Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds

Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of quantifier-free Presburger formulas in which most linear constraints are difference (separation) constraints, and the non-difference constraints are sparse. This class has been observed to commonly occur in software verification. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of non-difference constraints, in addition to traditional measures of formula size. In particular, we show that the number of bits needed per integer variable is linear in the number of non-difference constraints and logarithmic in the number and size of non-zero coefficients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifier-free Presburger formula to an equi-satisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. In addition to our main theoretical result, we discuss several optimizations for deriving tighter bounds in practice. Empirical evidence indicates that our decision procedure can greatly outperform other decision procedures.Comment: 26 page

Overexpression of caveolin-1 and -2 in cell lines and in human samples of inflammatory breast cancer

Inflammatory breast cancer (IBC) is the most aggressive form of locally advanced breast cancer (LABC). The IBC phenotype is characterized by an infiltrative growth pattern, increased (lymph)angiogenesis and the propensity to invade dermal lymphatics. In pancreatic cancer, interactions between caveolin-1 and RhoC GTPase, a key molecule in causing the IBC phenotype, regulate tumour cell motility and invasion. In this study we sought to investigate the role of caveolin-1 and -2 in IBC cell lines and in human IBC samples.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44235/1/10549_2005_Article_9002.pd

Rho-Regulatory Proteins in Breast Cancer Cell Motility and Invasion

The importance of the Rho-GTPases in cancer progression, particularly in the area of metastasis, is becoming increasingly evident. This review will provide an overview of the role of the Rho-regulatory proteins in breast cancer metastatis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44220/1/10549_2004_Article_5264599.pd