Fast Nonseparable Gaussian Stochastic Process with Application to
Methylation Level Interpolation
November 30, 2017
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Statistics
Methodology
Methodology
Gaussian stochastic process (GaSP) has been widely used as a prior over
functions due to its flexibility and tractability in modeling. However, the
computational cost in evaluating the likelihood is O(n3), where n is the
number of obse...
A Geometric Quantisation view on the AJ-conjecture for the Teichm\"uller
TQFT
November 30, 2017
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Mathematics
Differential Geometry
Quantum Algebra
We provide a Geometric Quantisation formulation of the AJ-conjecture for the
Teichm\"{u}ller TQFT, and we prove it in detail in the case of the knot
complements of 41 and 52. The conjecture states that the level-N
Andersen-Kashaev...
Invariants of rigid surface operators
November 28, 2017
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Mathematics
Representation Theory
Lusztig used the symbol invariant to describe the Springer correspondence for
classical groups. Similarly, the fingerprint invariant can describe the
Kazhdan-Lusztig map. Both invariants pertain to rigid semisimple operators
labeled by pair...
Sparse juntas on the biased hypercube
November 26, 2017
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Computer Science
Mathematics
Computational Complexity
Combinatorics
We give a structure theorem for Boolean functions on the p-biased hypercube
which are ϵ-close to degree~d in L2, showing that they are close
to \emph{sparse juntas}. Our structure theorem implies that such functions are
$O(\...
A Study to Optimize Heterogeneous Resources for Open IoT
November 24, 2017
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Computer Science
Distributed, Parallel, and Cluster Computing
Recently, IoT technologies have been progressed, and many sensors and
actuators are connected to networks. Previously, IoT services were developed by
vertical integration style. But now Open IoT concept has attracted attentions
which achiev...
Theory of Heat Equations for Sigma Functions
November 22, 2017
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Physics
Mathematics
Exactly Solvable and Integrable Systems
Algebraic Geometry
Number Theory
Exactly Solvable and Integrable Systems
Algebraic Geometry
Number Theory
We consider the heat equations satisfied by the sigma function associated
with a planar curve, extending and developing earlier pioneering work of
Buchstaber and Leykin. These heat equations lead to useful {\em linear}
recursive relations f...
Sparse Variable Selection on High Dimensional Heterogeneous Data with
Tree Structured Responses
November 22, 2017
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Statistics
Methodology
We consider the problem of sparse variable selection on high dimension
heterogeneous data sets, which has been taking on renewed interest recently due
to the growth of biological and medical data sets with complex, non-i.i.d.
structures and...
The Quantum A∞-Relations on the Elliptic Curve
November 21, 2017
Mathematics
Algebraic Geometry
We define and prove the existence of the Quantum A∞-relations on
the Fukaya category of the elliptic curve, using the notion of the Feynman
transform of a modular operad, as defined by Getzler and Kapranov. Following
Barannikov, t...
Computational analysis of short-range interactions between an edge
dislocation and an array of equally-spaced identical shearable or
non-shearable precipitates
November 20, 2017
Physics
Materials Science
The interaction between dislocations and precipitates plays an important role
in the mechanical behavior of alloys. To provide more insight into the physics
of this interaction, this research analyzes short-range interactions of an edge
dis...
Dirac and Weyl Fermions -- the Only Causal Systems
November 17, 2017
Physics
Mathematics
Mathematical Physics
Mathematical Physics
Quantum Physics
Causal systems describe the localizability of relativistic quantum systems
complying with the principles of special relativity and elementary causality.
At their classification we restrict ourselves to real mass and finite spinor
systems. I...