Condition (1.3) says that the pressure p vanishes outside the domain and condition (1.4) says that the boundary moves with the velocity V of the fluid particles at the boundary. Given a domain D0 ⊂ R, that is homeomorphic to the unit ball, and initial data v0, satisfying the constraint (1.2), we want to find a set D = ∪ 0≤t≤T {t} × Dt, Dt ⊂ R and a vector field v solving (1.1)-(1.4) with initia...

Algorithm 1: SoftBoost 1. Input: S = 〈(x1, y1), . . . , (xN , yN )〉, desired accuracy δ, and capping parameter ν ∈ [1, N ]. 2. Initialize: dn to the uniform distribution 3.Do for t = 1, . . . (a) Train classifier on dt−1 and {u1, . . . ,ut−1} and obtain hypothesis ht. Set un = h(xn)yn. (b) Calculate the edge γt of ht : γt = dt · ut (c) Set γ̂t = (minm=1...t γm)− δ (d) Set γ∗ = solution to the pr...

Background: Several studies have identified the radial nerve in arm using different anatomic landmarks, however, acontroversy remains. Deltoid tuberosity (DT) and brachioradialis (BR) are reproducible landmarks that can be used toidentify the radial nerve (RN) during fracture surgery.Methods: Dissection of RN was carried out in 17 fresh frozen adult cadavers. Using a calibrate...

The purification of detergent-solubilized kidney microvillar endopeptidase (EC 3.4.24.1 1) by immuno-adsorbent chromatography is described. The product (the d-form) was 270-fold purified compared with the homogenate of kidney cortex and was obtained in a yield of 5%. It was free of other peptidase activities and homogeneous by electrophoretic analyses. It contained about 15% carbohydrate and on...

Supplementary Material A. Background on Fokker-Planck Equation The Fokker-Planck equation (FPE) associated with a given stochastic differential equation (SDE) describes the time evolution of the distribution on the random variables under the specified stochastic dynamics. For example, consider the SDE: dz = g(z)dt+N (0, 2D(z)dt), (16) where z ∈ R, g(z) ∈ R, D(z) ∈ Rn×n. The distribution of z go...

Dual tree complex wavelet transform (DT-CWT) exhibits superiority of shift invariance, directional selectivity, perfect reconstruction (PR), and limited redundancy and can effectively separate various surface components. However, in nano scale the morphology contains pits and convexities and is more complex to characterize. This paper presents an improved approach which can simultaneously separ...

Diffusion Tensor MRI (DT-MRI) measurements are a discrete noisy sample of an underlying macroscopic effective diffusion tensor field, D(x), of water. This field is presumed to be piecewise continuous/smooth at a gross anatomical length scale. Here we describe a mathematical framework for obtaining an estimate of this tensor field from the measured DT-MRI data using a spline-based continuous app...

Consider a system of two polynomial equations in two variables: F (X,Y ) = G(X, Y ) = 0 where F ∈ R[X,Y ] has degree d ≥ 1 and G ∈ R[X,Y ] has t monomials. We show that the system has only O(dt + dt) real solutions when it has a finite number of real solutions. This is the first polynomial bound for this problem. In particular, the bounds coming from the theory of fewnomials are exponential in ...

For a prime p ≡ 1 mod 4, an odd integer n, and d = p +1 p+1 + p −1 2 , we investigate the cross-correlation values of p-ary m-sequence m(t) of period p − 1 and its decimated m-sequence m(dt). It is shown that the crosscorrelation function between m(t) and m(dt) takes the values in { −1,−1± p,−1± 1+ √ p 2 p,−1± 1− √ p 2 p,−1± p−1 2 p } .

then so is the curve x(−t), as is easily verified by direct computation. (Note that d/dt(x(−t)) = ẍ(−t), since the two derivatives pull out two minus signs.) In terms of trajectories in phase space, we note that dx(−t)/dt = −ẋ(−t). This means that the momentum of the particle along the time-reversed trajectory is the negative of the momentum along the original trajectory. We may therefore formu...