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Statically Indeterminate Problem Solving

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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...

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Updated: Jun 21, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Hiding quiet solutions in random constraint satisfaction problems.

Florent Krzakala¹, Lenka Zdeborová

¹CNRS and ESPCI ParisTech, UMR 7083 Gulliver, Paris, France.

Physical Review Letters

|August 8, 2009

Summary

This summary is machine-generated.

Constraint satisfaction problems in the planted random ensemble mirror properties of the standard random ensemble for graph coloring. This study reveals insights into structural phase transitions and computational complexity patterns.

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Last Updated: Jun 21, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Area of Science:

Theoretical Computer Science
Statistical Physics
Combinatorics

Background:

Constraint satisfaction problems (CSPs) are fundamental in computer science.
The random ensemble is a standard model for studying CSPs.
The planted random ensemble offers a different perspective on CSPs.

Purpose of the Study:

To investigate CSPs within the planted random ensemble framework.
To compare properties of the planted random ensemble with the standard random ensemble.
To analyze computational complexity and phase transitions in CSPs.

Main Methods:

Analysis of graph coloring as a representative CSP.
Comparison of ensemble properties.
Study of structural phase transitions.
Investigation of average computational complexity.
Examination of finite temperature phase diagrams.

Main Results:

Quantitative identity between planted and standard random ensembles for certain CSPs like graph coloring.
Characterization of structural phase transitions.
Identification of the easy-hard-easy computational complexity pattern.
Demonstration of a link to liquid-glass-solid phenomenology.

Conclusions:

The planted random ensemble shares key properties with the standard random ensemble for specific CSPs.
The study provides a deeper understanding of phase transitions and complexity in CSPs.
Connections are drawn between CSPs and concepts from statistical physics.