Accurate perception of moving objects would be useful; accurate visually guided action is crucial. Visual motion across the scene influences perceived object location and the trajectory of reaching movements to objects. In this commentary, I propose that the visual system assigns the position of any object based on the predominant motion present in the scene, and that this is used to guide reac...

A herringbone "easy axis" pattern is scribed into a polyimide alignment layer for liquid-crystal orientation using the stylus of an atomic force microscope. Owing to the liquid crystal's bend elasticity K33 , the nematic director is unable to follow the sharp turn in the scribed easy axis, but instead relaxes over an extrapolation length L=K33/W2φ, where W2φ is the quadratic azimuthal anchoring...

We consider the Arnold Tongue of the Arnold family of circle maps associated to a fixed Diophantine rotation number θ. The corresponding maps of the family are analytically conjugate to a rigid rotation. This conjugation is defined on a (maximal) complex strip of the circle and, after a suitable scaling, the size of this strip is given by an analytic function of the perturbative parameter. The ...

We show that if an operator T is bounded on weighted Lebesgue space L(w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T ] with a function b in BMO will obey a quadratic bound with respect to the A2 constant of the weight. We also prove that the kth-order commutator T k b = [b, T k−1 b ] will obey a bound that is a power (k + 1) of the A2 consta...

We present a framework for efficient extrapolation of reduced rank approximations, graph kernels, and locally linear embeddings (LLE) to unseen data. We also present a principled method to combine many of these kernels and then extrapolate them. Central to our method is a theorem for matrix approximation, and an extension of the representer theorem to handle multiple joint regularization constr...

We present new results for the water dimer equilibrium constant K(p)(T) in the range 190-390 K, using a flexible potential energy surface fitted to spectroscopical data. The increased numerical complexity due to explicit consideration of the monomer vibrations is handled via an adiabatic (6 + 6)d decoupling between intra- and intermolecular modes. The convergence of the canonical partition func...

A highly efficient extrapolative Brillouin-zone integration scheme is presented that requires a very low k-point sampling density for spectral integrations. It is important to use an extrapolative approach, since at low sampling densities interpolative schemes are hindered by problems associated with band crossing, which introduce spurious singularities in the density of states ~DOS!. The infor...

Ionization threshold energies of Al(n) (n = 32-95) nanoclusters are determined by laser ionization of free neutral metal clusters thermalized to several temperatures in the range from 65 K to 230 K. The photoion yield curves of cold clusters follow a quadratic energy dependence above threshold, in agreement with the Fowler law of surface photoemission. Accurate data collection and analysis proc...

Two kinds of error commonly arise in statistical inference. The most common one is sampling error, arising from small samples. The second is the error arising from unrepresentative samples. Such errors occur in curve-fitting examples when the curves are fitted in one domain and used for prediction in another, which might be referred to as an error of extrapolation. The problem with extrapolatio...