Fast Polynomial Root-Finding and Approximation of the Eigenvalues of a
Matrix
May 30, 2018
Computer Science
Numerical Analysis
Univariate polynomial root-finding has been studied for four millennia and
very intensively in the last decades. Our new near-optimal root-finders
approximate all zeros of a polynomial p almost as fast as one accesses its
coefficients with ...
The convex hull of a convex space curve with four vertices
May 29, 2018
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Mathematics
Differential Geometry
Differential Geometry
We obtain an upper bound for the volume of the convex hull of a simple closed
Frenet curve having exactly four vertices, i.e., four points of vanishing
torsion, and lying on the boundary of its convex hull. Moreover, we show that
the upper ...
Tilting Approximate Models
May 28, 2018
Economics
Econometrics
Model approximations are common practice when estimating structural or
quasi-structural models. The paper considers the econometric properties of
estimators that utilize projections to reimpose information about the exact
model in the form ...
How Electrons Spin
May 26, 2018
Physics
General Physics
Popular Physics
There are a number of reasons to think that the electron cannot truly be
spinning. Given how small the electron is generally taken to be, it would have
to rotate superluminally to have the right angular momentum and magnetic
moment. Also, t...
Size-varying reversible causal graph dynamics
May 25, 2018
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Computer Science
Discrete Mathematics
Consider a network that evolves according to a reversible, nearest neighbours
dynamics. Is the dynamics allowed to vary the size of the network? On the one
hand it seems that, being the principal carriers of information, nodes cannot
be des...
Reconciliation of weak pairwise spike-train correlations and highly
coherent local field potentials across space
May 25, 2018
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Quantitative Biology
Neurons and Cognition
Multi-electrode arrays covering several square millimeters of neural tissue
provide simultaneous access to population signals such as extracellular
potentials and spiking activity of one hundred or more individual neurons. The
interpretatio...
Seat Allocation and Seat Bias under the Jefferson--D'Hondt Method
May 21, 2018
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Physics
Physics and Society
We prove that under the Jefferson--D'Hondt method of apportionment, given
certain distributional assumptions regarding mean rounding residuals, as well
as absence of correlations between party vote shares, district sizes (in
votes), and mul...
On definite lattices bounded by a homology 3-sphere and Yang-Mills
instanton Floer theory
May 20, 2018
Mathematics
Geometric Topology
Using instanton Floer theory, extending methods due to Froyshov, we determine
the definite lattices that arise from smooth 4-manifolds bounded by certain
homology 3-spheres. For example, we show that for +1 surgery on the (2,5) torus
knot, ...
Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian and geometric
Satake equivalence (with appendix by Dennis Gaitsgory)
May 20, 2018
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Mathematics
Algebraic Geometry
Representation Theory
Let G be a reductive complex algebraic group. We fix a pair of opposite
Borel subgroups and consider the corresponding semiinfinite orbits in the
affine Grassmannian GrG. We prove Simon Schieder's conjecture identifying
his bialgebra f...
Hamiltonian formulation of general relativity and post-Newtonian
dynamics of compact binaries
May 18, 2018
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Physics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Hamiltonian formalisms provide powerful tools for the computation of
approximate analytic solutions of the Einstein field equations. The
post-Newtonian computations of the explicit analytic dynamics and motion of
compact binaries are discus...