A sharply 2-transitive permutation group of finite Morley rank and
characteristic 2 splits; a split sharply 2-transitive permutation group of
finite Morley rank and characteristic different from 2 is the group of affine
transformations of a...
Generalized weight properties of resultants and discriminants, and
applications to projective enumerative geometry
November 26, 2018
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Mathematics
Algebraic Geometry
Commutative Algebra
Algebraic Geometry
Commutative Algebra
The goal of this text is to understand and prove a formula stated by Salmon,
which gives the first terms of some Taylor expansion of the discriminant of a
plane algebraic curve. Salmon uses his formula to derive various enumerative
quantiti...
A new counterexample to Nguyen's conjecture on surface fibration
November 26, 2018
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Mathematics
Algebraic Geometry
Algebraic Geometry
Suppose f:S→P1 is a surface fibration of genus g with
3 singular fibers. If two of the singular fibers are semistable, Nguyen
conjectured that f does not exist for g≥2. However, a counterexample for
g=2 was...
Some differential equations for the Riemann θ-function on
Jacobians
November 26, 2018
Mathematics
Number Theory
Algebraic Geometry
We prove some differential equations for the Riemann theta function
associated to the Jacobian of a Riemann surface. The proof is based on some
variants of a formula by Fay for the theta function, which are motivated by
their analogues in A...
Spectral Theory of Sparse Non-Hermitian Random Matrices
November 26, 2018
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Mathematics
Physics
Mathematical Physics
Mathematical Physics
Disordered Systems and Neural Networks
Statistical Mechanics
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matri...
Rare Events Analysis in Stochastic Models for Bacterial Evolution
November 25, 2018
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Mathematics
Probability
Radical shifts in the genetic composition of large cell populations are rare
events with quite low probabilities, which direct numerical simulations
generally fail to evaluate accurately. In this paper, we develop a theoretical
large deviat...
Identification of Treatment Effects under Limited Exogenous Variation
November 24, 2018
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Economics
Statistics
Econometrics
Methodology
Econometrics
Methodology
Multidimensional heterogeneity and endogeneity are important features of a
wide class of econometric models. With control variables to correct for
endogeneity, nonparametric identification of treatment effects requires strong
support condit...
Amalgamation and Keisler's Order
November 24, 2018
Mathematics
Logic
Malliaris and Shelah famously proved that Keisler's order ⊴
has infinitely many classes. In more detail, for each 2≤k<n<ω,
let Tn,k be the theory of the random k-ary n-clique free hypergraph.
Mallia...
On three domination-based identification problems in block graphs
November 23, 2018
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Mathematics
Computer Science
Combinatorics
Discrete Mathematics
The problems of determining the minimum-sized \emph{identifying},
\emph{locating-dominating} and \emph{open locating-dominating codes} of an
input graph are special search problems that are challenging from both
theoretical and computationa...
Three-term Machin-type formulae
November 22, 2018
Mathematics
Number Theory
We shall show that there exist only finitely many nondegenerate three-term
Machin-type formulae and give explicit upper bounds for the sizes of variables....