Quantum Algorithms for Learning and Testing Juntas

In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity has no dependence on n, the dimension of the domain the Boolean functions are defined over; - with no access to any classical or quantum membership ("black-box") queries. Instead, our algorithms use only classical examples generated uniformly at random and fixed quantum superpositions of such classical examples; - which require only a few quantum examples but possibly many classical random examples (which are considered quite "cheap" relative to quantum examples). Our quantum algorithms are based on a subroutine FS which enables sampling according to the Fourier spectrum of f; the FS subroutine was used in earlier work of Bshouty and Jackson on quantum learning. Our results are as follows: - We give an algorithm for testing k-juntas to accuracy $\epsilon$ that uses $O(k/\epsilon)$ quantum examples. This improves on the number of examples used by the best known classical algorithm. - We establish the following lower bound: any FS-based k-junta testing algorithm requires $\Omega(\sqrt{k})$ queries. - We give an algorithm for learning $k$-juntas to accuracy $\epsilon$ that uses $O(\epsilon^{-1} k\log k)$ quantum examples and $O(2^k \log(1/\epsilon))$ random examples. We show that this learning algorithms is close to optimal by giving a related lower bound.Comment: 15 pages, 1 figure. Uses synttree package. To appear in Quantum Information Processin

The somatostatin analogue octreotide confers sensitivity to rapamycin treatment on pituitary tumor cells

Rapamycin and its analogues have significant antiproliferative action against a variety of tumors. However, sensitivity to rapamycin is reduced by Akt activation that results from the ablative effects of rapamycin on a p70 S6K-induced negative feedback loop that blunts phosphoinositide 3-kinase (PI3K)-mediated support for Akt activity. Thus, sensitivity to rapamycin might be increased by imposing an upstream blockade to the PI3K/Akt pathway. Here, we investigated this model using the somatostatin analogue octreotide as a tool to decrease levels of activated Ser(473)-phosphorylated Akt (pAkt-Ser(473)) in pituitary tumor cells that express somatostatin receptors. Octreotide increased levels of phosphorylated insulin receptor substrate-1 that were suppressed by rapamycin, subsequently decreasing levels of pAkt-Ser(473) through effects on phosphotyrosine phosphatase SHP-1. Octreotide potentiated the antiproliferative effects of rapamycin in immortalized pituitary tumor cells or human nonfunctioning pituitary adenoma cells in primary cell culture, sensitizing tumor cells even to low rapamycin concentrations. Combined treatment of octreotide and rapamycin triggered G(1) cell cycle arrest, decreasing E2F transcriptional activity and cyclin E levels by increasing levels of p27/Kip1. These findings show that adjuvant treatment with a somatostatin analogue can sensitize pituitary tumor cells to the antiproliferative effects of rapamycin

Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata

After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection with the regular languages, and, finally, establish strict inclusions in the parallel computation classes $\mathsf{SC}$ and (uniform) $\mathsf{AC}$. As an addendum, we introduce and investigate the concept of a decider ACA (DACA) as a candidate for a decider counterpart to (acceptor) ACAs. We show the class of languages decidable in constant time by DACAs equals the locally testable languages, and we also determine $\Omega(\sqrt{n})$ as the (tight) time complexity threshold for DACAs up to which no advantage compared to constant time is possible.Comment: 16 pages, 2 figures, to appear at DLT 202

Cube Testers and Key Recovery Attacks On Reduced-Round MD6 and Trivium

CRYPTO 2008 saw the introduction of the hash function MD6 and of cube attacks, a type of algebraic attack applicable to cryptographic functions having a low-degree algebraic normal form over GF(2). This paper applies cube attacks to reduced round MD6, finding the full 128-bit key of a 14-round MD6 with complexity 2^22 (which takes less than a minute on a single PC). This is the best key recovery attack announced so far for MD6. We then introduce a new class of attacks called cube testers, based on efficient property-testing algorithms, and apply them to MD6 and to the stream cipher Trivium. Unlike the standard cube attacks, cube testers detect nonrandom behavior rather than performing key extraction, but they can also attack cryptographic schemes described by nonrandom polynomials of relatively high degree. Applied to MD6, cube testers detect nonrandomness over 18 rounds in 2^17 complexity; applied to a slightly modified version of the MD6 compression function, they can distinguish 66 rounds from random in 2^24 complexity. Cube testers give distinguishers on Trivium reduced to 790 rounds from random with 2^30 complexity and detect nonrandomness over 885 rounds in 2^27, improving on the original 767-round cube attack

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

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

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

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