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Weak Base Solutions03:21

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Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...
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Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majority of dissolved molecules in their original form and generating a relatively small amount of hydronium ions. Weak acids are commonly encountered in nature, being the substances partly responsible for the tangy taste of citrus fruits, the stinging sensation of insect bites, and the unpleasant smells associated with body odor. A familiar example of a...
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Weak acids and bases do not undergo dissociation completely, and titrations between these two are rarely studied. When such studies are performed, say, for the titration of a weak acid with a weak base, the titration curve plots the change in pH as a function of the volume of base added. Take the titration of acetic acid with ammonia, for instance. During the titration, these two species form ammonium acetate and water, but the pH change is slow and gradual.
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The different configurations of source-load connections include wye (star) and delta connections. The relationship between line and phase voltages and currents varies depending on the configuration. When the source is supplying power, it is transmitted through the wires to the load, and during this transmission, some power is absorbed by the wires, leading to line loss.
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In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
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Constrained-CNN losses for weakly supervised segmentation.

Hoel Kervadec1, Jose Dolz1, Meng Tang2

  • 1ÉTS Montréal, QC, Canada.

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Summary
This summary is machine-generated.

This study introduces a new weakly-supervised learning method for CNN segmentation that uses a differentiable penalty to enforce inequality constraints. This approach achieves segmentation performance comparable to full supervision while reducing computational costs.

Keywords:
CNN constraintsDeep learningSemantic segmentationWeakly-supervised learning

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Area of Science:

  • Computer Vision
  • Machine Learning
  • Medical Image Analysis

Background:

  • Weakly-supervised learning reduces annotation effort in CNN segmentation.
  • Inequality constraints leverage unlabeled data and domain knowledge.
  • Existing methods using Lagrangian dual optimization are computationally expensive.

Purpose of the Study:

  • To develop a computationally efficient method for weakly-supervised segmentation using inequality constraints.
  • To improve segmentation performance by directly enforcing constraints within the loss function.
  • To enable comparable performance to fully supervised methods with minimal annotations.

Main Methods:

  • Introduced a differentiable penalty to enforce inequality constraints directly in the loss function.
  • Avoided complex Lagrangian dual iterates and proposal generation.
  • Applied the method to CNN segmentation tasks with linear constraints like region size and image tags.

Main Results:

  • The penalty-based approach significantly outperformed previous Lagrangian-based methods.
  • Achieved segmentation performance comparable to full supervision with partial pixel annotations.
  • Reduced computational demand during training.

Conclusions:

  • The proposed differentiable penalty method offers a more efficient and effective approach to weakly-supervised segmentation.
  • The framework is extensible to various non-linear constraints, showing potential for semantic medical image segmentation.
  • Publicly available code facilitates further research and application.