Testing Linear-Invariant Non-Linear Properties

We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has mostly focused on such tasks for linear properties. The one exception is a test due to Green for "triangle freeness": a function f:\cube^{n}\to\cube satisfies this property if $f(x),f(y),f(x+y)$ do not all equal 1, for any pair x,y\in\cube^{n}. Here we extend this test to a more systematic study of testing for linear-invariant non-linear properties. We consider properties that are described by a single forbidden pattern (and its linear transformations), i.e., a property is given by $k$ points v_{1},...,v_{k}\in\cube^{k} and f:\cube^{n}\to\cube satisfies the property that if for all linear maps L:\cube^{k}\to\cube^{n} it is the case that $f(L(v_{1})),...,f(L(v_{k}))$ do not all equal 1. We show that this property is testable if the underlying matroid specified by $v_{1},...,v_{k}$ is a graphic matroid. This extends Green's result to an infinite class of new properties. Our techniques extend those of Green and in particular we establish a link between the notion of "1-complexity linear systems" of Green and Tao, and graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the proceedings of STACS 200

Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs

For a graph $G$, let $Z(G,\lambda)$ be the partition function of the monomer-dimer system defined by $\sum_k m_k(G)\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating $\log Z(G,\lambda)$ at an arbitrary value $\lambda>0$ within additive error $\epsilon n$ with high probability. The query complexity of our algorithm does not depend on the size of $G$ and is polynomial in $1/\epsilon$, and we also provide a lower bound quadratic in $1/\epsilon$ for this problem. This is the first analysis of a sublinear-time approximation algorithm for a # P-complete problem. Our approach is based on the correlation decay of the Gibbs distribution associated with $Z(G,\lambda)$. We show that our algorithm approximates the probability for a vertex to be covered by a matching, sampled according to this Gibbs distribution, in a near-optimal sublinear time. We extend our results to approximate the average size and the entropy of such a matching within an additive error with high probability, where again the query complexity is polynomial in $1/\epsilon$ and the lower bound is quadratic in $1/\epsilon$. Our algorithms are simple to implement and of practical use when dealing with massive datasets. Our results extend to other systems where the correlation decay is known to hold as for the independent set problem up to the critical activity

Kinetics of Wnt-Driven β-Catenin Stabilization Revealed by Quantitative and Temporal Imaging

The Wnt/β-catenin signal transduction pathway regulates a broad range of developmental processes. Aberrant activation of the Wnt pathway leads to cancer and degenerative diseases. β-catenin is a key signaling molecule that is frequently used as a direct monitor of Wnt pathway activation. This paper describes a multi-parametric method for quantitative analysis of cellular β-catenin protein levels in a rapid and high-throughput manner. The assay offers temporally resolved detection of Wnt-stimulated accumulation of β-catenin, simultaneously detecting cell number, and it sheds light onto the kinetics of posttranslational stabilization of β-catenin

Mutations of the β- and γ-catenin genes are uncommon in human lung, breast, kidney, cervical and ovarian carcinomas

β-catenin forms complexes with Tcf and Lef-1 and functions as a transcriptional activator in the Wnt signalling pathway. Although recent investigations have been focused on the role of the adenomatous polyposis coli (APC)/ β-catenin/Tcf pathway in human tumorigenesis, there have been very few reports on mutations of the β-catenin gene in a variety of tumour types. Using PCR and single-strand conformational polymorphism analysis, we examined 93 lung, 9 breast, 6 kidney, 19 cervical and 7 ovarian carcinoma cell lines for mutations in exon 3 of the β-catenin gene. In addition, we tested these same samples for mutations in the NH2-terminal regulatory region of the γ-catenin gene. Mutational analysis for the entire coding region of β-catenin cDNA was also undertaken in 20 lung, 9 breast, 5 kidney and 6 cervical carcinoma cell lines. Deletion of most β-catenin coding exons was confirmed in line NCI-H28 (lung mesothelioma) and a silent mutation at codon 214 in exon 5 was found in HeLa (cervical adenocarcinoma). A missense mutation at codon 19 and a silent mutation at codon 28 in the NH2-terminal regulatory region of the γ-catenin gene were found in H1726 (squamous cell lung carcinoma) and H1048 (small cell lung carcinoma), respectively. Neither deletions nor mutations of these genes were detected in the other cell lines examined. These results suggest that β- and γ-catenins are infrequent mutational targets during development of human lung, breast, kidney, cervical and ovarian carcinomas. © 2001 Cancer Research Campaign http://www.bjcancer.co

Cadherin–catenin expression in primary colorectal cancer: a survival analysis

Both cell adhesion and cell signalling events are mediated by components of the cadherin-catenin complex. Loss of expression of the components of this complex have been shown to correlate with invasive behaviour in many tumour types although their exact role in colorectal cancer remains unclear. Immunohistochemical analysis of the expression of components of the cadherin-catenin complex in colorectal cancers from 60 patients was undertaken. Loss of memberanous expression of E-cadherin, alpha-catenin and beta-catenin was demonstrated in 52%, 85% and 40% of tumours respectively. Focal nuclear expression of beta-catenin ( 75% of tumour cells per section) was seen in 11 (18%) tumours. Loss of membranous alpha-catenin expression significantly correlated with tumour de-differentiation (P = 0.009). There was a trend towards an association between advanced tumour stage and loss of membranous expression of alpha-catenin or beta-catenin, although these associations were not statistically significant. Univariate analysis revealed that advanced Dukes' stage, tumour de-differentiation, loss of membranous beta-catenin expression, cytoplasmic beta-catenin expression and widespread nuclear expression of beta-catenin all correlated with short survival following apparently curative resection of the primary tumour. However, only Dukes' stage (P = 0.002), tumour grade (P = 0.02) and widespread nuclear expression of beta-catenin (P = 0.002) were independent predictors of short survival. Disturbed growth signalling events in colorectal tumours are thought to result in nuclear accumulation of beta-catenin. Consequently, tumours with widespread nuclear expression of beta-catenin are likely to have severely abnormal growth characteristics, and which therefore might be predictive of short survival in these patients

A study of patent thickets

Report analysing whether entry of UK enterprises into patenting in a technology area is affected by patent thickets in the technology area

Inhibition of Cell Proliferation and MAP Kinase and Akt Pathways in Oral Squamous cell Carcinoma by Genistein and Biochanin A

High morbidity and mortality associated with oral squamous cell carcinoma (OSCC) are largely attributable to late stage diagnosis. Despite significant advances in therapeutic strategies, the five-year survival rate for oral cancer remains at about 50%. A chemopreventive approach may be an effective alternative or adjunct to current therapies. Previous studies have shown anti-tumor effects of isoflavones in several cancers, including oral cancer. However, their mechanisms of action are still unclear. We hypothesized that isoflavones inhibit multiple signaling pathways implicated in oral carcinogenesis. To address our hypothesis, we investigated the effects of three isoflavone derivatives, genistein, biochanin A and daidzein, on SCC15 and SCC25 squamous cell carcinoma cell lines. In cell proliferation experiments, we found that genistein and biochanin A inhibited SCC15 and SCC25 cell growth with an IC50 of 50 μM. We also investigated the effect of isoflavones on ERK and Akt pathways. Our results, from western blot analysis, suggest that both genistein and biochanin A induced decreases in phosphorylation of ERK and Akt at treatment concentrations of 20, 50 and 100 μM. Taken together, our results clearly demonstrate a differential regulation of signaling pathways by various isoflavones in OSCC cell lines. Thus, tumor progression models can be utilized to study the preventive and therapeutic roles of isoflavones in oral cancer cell lines

Wnt expression is not correlated with β-catenin dysregulation in Dupuytren's Disease

BACKGROUND: Dupuytren's contracture or disease (DD) is a fibro-proliferative disease of the hand that results in finger flexion contractures. Increased cellular β-catenin levels have been identified as characteristic of this disease. As Wnts are the most widely recognized upstream regulators of cellular β-catenin accumulation, we have examined Wnt gene expression in surgical specimens and in DD-derived primary cell cultures grown in two-dimensional monolayer culture or in three-dimensional FPCL collagen lattice cultures. RESULTS: The Wnt expression profile of patient-matched DD and unaffected control palmar fascia tissue was determined by a variety of complimentary methods; Affymetrix Microarray analysis, specific Wnt and degenerative primer-based Reverse Transcriptase (RT)-PCR, and Real Time PCR. Microarray analysis identified 13 Wnts associated with DD and control tissues. Degenerate Wnt RT-PCR analysis identified Wnts 10b and 11, and to a lesser extent 5a and 9a, as the major Wnt family members expressed in our patient samples. Competitive RT-PCR analysis identified significant differences between the levels of expression of Wnts 9a, 10b and 11 in tissue samples and in primary cell cultures grown as monolayer or in FPCL, where the mRNA levels in tissue > FPCL cultures > monolayer cultures. Real Time PCR data confirmed the down-regulation of Wnt 11 mRNA in DD while Wnt 10b, the most frequently isolated Wnt in DD and control palmar fascia, displayed widely variable expression between the methods of analysis. CONCLUSION: These data indicate that changes in Wnt expression per se are unlikely to be the cause of the observed dysregulation of β-catenin expression in DD