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...
Topologies on the future causal completion
September 9, 2019
|
Mathematics
Differential Geometry
Differential Geometry
On the Geroch-Kronheimer-Penrose future completion IP(X) of a spacetime
X, there are two frequently used topologies. We systematically examine
τ+, the stronger (metrizable) of them, which is the coarsest causally
continuous topolo...
Definable (co)homology, pro-torus rigidity, and (co)homological
classification
September 9, 2019
| |
Mathematics
Algebraic Topology
Logic
Operator Algebras
We show that the classical homology theory of Steenrod may be enriched with
descriptive set-theoretic information. We prove that the resulting definable
homology theory provides a strictly finer invariant than Steenrod homology for
compact ...
Learning Concepts Definable in First-Order Logic with Counting
September 9, 2019
Computer Science
Logic in Computer Science
Artificial Intelligence
Machine Learning
We study Boolean classification problems over relational background
structures in the logical framework introduced by Grohe and Tur\'an (TOCS
2004). It is known (Grohe and Ritzert, LICS 2017) that classifiers definable in
first-order logic ...
Certain smooth real surfaces in C2 with singularity
September 9, 2019
Mathematics
Complex Variables
Under certain geometric condition, the surfaces in C2 with
isolated CR singularity at the origin and with cubic lowest degree homogeneous
term in its graph near the origin, can be reduced, up to biholomorphism of
C2,...