Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Sinha, Dev P."'
We show that Hopf invariants, defined by evaluation in Harrison cohomology of the commutative cochains of a space, calculate the logarithm map from a fundamental group to its Malcev Lie algebra. They thus present the zeroth Harrison cohomology as a u
Externí odkaz:
http://arxiv.org/abs/2403.20264
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product of such s
Externí odkaz:
http://arxiv.org/abs/2212.07482
We use a vector field flow defined through a cubulation of a closed manifold to reconcile the partially defined commutative product on geometric cochains with the standard cup product on cubical cochains, which is fully defined and commutative only u
Externí odkaz:
http://arxiv.org/abs/2106.05986
Autor:
Masden, Marissa, Sinha, Dev
Informed by the basic geometry underlying feed forward neural networks, we initialize the weights of the first layer of a neural network using the linear discriminants which best distinguish individual classes. Networks initialized in this way take f
Externí odkaz:
http://arxiv.org/abs/2007.12782
Autor:
Monroe, Jeff, Sinha, Dev
We develop invariants of the lower central series of free groups through linking of letters, showing they span the rational linear dual of the lower central series subquotients. We build on an approach to Lie coalgebras through operads, setting the s
Externí odkaz:
http://arxiv.org/abs/2006.00989
Akademický článek
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Autor:
Pengelley, David, Sinha, Dev
There are compelling reasons to shift our pedagogy toward evidence-based active learning methods that substantially improve student success, and now plenty of resources to aid in that shift. These include the recent CBMS Statement on Active Learning,
Externí odkaz:
http://arxiv.org/abs/1907.12128
Akademický článek
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Autor:
Sinha, Dev P.
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction, sophistication of re
Externí odkaz:
http://arxiv.org/abs/1812.11947
Autor:
Giusti, Chad, Sinha, Dev
We calculate the mod-two cohomology of all alternating groups together, with both cup and transfer product structures, which in particular determines the additive structure and ring structure of the cohomology of individual groups. We show that there
Externí odkaz:
http://arxiv.org/abs/1705.01141