuous range numerical outputs, so the model can output coordinates of bounding boxes, exact angles and distances, pose estimations, scores, and more. It goes a lot beyond typical classification which just pick a label. Excited to see where this goes. Available now!

Harsha Gundala

43,276 görüntüleme • 15 gün önce