The Griffiths height of a variation of Hodge structures over a projective
curve is defined as the degree of its canonical line bundle, as defined by
Griffiths and generalized by Peters to allow bad reduction points. It may be
seen as a geom...
Differentially Private Decentralized Optimization with Relay
Communication
December 21, 2022
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Mathematics
Computer Science
Optimization and Control
Cryptography and Security
Optimization and Control
Cryptography and Security
Security concerns in large-scale networked environments are becoming
increasingly critical. To further improve the algorithm security from the
design perspective of decentralized optimization algorithms, we introduce a new
measure: Privacy ...
Faster Accelerated First-order Methods for Convex Optimization with
Strongly Convex Function Constraints
December 21, 2022
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Mathematics
Computer Science
Optimization and Control
Machine Learning
Optimization and Control
Machine Learning
In this paper, we introduce faster accelerated primal-dual algorithms for
minimizing a convex function subject to strongly convex function constraints.
Prior to our work, the best complexity bound was
O(1/ε), regardl...
Suprema of L\'evy processes with completely monotone jumps:
spectral-theoretic approach
December 21, 2022
Mathematics
Spectral Theory
Probability
We study spectral-theoretic properties of non-self-adjoint operators arising
in the study of one-dimensional L\'evy processes with completely monotone jumps
with a one-sided barrier. With no further assumptions, we provide an integral
expre...
Tighter Bounds for Query Answering with Guarded TGDs
December 21, 2022
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Computer Science
Logic in Computer Science
Logic in Computer Science
We consider the complexity of the open-world query answering problem, where
we wish to determine certain answers to conjunctive queries over incomplete
datasets specified by an initial set of facts and a set of guarded TGDs. This
problem ha...
Wirtinger operators for functions of several quaternionic variables
December 21, 2022
Mathematics
Complex Variables
We introduce Wirtinger operators for functions of several quaternionic
variables. These operators are real linear partial differential operators which
behave well on quaternionic polynomials, with properties analogous to the ones
satisfied ...
Positivity of the Cotangent Bundle of Complex Hyperbolic Manifolds with
Cusps
December 21, 2022
Mathematics
Algebraic Geometry
Complex Variables
Differential Geometry
Let X be the toroidal compactification of a cusped complex
hyperbolic manifold X=Bn/Γ with the boundary divisor
D=X∖X. The main goal of this paper is to find the
positivity properties of $...
Injectivity, stability, and positive definiteness of max filtering
December 21, 2022
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Mathematics
Computer Science
Functional Analysis
Information Theory
Information Theory
Given a real inner product space V and a group G of linear isometries, max
filtering offers a rich class of G-invariant maps. In this paper, we identify
nearly sharp conditions under which these maps injectively embed the orbit
space V/G in...
Quantization dimensions for the bi-Lipschitz recurrent Iterated function
systems
December 21, 2022
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Mathematics
Dynamical Systems
In this paper, the quantization dimensions of the Borel probability measures
supported on the limit sets of the bi-Lipschitz recurrent iterated function
systems under the strong open set condition in terms of the spectral radius
have been e...
Second-order optimality conditions for the bilinear optimal control of a
degenerate equation
December 21, 2022
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Mathematics
Optimization and Control
Analysis of PDEs
The main purpose of this paper is the study of second-order optimality
conditions for the bilinear control of a strongly degenerate parabolic
equation. The equation is degenerate at the boundary of the spatial domain. The
well-posedness of ...