We prove that a bounded open set U in R n has k-width less than C(n) Volume(U) k/n. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in R n. In particular, we estimate the smallest (n-1)-dilation of any degree 1 map between two n-dimensional rectangles. For any pair of rectangles, our estimate is accurate up to a dimensional constant C(n). We...

A study of general properties of the narrow-width approximation (NWA) with polarization/spin decorrelation is presented. We prove for sufficiently inclusive differential rates of arbitrary resonant decay or scattering processes with an on-shell intermediate state decaying via a cubic or quartic vertex that decorrelation effects vanish and the NWA is of order Γ. Its accuracy is then determined n...

To satisfy the demand for higher performance, modern processors are designed with a high degree of speculation. While speculation enhances performance, it burns power unnecessarily. The cache, store queue, and load queue are accessed associatively before a matching entry is determined. A significant amount of power is wasted to search entries that are not picked. Modern processors speculatively...

We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. For many graph problems this number is the runtime bottleneck when using a divide-and-conquer approach. Boolean-width is similar to rank-width, which is related to the number of GF [2]-sums (1+1=0) of neighborhoods instead of the Boolean-sums (1+1=1) used for boole...

We prove that CSP(A) for an idempotent algebra A has bounded relational width if and only if var(A) omits the unary and affine types. If it has bounded relational width it has relational width at most 3. The problem, given a relational structure A, decide if CSP(A) has bounded relational width (equivalently, if the variety generated by the corresponding algebra omits the Boolean and affine type...

Perceived brightness of a stimulus depends on the background against which the stimulus is set, a phenomenon known as simultaneous contrast. For instance, the same gray stimulus can look light against a black background or dark against a white background. Here we quantified the perceptual strength of simultaneous contrast as a function of stimulus width. Previous studies have reported that wide...

background: considering the effectiveness of craniofacial photographic analysis for diagnosis and management of obstructive sleep apnea-hypopnea syndrome (osahs) as well as ethnic differences in indexes measured by this method, this study designed to compare the surface facial dimensions, including nose width, intercanthal width and mandibular width of iranian patients with mild, moderate and s...

We introduce a new matroid width parameter based on the operation of matroid amalgamation, which we call amalgam-width. The parameter is linearly related to branch-width on finitely representable matroids, while still allowing the algorithmic application on non-representable matroids (which is not possible for branch-width). In particular, any property expressible in the monadic second order lo...