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One thing missing from the methodology used by Dr. Joseph H. Greenberg to explore deep relationships between languages ("What We All Spoke When the World Was Young," Feb. 1) is any way to evaluate similarities that they exhibit.
Working with James W. Cogdell, his main collaborator over a quarter-century, starting in the mid-1970s, Dr. Piatetski-Shapiro shaped a proof of what is known as the Converse Theorem, which finds some deep relationships between different fields of mathematics.
In this paper, we extend our earlier work in [25] to systematically capture time information as well as latent (deep) relationships between a source speaker's and a target speaker's features in a single network.
Vegetarianism in itself is inherently complicated; the deep relationships between the livestock and dairy industries make for considerable debate when choosing to exclude meat from a diet but not cheese and milk.
However, we would argue that there are deep relationships between the two and that they potentially cover each other's shortcomings.
The potential new, deep relationships between bacterial lineages revealed during this analysis should be considered preliminary and treated with caution.
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Wen Jiabao, the premier, knows the deep relationship between happiness and a moral way of life.
Now, in her first fantasy book for children, that same deep relationship between place and culture is evident.
"This is another blow, another demonstration of the deep relationship between narcotrafficking and paramilitarism," said Daniel Garcia-Peña, a former government peace negotiator.
Now there is a theorem due to the mathematician Emmy Noether which is well-known to physicists, and which states a deep relationship between conservation laws and symmetries.
"There is a deep relationship between what we see and what we know," said Dr. Robert Schultz, an associate professor at Yale's Child Study Center.
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