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Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
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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.
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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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Language serves as a bridge between ideas and communication, influencing how individuals perceive and interact with the world. Psychologists have long debated whether language shapes thought or vice versa. This discussion gained grip with Edward Sapir and Benjamin Lee Whorf in the 1940s, who proposed that language determines thought, a concept known as linguistic determinism. They suggested that the vocabulary and structure of a language influence how its speakers think and perceive reality.
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The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam...
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Large language models (LLMs) can now make scientific discoveries using FunSearch, an evolutionary method that pairs LLMs with evaluators to overcome confabulations and solve complex problems.

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Area of Science:

  • Artificial Intelligence
  • Combinatorics
  • Computer Science

Background:

  • Large language models (LLMs) excel at complex tasks but often confabulate, limiting their scientific application.
  • Existing LLM approaches struggle with scientific discovery due to inaccuracies.

Purpose of the Study:

  • Introduce FunSearch, an evolutionary procedure to enhance LLM capabilities for scientific discovery.
  • Demonstrate FunSearch's effectiveness in solving established open problems.

Main Methods:

  • Pairing a pretrained LLM with a systematic evaluator in an evolutionary search.
  • Applying FunSearch to extremal combinatorics (cap set problem) and algorithmic problems (online bin packing).

Main Results:

  • Discovered new, improved constructions for large cap sets in both finite dimensional and asymptotic cases.
  • Identified novel heuristics for online bin packing, outperforming existing baselines.
  • Showcased FunSearch's ability to generate interpretable programs for problem-solving.

Conclusions:

  • FunSearch enables LLMs to make significant discoveries in established scientific domains.
  • The approach overcomes LLM confabulations, enhancing reliability for scientific applications.
  • FunSearch offers a scalable and interpretable method for AI-driven scientific discovery.