The renormalization theory of critical circle maps was developed in the late 1970’s–early 1980’s to explain the occurence of certain universality phenomena. These phenomena can be observed empirically in smooth families of circle homeomorphisms with one critical point, the so-called critical circle maps, and are analogous to Feigenbaum universality in the dynamics of unimodal maps. In the works...

background: in general, measurements of solar ultraviolet (uv) radiation are related to horizontal surfaces. while the hu­mans walking and standing outdoors expose to the natural solar uv radiation, their eyes, cheeks, extremities, trunks, or many other anatomical sites are close to vertical plane and random orient to different directions. in this study, we character­ized the diurnal variations...

In filtering problems the (posterior) state distribution p(x) is recursively estimated given observations y and state dynamics. For nonlinear observation functions, the state distribution can becomemultimodal. Common Solutions are 1.Unimodal Gaussian filter using linearization of obs. function. 2. “Bank of filters” using multiple independent unimodal filters. We present a variational approach f...

A certain unimodal conjecture in matroid theory states the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r = bn/2c. We show that this conjecture holds up to r = 3 by constructing a map from a class of rank-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless ...

George Woodworth Dec 13, 1999 (Draft please send comments to [email protected]) 1. Background Speech Articulation Data The data in Figure 1 were obtained by asking 51 subjects ranging in age from 8 to 73 years to track, using jaw movements alone, a dot moving sinusoidally in one dimension at .6 Hz on a video monitor. Their jaw movements were captured electronically by means of strain g...

Consider an unknown distribution with a symmetric unimodal density and the induced location-scale family. We study confidence intervals for the location parameter based on Student’s t-statistic, and we conjecture that the uniform distribution is least favorable in that it leads to confidence intervals that are largest given their coverage probability, provided the nominal confidence level is la...

Unimodal (i.e. single-humped) permutations may be decomposed into a product of disjoint cycles. Some enumerative results concerning their cyclic structure — e.g. 23 of them contain fixed points — are given. We also obtain in effect a kind of combinatorial universality for continuous unimodal maps, by severely constraining the possible ways periodic orbits of any such map can nestle together. Bu...

We discuss a robust data sharpening method for rendering a standard kernel estimator, with a given bandwidth, unimodal. It has theoretical and numerical properties of the type that one would like such a technique to enjoy. In particular, we show theoretically that, with probability converging to 1 as sample size diverges, our technique alters the kernel estimator only in places where the latter...