TheNontrivial Projection Problem asks whether every finite-dimensional normed space admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension) is approximately affinely equivalent to a direct product of two bodies of non-trivial dimension. We show that this is true “up to a logarithmic factor.”

Significant relationships exist between areal bone mineral density (BMD) derived from dual energy X-ray absorptiometry (DXA) and bone strength. However, the predictive validity of BMD for osteoporotic vertebral fractures remains suboptimal. The diagnostic sensitivity of DXA in the lumbar spine may be improved by assessing BMD from lateral-projection scans, as these might better approximate the ...

In this paper we present a new approach for dynamic motion planning for legged robots. We formulate a trajectory optimization problem based on a compact form of the robot dynamics. Such a form is obtained by projecting the rigid body dynamics onto the null space of the Constraint Jacobian. As consequence of the projection, contact forces are removed from the model but their effects are still ta...

Voice, as a secondary sexual characteristic, is known to affect the perceived attractiveness of human individuals. But the underlying mechanism of vocal attractiveness has remained unclear. Here, we presented human listeners with acoustically altered natural sentences and fully synthetic sentences with systematically manipulated pitch, formants and voice quality based on a principle of body siz...

THERE are but few accounts of the study of the cortical distribution of the auditory radiation by means of lesions of the medial geniculate body. Apart from clinico-pathological studies in man, most of the investigations have been made by means of cortical stimulation and ablation. In man and the monkeys there is general agreement that the auditory radiation ends in the superior temporal gyrus ...

This study attempts to extend the line of research on using body size projection theory to account for emotional speech. It is predicted by the theory that anger is expressed by projecting a large body size with low pitch, rough voice and long vocal tract; happiness is expressed by projecting a small body size with high pitch, breathy voice and short vocal tract. Ten native speakers of Mandarin...

Many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow. Here we present a method for calculating time-dependent incompressible inviscid flow which combines a projection method with a “Cartesian grid” approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. Th...

Many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow. Here we present a method for calculating time-dependent incompressible inviscid flow which combines a projection method with a “Cartesian grid” approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. Th...