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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

2,303 subscribers

49,120 Aufrufe • vor 2 Jahren •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

3 Kommentare

Profilbild von BuyHoldAndSTFU

BuyHoldAndSTFUvor 2 Jahren

@stevenstrogatz Beautiful.

Profilbild von George Haller

George Hallervor 2 Jahren

@stevenstrogatz Thanks!

Profilbild von Algebrium

Algebriumvor 2 Jahren

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.

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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.

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