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 ...