Results 11  20
of
1,071
Existence of Ideal Knots
"... Ideal knots are curves that maximize the scale invariant ratio of thickness to length. Here we present a simple argument to establish the existence of ideal knots for each knot type and each isotopy class and show that they are C curves. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Ideal knots are curves that maximize the scale invariant ratio of thickness to length. Here we present a simple argument to establish the existence of ideal knots for each knot type and each isotopy class and show that they are C curves.
Subsmooth sets: functional characterizations and related concepts
 Trans. Amer. Math. Soc
"... Abstract. Proxregularity of a set (PoliquinRockafellarThibault [25]), or its global version, proximal smoothness (ClarkeSternWolenski [5]) plays an important role in variational analysis, not only because it is associated with some fundamental properties as the local continuous differentiabilit ..."
Abstract

Cited by 34 (5 self)
 Add to MetaCart
Abstract. Proxregularity of a set (PoliquinRockafellarThibault [25]), or its global version, proximal smoothness (ClarkeSternWolenski [5]) plays an important role in variational analysis, not only because it is associated with some fundamental properties as the local continuous differentiability of the function dist (C; ·), or the local uniqueness of the projection mapping, but also because in the case where C is the epigraph of a locally Lipschitz function, it is equivalent to the weak convexity (lowerC2 property) of the function. In this paper we provide an adapted geometrical concept, called subsmoothness, which permits an epigraphic characterization of the approximate convex functions (or lowerC1 property). Subsmooth sets turn out to be naturally situated between the classes of proxregular and of nearly radial sets. This latter class has been recently introduced by Lewis in [18]. We hereby relate it to the Mifflin semismooth functions. 1.
Formal Proofs for Nonlinear Optimization
"... We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K. This method allows to bound in a modul ..."
Abstract
 Add to MetaCart
modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums
Large Sample Theory for Semiparametric Regression Models with TwoPhase, Outcome Dependent Sampling
, 2000
"... Outcomedependent, twophase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and inuenc ..."
Abstract

Cited by 30 (9 self)
 Add to MetaCart
Outcomedependent, twophase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and inuence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under twophase sampling designs. We relate the efficient score to the leastfavorable parametric submodel by use of formal calculations suggested by Newey (1994). We then proceed to show that the maximum likelihood estimators proposed by Lawless, Kalbfleisch, and Wild (1999) for both the parametric and nonparametric parts of the model are asymptotically normal and efficient, and that the efficient influence function for the parametric part agrees with the more general calculations of Robins, Hsieh, and Newey (1995).
Nonparametric Checks For SingleIndex Models
 Ann. Statist
, 2005
"... In this paper we study goodnessoffit testing of singleindex models. The large sample behavior of certain scoretype test statistics is investigated. As a byproduct, we obtain asymptotically distributionfree maximin tests for a large class of local alternatives. Furthermore, characteristic functi ..."
Abstract

Cited by 25 (6 self)
 Add to MetaCart
In this paper we study goodnessoffit testing of singleindex models. The large sample behavior of certain scoretype test statistics is investigated. As a byproduct, we obtain asymptotically distributionfree maximin tests for a large class of local alternatives. Furthermore, characteristic
Quasiprojections in Teichmüller space
 J. Reine Angew. Math
, 1996
"... Many parallels have been drawn between the geometric properties of the Teichmüller space of a Riemann surface, and those of complete, negatively curved spaces (see for example [B, K2, W]). This paper investigates one such parallel – the contracting properties of certain projections to geodesics. We ..."
Abstract

Cited by 24 (1 self)
 Add to MetaCart
Many parallels have been drawn between the geometric properties of the Teichmüller space of a Riemann surface, and those of complete, negatively curved spaces (see for example [B, K2, W]). This paper investigates one such parallel – the contracting properties of certain projections to geodesics. We will use the Teichmüller metric throughout the paper (the other famous metric on Teichmüller space, the WeilPetersson metric, is negatively curved although it is not complete. The Teichmüller metric is complete, but not negatively curved – see [Ma].) Every closed subset C of a complete metric space X determines a “closestpoints” projection, defined as a map πC: X → P(C), where P(C) is the set of closed subsets of C. Namely, πC(x) = {y ∈ C: d(x,y) = d(x,C)} where d(x,C) = infy∈C d(x,y). Suppose now that X is a simplyconnected Riemannian manifold with nonpositive sectional curvatures, and that C is a geodesic segment, ray or line. In this case πC(x) always contains a single point. If the sectional
Signal Propagation and Noisy Circuits
 IEEE Trans. Inform. Theory
, 1999
"... The information carried by a signal decays when the signal is corrupted by random noise. This occurs when a message is transmitted over a noisy channel, as well as when a noisy component performs computation. We rst study this signal decay in the context of communication and obtain a tight bound on ..."
Abstract

Cited by 23 (2 self)
 Add to MetaCart
The information carried by a signal decays when the signal is corrupted by random noise. This occurs when a message is transmitted over a noisy channel, as well as when a noisy component performs computation. We rst study this signal decay in the context of communication and obtain a tight bound on the rate at which information decreases as a signal crosses a noisy channel. We then use this information theoretic result to obtain depth lower bounds in the noisy circuit model of computation dened by von Neumann. In this model, each component fails (produces 1 instead of 0 or viceversa) independently with a xed probability, and yet the output of the circuit is required to be correct with high probability. Von Neumann showed how to construct circuits in this model that reliably compute a function and are no more than a constant factor deeper than noiseless circuits for the function. We provide a lower bound on the multiplicative increase in circuit depth necessary for reliable computa...
Testing for Changes in Polynomial Regression
"... Abstract: We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value distribution of a maximum–type test statistic which is as ..."
Abstract
 Add to MetaCart
Abstract: We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value distribution of a maximum–type test statistic which
Performance and Implementation Aspects of Nonlinear Filtering
 DEPARTMENT OF ELECTRICAL ENGINEERING, LINKÖPING UNIVERSITY
, 2008
"... ..."
Results 11  20
of
1,071