All frame-spun knots are slice

Frame-spun knots are constructed by spinning a knot of lower dimension about a framed submanifold of . We show that all frame-spun knots are slice (null-cobordant).

     

Improving motion estimation by accounting for local image distortion

Cardiac elastography is a useful diagnostic technique for detection of heart function abnormalities, based on analysis of echocardiograms. The analysis of the regional heart motion allows assessing the extent of myocardial ischemia and infarction. In this paper, a new two-stage algorithm for cardiac motion estimation is proposed, where the data is taken from a sequence of 2D echocardiograms. The method combines the advantages of block-matching and optical flow techniques. The first stage employs a standard block-matching algorithm (sum of absolute differences) to provide a displacement estimate with accuracy of up to one pixel. At the second stage, this estimate is corrected by estimating the parameters of a local image transform within a test window. The parameters of the image transform are estimated in the least-square sense. In order to account for typical heart motions, like contraction/expansion, translation and rotation, a local affine model is assumed within the test window. The accuracy of the new algorithm is evaluated using a sequence of 500 grayscale B-mode images, which are generated as distorted, but known copies of an original ROI, taken from a real echocardiogram. The accuracy of the motion estimation is expressed in terms of errors: maximum absolute error, root-mean-square error, average error and standard deviation. The errors of the proposed algorithm are compared with these of the known block-matching technique with cross-correlation and interpolation in the sub-pixel space. Statistical analysis of the errors shows that the proposed algorithm provides more accurate estimates of the heart motion than the cross-correlation technique with interpolation in the sub-pixel space.     

Research Note: Mobility of Herbicide Microcapsules in Saturated Granular Media

The mobility of the microcapsules in saturated granular media was estimated on the basis of conventional breakthrough experiments in vertical columns packed with sands for various physical and chemical conditions. Four types of microcapsules have been tested, all of them were found to have reasonable mobility in clean quartz sand, but not in sandy soil. The immobility in the sandy soil was attributed to some production deficiencies in terms of shape, size and quality of the coating surface. The size of the microcapsules should be considerably smaller than those produced with an order of magnitude of a few micrometers. They should also be more spherical and with a smoother surface. The addition of a proper dispersant had stabilized the microcapsules suspension, and facilitated their transport in the sand. A major flow factor affecting microcapsules mobility is the water flux. The microcapsules should be applied at a high irrigation rate, which also implies a high water content in the soil profile. Considering solely the mobility aspect, it seems that the prospect for successful application of the new method for weed control is limited to granular soils with a high hydraulic conductivity at/or near saturation. However, for the time being the most limiting problem is the production of quality microcapsules with good physical and chemical properties.     

Inverse problems for scattering by periodic structures

Suppose the 3-dimensional space is filled with three materials having dielectric constants ? ₁ above S ₁={x ₂=f ₁(x ₁), x ₃ arbitrary}, ? ₂ below S ₂ = {x ₂ =f ₂(x ₁), x ₃ arbitrary} and ? _o in {f ₂(x ₁) <x ₂ 1(x ₁), x ₃ arbitrary} where f ₁ f ₂ are periodic functions. Suppose for a plane wave incident on S ₁ from above we can measure the reflected and transmitted waves of the corresponding time-harmonic solution of the Maxwell equations, say at x ₂=±b,b large. To what extent can we infer from these measurements the location of the pair (S ₁, S ₂ ? In this paper, we establish a local stability: If ( $\tilde S_1 ,\tilde S_2$ ) is another pair of periodic curves “close” to (S ₁, S₂), then, for any δ>0, if the measurements for the two pairs are δ-close, then $\tilde S_1$ and $\tilde S_2$ are 0(δ)-close to S ₁ and S ₂, respectively.