Given a graph G and a collection C of subsets of Rd
indexed by the subsets of vertices of G, a constrained drawing of G is a
drawing, where each edge is drawn inside some set from C, in such a
way tha...
Robust statistical modeling of monthly rainfall: The minimum density
power divergence approach
September 17, 2019
|
Statistics
Applications
Statistical modeling of monthly, seasonal, or annual rainfall data is an
important research area in meteorology. These models play a crucial role in
rainfed agriculture, where a proper assessment of the future availability of
rainwater is n...
Counterfactual restrictions and Bell's theorem
September 14, 2019
|
Physics
Quantum Physics
History and Philosophy of Physics
Quantum Physics
History and Philosophy of Physics
We show that the ability to consider counterfactual situations is a necessary
assumption of Bell's theorem, and that, to allow Bell inequality violations
while maintaining all other assumptions, we just require certain measurement
choices b...
Special Orthogonal Group SO(3), Euler Angles, Angle-axis, Rodriguez
Vector and Unit-Quaternion: Overview, Mapping and Challenges
September 14, 2019
Mathematics
Computer Science
Electrical Engineering and Systems Science
Optimization and Control
Systems and Control
Systems and Control
The attitude of a rigid-body in the three dimensional space has a unique and
global definition on the Special Orthogonal Group SO (3). This paper gives an
overview of the rotation matrix, attitude kinematics and parameterization. The
four m...
Reducing non-negativity over general semialgebraic sets to
non-negativity over simple sets
September 14, 2019
| |
Mathematics
Optimization and Control
A non-negativity certificate (NNC) is a way to write a polynomial so that its
non-negativity on a semialgebraic set becomes evident. Positivstellens\"atze
(Ps\"atze) guarantee the existence of NNCs. Both, NNCs and Ps\"atze underlie
powerful...
A new model for natural groupings in high-dimensional data
September 13, 2019
|
Statistics
Computer Science
Machine Learning
Machine Learning
Clustering aims to divide a set of points into groups. The current paradigm
assumes that the grouping is well-defined (unique) given the probability model
from which the data is drawn. Yet, recent experiments have uncovered several
high-dim...
Flag versions of quiver Grassmannians for Dynkin quivers have no odd
cohomology
September 11, 2019
|
Mathematics
Representation Theory
Algebraic Geometry
Representation Theory
Algebraic Geometry
We prove the conjecture that flag versions of quiver Grassmannians (also
known as Lusztig's fibers) for Dynkin quivers (types A, D, E) have no odd
cohomology groups over an arbitrary ring. Moreover, for types A and D we prove
that the...
Returning to Shannon's Original Meaning
September 11, 2019
Computer Science
Mathematics
Information Theory
Information Theory
Shannon theory is revisited to show that ergodicity is an indispensable
element of channel capacity. The generalized channel capacity
C=supXI(X;Y) is checked with a negative
conclusion and the popular asser...
Boltzmann machine learning and regularization methods for inferring
evolutionary fields and couplings from a multiple sequence alignment
September 10, 2019
Quantitative Biology
Physics
Computer Science
Statistics
Populations and Evolution
Statistical Mechanics
Machine Learning
Biomolecules
Machine Learning
The inverse Potts problem to infer a Boltzmann distribution for homologous
protein sequences from their single-site and pairwise amino acid frequencies
recently attracts a great deal of attention in the studies of protein structure
and evol...
Wall crossing for K-moduli spaces of plane curves
September 10, 2019
| |
Mathematics
Algebraic Geometry
Differential Geometry
We construct proper good moduli spaces parametrizing K-polystable
Q-Gorenstein smoothable log Fano pairs (X,cD), where X is a
Fano variety and D is a rational multiple of the anti-canonical divisor. We
then establish a wal...