With the popularity of social media, people are more and more interested in mining opinions from it. Learning from social media not only has value for research, but also good for business use. RepLab 2012 had Profiling task and Monitoring task to understand the company related tweets. Profiling task aims to determine the Ambiguity and Polarity for tweets. In order to determine this Ambiguity an...

iii Acknowledgments iv Chapter 1. A Hierarchy of Polyhedral Arrangements 1 1.1. Polyhedral Arrangements 1 1.2. Polyhedral Dissections 1 1.3. Polyhedral Complexes 5 1.4. Polyhedral Triangulations 8 1.5. A Hierarchy of Polyhedral Arrangements 9 Chapter 2. Computation on Polyhedral Arrangements 12 2.1. Bucket Method 12 2.2. Sage Code 13 2.3. Experiments 16 Chapter 3. Regular Triangulations 22 3.1....

We prove a regularity result for the anisotropic elasticity equation Pu := div ` C · ∇u) = f , with mixed (displacement and traction) boundary conditions Lk on a curved polyhedral domain Ω ⊂ R 3 in weighted Sobolev spaces Ka (Ω), for which the weight given by the distance to the set of edges. In particular, we show that there is no loss of Ka –regularity. Our curved polyhedral domains are allow...

Thie paper presents a representation echeme for polyhedral objects in arbitrary dimensions. Each object ie represented as the algebraic sum of convex polyhedra (cells). Each cell in turn ie represented ae the intereection of halfspacee and encoded in a vector. The notion of vertices is abandoned completely aa it ie not needed for the eet and eearch operators we intend to support. We ehow how th...

An eutactic star is a set of N vectors in Rn (N > n) that are projections of N orthogonal vectors in RN. First introduced in the context of regular polytopes, eutactic stars are particularly useful in the field of quasicrystals where a method to generate quasiperiodic tilings is by projecting higher-dimensional lattices. Here are defined the concepts of eutactic transformations (as mappings tha...

Graphite is the loop transformation framework that was introduced in GCC 4.4. This paper gives a detailed description of the design and future directions of this infrastructure. Graphite uses the polyhedral model as the internal representation (GPOLY). The plan is to create a polyhedral compilation package (PCP) that will provide loop optimization and analysis capabilities to GCC. This package ...

We study the facial structure of the set E nn of correlation matrices (i.e., the positive semideenite matrices with diagonal entries equal to 1). In particular, we determine the possible dimensions for a face, as well as for a polyhedral face of E nn. It turns out that the spectrum of face dimensions is lacunary and that E nn has polyhedral faces of dimension up to p 2n. As an application, we d...

We present a new equivalence result between restricted b-factors in bipartite graphs and combinatorial t-designs. This result is useful in the construction of t-designs by polyhedral methods. We propose a novel linear integer programming formulation, which we call GDP, for the problem of finding t-designs that has a noteworthy advantage compared to the traditional set-covering formulation. We a...

At any given point in time, the collection of assets that exist in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not publicly known along with an asset (in a broad sense) that pays contingent on those states. The crea...

Newton’s method for solving variational inequalities is known to be locally quadratically convergent. By incorporating a line search strategy for the regularized gap function, Taji et al. (Mathematical Programming, 1993) have proposed a modification of a Newton’s method which is globally convergent and whose rate of convergence is quadratic. But the quadratic convergence has been shown only und...