Mathematics
https://openalex.org/C33923547
https://www.wikidata.org/wiki/Q395
Algorithm
https://openalex.org/C11413529
https://www.wikidata.org/wiki/Q8366
Noise (video)
https://openalex.org/C99498987
https://www.wikidata.org/wiki/Q2210247
Constraint (computer-aided design)
https://openalex.org/C2776036281
https://www.wikidata.org/wiki/Q48769818
Image (mathematics)
https://openalex.org/C115961682
https://www.wikidata.org/wiki/Q860623
Curvature
https://openalex.org/C195065555
https://www.wikidata.org/wiki/Q214881
Projection (relational algebra)
https://openalex.org/C57493831
https://www.wikidata.org/wiki/Q3134666
Manifold (fluid mechanics)
https://openalex.org/C529865628
https://www.wikidata.org/wiki/Q1790740
Partial differential equation
https://openalex.org/C93779851
https://www.wikidata.org/wiki/Q271977
Nonlinear system
https://openalex.org/C158622935
https://www.wikidata.org/wiki/Q660848
Set (abstract data type)
https://openalex.org/C177264268
https://www.wikidata.org/wiki/Q1514741
Image noise
https://openalex.org/C35772409
https://www.wikidata.org/wiki/Q1323086
Mathematical optimization
https://openalex.org/C126255220
https://www.wikidata.org/wiki/Q141495
Stating the aims of the current research (note frequent use of past tense)
This study set out to investigate the usefulness of ...
[INST] Please produce a sentence from the paper. The sentence should not mention the title of the paper, rather it be extracted from the Introducing Work section of the paper.
Please provide one singular full sentence from the paper that serves the function provided, using the example as guidance. Be specific, using relevant terminology from the paper.
Refrain from vague or generic statements. Finally produce a search query in the form of a question targeted towards the knowledge contained therein. 
You must output json with the structure of {'Sentence': sentence, 'Query': query}.
Field: "Algorithm".
Paper: "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations"
Function: "Stating the aims of the current research (note frequent use of past tense)".
Example Sentence: "This study set out to investigate the usefulness of ...". [/INST]