A power structure over the Grothendieck ring of geometric dg categories
September 6, 2017
Mathematics
Algebraic Geometry
We prove the existence of a power structure over the Grothendieck ring of
geometric dg categories. We show that a conjecture by Galkin and Shinder
(proved recently by Bergh, Gorchinskiy, Larsen, and Lunts) relating the motivic
and categoric...
The Recursive Stopping Time Structure of the 3x+1 Function
September 5, 2017
Mathematics
General Mathematics
The 3x+1 problem concerns iteration of the map
T:Z→Z given by \begin{align*}
T(x)=\left\{\begin{array}{lcr}\;\;\;\;\displaystyle{\frac{x}{2}} & \mbox{if
x≡0(mod2)},\\ \\\displaystyle{\fra...
Modeling Interference Via Symmetric Treatment Decomposition
September 4, 2017
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Statistics
Methodology
Classical causal inference assumes treatments meant for a given unit do not
have an effect on other units. This assumption is violated in interference
problems, where new types of spillover causal effects arise, and causal
inference becomes...
Amalgamation and Symmetry: From Local to Global Consistency in The
Finite
August 31, 2017
Mathematics
Combinatorics
We present a generic construction of finite realisations of amalgamation
patterns. An amalgamation pattern is specified by a finite collection of finite
template structures together with a collection of partial isomorphisms between
them. A ...
Paradigm Completion for Derivational Morphology
August 30, 2017
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Computer Science
Computation and Language
Computation and Language
The generation of complex derived word forms has been an overlooked problem
in NLP; we fill this gap by applying neural sequence-to-sequence models to the
task. We overview the theoretical motivation for a paradigmatic treatment of
derivati...
Even for common NLP tasks, sufficient supervision is not available in many
languages -- morphological tagging is no exception. In the work presented here,
we explore a transfer learning scheme, whereby we train character-level
recurrent neu...
Stability results of octahedrality in tensor product spaces
August 24, 2017
Mathematics
Functional Analysis
We prove that there exists a finite-dimensional Banach space X such that
L1C([0,1])⊗εX fails the strong diameter
two property and L∞C([0,1])⊗πX∗ fails to
have o...
Quantum Mechanical Foundations of Epistemology
August 24, 2017
Physics
History and Philosophy of Physics
Quantum Physics
Scholars of the history and philosophy of science have asked what would
decolonized science would look like. This paper develops an answer by
interrogating the assumption that observations need to be recorded and
communicated using the lang...
Matrix recursion for positive characteristic diagrammatic Soergel
bimodules for affine Weyl groups
August 23, 2017
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Mathematics
Representation Theory
Representation Theory
Let W be an affine Weyl group, and let k be a field of characteristic
p>0. The diagrammatic Hecke category D for W over k is a
categorification of the Hecke algebra for W with rich connections to modular
repr...
Promotion through Connections: Favors or Information?
August 23, 2017
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Quantitative Finance
Economics
Connections appear to be helpful in many contexts, such as obtaining a job, a
promotion, a grant, a loan, or publishing a paper. This may be due either to
favoritism or to information conveyed by connections. Attempts at identifying
both ef...