This paper discusses wavelet thresholding in smoothing from non-equispaced, noisy data in one dimension. To deal with the irregularity of the grid we use so called second generation wavelets, based on the lifting scheme. The lifting scheme itself leads to a gridadaptive wavelet transform. We explain that a good numerical condition is an absolute requisite for successful thresholding. If this co...

We explore the lifting question in the context of cut-generating functions. Most of the prior literature on lifting for cut-generating functions focuses on which cut-generating functions have the unique lifting property. Here we develop a general theory for understanding how to do lifting for cut-generating functions which do not have the unique lifting property.

The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the total weight of edges joining different sets is optimized. In this paper we simplify a known matrix-lifting semidefinite programming relaxation of the graph partition problem for several classes of graphs and also show how to aggregate additional triangle...

The study documented three-dimensional spinal loading during lifting from an industrial bin. Two lifting styles and two bin design factors were examined in Phase I. The lifting style measures in Phase I were one hand versus two hand and standing on one foot versus two feet. The bin design variables were region of load in the bin and bin height. The Phase II study examined one-handed lifting sty...

Two-person or team lifting is a popular method for handling materials under awkward or heavy lifting conditions. While many guidelines and standards address safe lifting limits for individual lifting, there are no such limits for team lifting, and these lifts are poorly understood. The literature associated with team lifting offers some interesting paradoxes. Many studies have indicated that pe...

The classical and intensively studied problem of solving a Toeplitz/Hankel linear system of equations is omnipresent in computations in sciences, engineering and communication. Its equivalent formulations include computing polynomial gcd and lcm, Padé approximation, and BerlekampMassey’s problem of recovering the linear recurrence coefficients. To improve the current record asymptotic bit opera...

We present a polyhedral study of the complementarity knapsack problem. Traditionally, complementarity constraints are modeled by introducing auxiliary binary variables and additional constraints, and the model is tightened by introducing strong inequalities valid for the resulting MIP. We use an alternative approach, in which we keep in the model only the continuous variables, and we tighten th...

A study in lossless image compression using the lifting scheme is presented. We first suggest why lossless image compression is an important issue and the general idea behind lifting. A detailed approach to generating biorthogonal wavelets using the lifting scheme is provided, which is followed by a small example. The results from applying lifting to a variety of images are given in order to te...

Let V be a G-module where G is a complex reductive group. Let Z := V//G denote the categorical quotient and let π : V → Z be the morphism dual to the inclusion O(V ) ⊂ O(V ). Let φ : Z → Z be an algebraic automorphism. Then one can ask if there is an algebraic map Φ: V → V which lifts φ, i.e., π(Φ(v)) = φ(π(v)) for all v ∈ V . In Kuttler [Kut11] the case is treated where V = rg is a multiple of...

Recently Andersen et al. [1], Borozan and Cornuéjols [6] and Cornuéjols and Margot [10] have characterized the extreme valid inequalities of a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. These inequalities are either split cuts or intersection cuts derived using maximal lattice-free convex sets. In order to use these inequ...