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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

100
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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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.7K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.7K
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

3.3K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.3K
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

4.5K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
4.5K
Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

494
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
494
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

126
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
126

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A Prediction Error-driven Retrieval Procedure for Destabilizing and Rewriting Maladaptive Reward Memories in Hazardous Drinkers
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非形回帰関数を持つ二段階のストキャスティックプログラムのための分解アルゴリズム

Hanyang Li1, Ying Cui1

  • 1Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA 94720 USA.

SIAM journal on optimization : a publication of the Society for Industrial and Applied Mathematics
|August 25, 2025
PubMed
まとめ
この要約は機械生成です。

この研究は,複雑な2段階のストキャスティックプログラムを解くための新しい分解法を導入しています. 新しいアプローチは,非凸性を効果的に処理し,困難な最適化問題に対する堅固な解決策を提供します.

キーワード:
90C15 について90C26 について分解するノンコンベックスリサーチ2段階ストキャスティックプログラム

さらに関連する動画

Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules
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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

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関連する実験動画

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Protein WISDOM: A Workbench for In silico De novo Design of BioMolecules
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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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科学分野:

  • 最適化について
  • 数学プログラミング
  • コンピュータ科学

背景:

  • クラシック分解法では,2段階のストキャスティックプログラムでは,非凸のリサーチ関数では失敗する.
  • 第1段階の変数による非線形パラメータ化は,第2段階の目標と制約を複雑にする.
  • クラークの規則性欠陥は,ベンダーズやラグランジーのアルゴリズムを直接一般化することを妨げます.

研究 の 目的:

  • 非凸の2段階ストキャスティックプログラムのための新しい分解フレームワークを開発する.
  • クラークの規則性がない場合,既存の方法の限界に対処する.
  • 非線形パラメータ化された第2段階のリサーチ関数に関する問題の効果的なアルゴリズムを提供する.

主な方法:

  • リソース関数の暗黙の凸構造の探求.
  • 部分的なモロー封筒を利用した分解枠の導入.
  • リキュース関数の強い凸の二次近似の連続生成.
  • 第2段階の凸子問題の解を介して,第1段階のマスター問題への近似の統合.

主要な成果:

  • 固定されたシナリオと順次サンプリングされたシナリオの両方に収束が確立されました.
  • 数値実験を通じて提案されたアルゴリズムの有効性を実証した.
  • 2段階のストキャスティックプログラミングにおける非凸性の課題に成功しました.

結論:

  • 新しい部分モローエンベローベースの分解フレームワークは,非凸の2段階ストキャスティックプログラムに有効です.
  • この方法は,古典的な分解アルゴリズムの限界を克服します.
  • このアプローチは,非線形パラメータ化されたリサーチ関数の複雑な最適化問題に対する実行可能な解決策を提供します.