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On a Generalization of Blaschke’s Rolling Theorem and the Smoothing of Surfaces
Blaschke’s Rolling Theorem generalized convexity
2015/8/20
A generalization of Blaschke’s Rolling Theorem for not necessarily convex sets is proved that exhibits an
intimate connection between a generalized notion of convexity, various concepts in mathematic...
MONTE CARLO SAMPLING IN DUAL SPACE FOR APPROXIMATING THE EMPIRICAL HALFSPACE DISTANCE
SPACE FOR APPROXIMATING EMPIRICAL HALFSPACE DISTANCE
2015/8/20
The Kolmogorov]Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate
settings, an analogous role is played by the halfspace di...
Solving interpolation problems via generalized eigenvalue minimization
Generalized eigenvalue interpolation control system the analysis of linear matrix inequality
2015/8/12
A number of problems in the analysis and design of control systems may be reformulated as the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices which depend affi...
Convex optimization of graph Laplacian eigenvalues
Graph theory Laplacian matrix Convex optimization Semidefinite pro-gramming Markov chain Distributed averaging Effective resistance
2015/8/10
We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constrain...
A distributed algorithm for fitting generalized additive models
Convex optimization Distributed optimization Generalized additive models
2015/8/7
Generalized additive models are an effective regression tool, popular in the statistics literature, that provide an automatic extension of traditional linear models to nonlinear systems. We pres...
A splitting method for optimal control
Operator splitting algorithm the secondary control operation
2015/8/7
We apply an operator splitting technique to a generic linear-convex optimal control problem, which results in an algorithm that alternates between solving a quadratic control problem, for which there ...
Metric selection in Douglas-Rachford splitting and ADMM
Divided multiplier literature linear convergence and linear convergence parameter optimization algorithm
2015/8/7
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show linea...
Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets c...
An Exact Test for Multiple Inequality and Equality Constraints in the Linear Regression Model
Multiple Inequality Equality Constraints
2015/7/31
In this article we consider the linear regression model y = X,B + a,
where e is N(O, a21). In this context we derive exact tests of the form
H: Rft ? r versus K: f E R K for the case in which a2 i...
A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into P n
Genus-One Stable Maps Moduli
2015/7/14
We construct a natural smooth compacti cation of the space of smooth genus-one curves with
k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth
compacti ca...
A DESCRIPTION OF THE OUTER AUTOMORPHISM OF S6, AND THE INVARIANTS OF SIX POINTS IN PROJECTIVE SPACE
PROJECTIVE SPACE OUTER AUTOMORPHISM
2015/7/14
The latter two descriptions do
not distinguish any of the six points. Of course, these descriptions are equivalent to the
traditional one (x1.4) there is after all only one nontrivial outer automor...
The moduli space of curves has proven itself a central object in geometry. The past
decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, fro...
RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
VIRTUAL LOCALIZATION VANISHING
2015/7/14
We prove a localization formula for the moduli space of stable relative maps.
As an application, we prove that all codimension i tautological classes on the moduli space
of stable pointed curves van...
RELATIVE VIRTUAL LOCALIZATION AND VANISHING OF TAUTOLOGICAL CLASSES ON MODULI SPACES OF CURVES
VIRTUAL LOCALIZATION VANISHING
2015/7/14
We prove a localization formula for the moduli space of stable relative maps.
As an application, we prove that all codimension i tautological classes on the moduli space
of stable pointed curves van...
Spatiotemporal Analysis with ST Helixes.