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Related Concept Videos

Newton's Second Law00:55

Newton's Second Law

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Newton's second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes in motion. Newton's second law is quantitative and is used extensively to calculate what happens in situations involving a force. All external forces acting on a system add together to produce a net force Fnet. A larger net external force produces a larger acceleration. This acceleration is directly proportional to, and in the same...
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Newtonian Fluid: Problem Solving01:18

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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Acceleration Vectors01:30

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In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv, therefore the greater the acceleration, the greater the change in velocity over a given time. Since velocity is a vector, it can change in magnitude, direction, or both. Thus acceleration is a change in speed or direction, or both. For example, if a runner traveling at 10 km/h due east slows to a stop, reverses direction, and continues their run at 10 km/h...
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Newton's Law of Motion01:20

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When we observe objects around us, one question that comes to mind is why they move or stay still. The answer to this question can be explained using Newton's laws of motion. These laws describe the fundamental principles of motion and the effects of forces on objects.
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Newton's Third Law: Introduction00:58

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Whenever one body exerts a force on a second body, the first body experiences a force equal in magnitude and opposite in direction, to the force that it exerts. For instance, when a person pushes on a wall, the wall exerts an equal and opposite force towards the person. This brings us to Newton's third law of motion. Newton's third law represents a certain symmetry in nature: Forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself.
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Swin-PSAxialNet: An Efficient Multi-Organ Segmentation Technique
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Accelerated Proximal Subsampled Newton Method.

Haishan Ye, Luo Luo, Zhihua Zhang

    IEEE Transactions on Neural Networks and Learning Systems
    |September 9, 2020
    PubMed
    Summary
    This summary is machine-generated.

    We developed a new algorithm, the accelerated proximal subsampled Newton method (APSSN), for efficient composite function optimization. APSSN significantly speeds up machine learning tasks by using a small data subset for faster computations while maintaining accuracy.

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    Area of Science:

    • Optimization
    • Machine Learning
    • Numerical Analysis

    Background:

    • Composite function optimization is crucial in machine learning, particularly for regularized empirical minimization.
    • Existing Newton-type proximal methods can be computationally intensive.

    Purpose of the Study:

    • To introduce an acceleration technique to Newton-type proximal methods.
    • To propose a novel, computationally efficient algorithm for composite function optimization problems.

    Main Methods:

    • Developed the accelerated proximal subsampled Newton method (APSSN).
    • Employed a subsampling strategy to construct an approximate Hessian for computational efficiency.
    • Utilized the semismooth Newton method to efficiently solve the dual problem for the scaled proximal mapping.

    Main Results:

    • APSSN achieves computational efficiency by using a small subset of samples for Hessian approximation.
    • The algorithm maintains a fast convergence rate.
    • Efficient computation of the scaled proximal mapping is achieved through the sampling strategy and the semismooth Newton method.

    Conclusions:

    • APSSN is an effective and computationally efficient algorithm for composite function optimization.
    • The proposed method offers a significant improvement over existing techniques for regularized empirical minimization.