A classification of the semisimple subalgebras of the Lie algebra of
traceless 3×3 matrices with complex entries, denoted A2, is
well-known. We classify its nonsemisimple subalgebras, thus completing the
classification of the sub...
The rectilinear local crossing number of Kn
August 31, 2015
|
Mathematics
Combinatorics
We determine lcrˉ(Kn), the rectilinear local crossing number
of the complete graph Kn for every n. More precisely, for every n∈/{8,14}, \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left(
n-3-\left\lceil...
Limit Models in Strictly Stable Abstract Elementary Classes
August 19, 2015
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Mathematics
Logic
In this paper, we examine the locality condition for non-splitting and
determine the level of uniqueness of limit models that can be recovered in some
stable, but not superstable, abstract elementary classes. In particular we
prove (note th...
On the minimal modules for exceptional Lie algebras: Jordan blocks and
stabilisers
August 12, 2015
Mathematics
Representation Theory
Group Theory
Rings and Algebras
Let G be a simple simple-connected exceptional algebraic group of type G_2,
F_4, E_6 or E_7 over an algebraically closed field k of characteristic p>0 with
\g=Lie(G). For each nilpotent orbit G.e of \g, we list the Jordan blocks of the
acti...
What is the force on a magnetic dipole?
August 6, 2015
Physics
Classical Physics
We show that attempts to modify the force on a magnetic dipole by introducing
either hidden momentum or internal forces are not correct. The standard
textbook result {\bf F=\nabla(\bmu\cdot B)} is correct even in the presence
of time depe...
The Divergence Index: A Decomposable Measure of Segregation and
Inequality
August 5, 2015
Physics
Mathematics
Computer Science
Statistics
Physics and Society
Information Theory
Information Theory
Methodology
Decomposition analysis is a critical tool for understanding the social and
spatial dimensions of segregation and diversity. In this paper, I highlight the
conceptual, mathematical, and empirical distinctions between segregation and
diversit...
The Neumann Problem for Hessian Equations
August 2, 2015
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Mathematics
Analysis of PDEs
Differential Geometry
In this paper, we prove the existence of a classical solution to a Neumann
boundary problem for Hessian equations in uniformly convex domain. The methods
depend upon the established of a priori derivative estimates up to second
order. So we...
Multiple Outlier Detection in Samples with Exponential & Pareto Tails:
Redeeming the Inward Approach & Detecting Dragon Kings
July 30, 2015
|
Statistics
Methodology
We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and
sum-robust-sum (SRS), designed to enhance the robustness of outlier detection
in samples with exponential or Pareto tails. We also reintroduce the inward
sequenti...
Anomalous Hall effect and quantum criticality in geometrically
frustrated heavy fermion metals
July 27, 2015
| | |
Physics
Strongly Correlated Electrons
Studies on the heavy-fermion pyrochlore iridate (Pr2Ir2O7) point to
the role of time-reversal-symmetry breaking in geometrically frustrated Kondo
lattices. With this motivation, here we study the effect of Kondo coupling and
chiral...
Pareto Smoothed Importance Sampling
July 9, 2015
| | | |
Statistics
Computation
Methodology
Machine Learning
Importance weighting is a general way to adjust Monte Carlo integration to
account for draws from the wrong distribution, but the resulting estimate can
be highly variable when the importance ratios have a heavy right tail. This
routinely o...