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

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

Testing non-uniform k-wise independent distributions over product spaces (extended abstract)

A distribution D over Σ1× ⋯ ×Σ n is called (non-uniform) k-wise independent if for any set of k indices {i 1, ..., i k } and for any z1zki1ik, PrXD[Xi1Xik=z1zk]=PrXD[Xi1=z1]PrXD[Xik=zk]. We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al. [1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.National Science Foundation (U.S.) (NSF grant 0514771)National Science Foundation (U.S.) (grant 0728645)National Science Foundation (U.S.) (Grant 0732334)Marie Curie International Reintegration Grants (Grant PIRG03-GA-2008-231077)Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09)Massachusetts Institute of Technology (Akamai Presidential Fellowship

Antitrust for Institutional Investors

In this article, we address the fundamental antitrust issues presented by common ownership by large, diversified investors

Extended Thromboprophylaxis with Betrixaban in Acutely Ill Medical Patients

Background Patients with acute medical illnesses are at prolonged risk for venous thrombosis. However, the appropriate duration of thromboprophylaxis remains unknown. Methods Patients who were hospitalized for acute medical illnesses were randomly assigned to receive subcutaneous enoxaparin (at a dose of 40 mg once daily) for 10±4 days plus oral betrixaban placebo for 35 to 42 days or subcutaneous enoxaparin placebo for 10±4 days plus oral betrixaban (at a dose of 80 mg once daily) for 35 to 42 days. We performed sequential analyses in three prespecified, progressively inclusive cohorts: patients with an elevated d-dimer level (cohort 1), patients with an elevated d-dimer level or an age of at least 75 years (cohort 2), and all the enrolled patients (overall population cohort). The statistical analysis plan specified that if the between-group difference in any analysis in this sequence was not significant, the other analyses would be considered exploratory. The primary efficacy outcome was a composite of asymptomatic proximal deep-vein thrombosis and symptomatic venous thromboembolism. The principal safety outcome was major bleeding. Results A total of 7513 patients underwent randomization. In cohort 1, the primary efficacy outcome occurred in 6.9% of patients receiving betrixaban and 8.5% receiving enoxaparin (relative risk in the betrixaban group, 0.81; 95% confidence interval [CI], 0.65 to 1.00; P=0.054). The rates were 5.6% and 7.1%, respectively (relative risk, 0.80; 95% CI, 0.66 to 0.98; P=0.03) in cohort 2 and 5.3% and 7.0% (relative risk, 0.76; 95% CI, 0.63 to 0.92; P=0.006) in the overall population. (The last two analyses were considered to be exploratory owing to the result in cohort 1.) In the overall population, major bleeding occurred in 0.7% of the betrixaban group and 0.6% of the enoxaparin group (relative risk, 1.19; 95% CI, 0.67 to 2.12; P=0.55). Conclusions Among acutely ill medical patients with an elevated d-dimer level, there was no significant difference between extended-duration betrixaban and a standard regimen of enoxaparin in the prespecified primary efficacy outcome. However, prespecified exploratory analyses provided evidence suggesting a benefit for betrixaban in the two larger cohorts. (Funded by Portola Pharmaceuticals; APEX ClinicalTrials.gov number, NCT01583218. opens in new tab.

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

Völkisch und sozial? : Neonazistische Agitation gegen die neue EU-Freizügigkeit für Arbeitnehmerinnen

Wnt/β-catenin signalling pathway is crucial for the formation of many tissues and organs during development. In recent years, this pathway has also been found to regulate the biology of stem cells in the intestine and probably in other organs in adult life. Abnormal activation of Wnt/β-catenin signalling, which controls the expression of a high number of genes, is critical for the initiation and progression of most colorectal cancers. In line with this, the gene expression signature induced by activation of the Wnt/β-catenin pathway defines the intestinal stem cells present at the bottom of the crypts and also colon cancer stem cells. This supports the importance of inhibitors of the Wnt/β-catenin pathway as potential agents in colorectal cancer therapy. However, the complexity, wide activity in the organism modulating the biology of several cell types, and characteristics of this pathway have delayed the identification of suitable targets and so, the development of such inhibitors that are only now reaching the clinic.Peer reviewe

Wnt-signalling pathway in ovarian epithelial tumours: increased expression of β-catenin and GSK3β

Beta-catenin is involved in both cell-cell adhesion and in transcriptional regulation by the Wingless/Wnt signalling pathway. Alterations of components of this pathway have been suggested to play a central role in tumorigenesis. The present study investigated, by immunohistochemistry and immunoblotting, the protein expression and localisation of beta-catenin, adenomatous polyposis coli (APC), glycogen synthase kinase 3beta (GSK3beta) and lymphocyte enhancer factor-1 (Lef-1) in normal human ovaries and in epithelial ovarian tumours in vivo and in vitro. Immortalised human ovarian surface epithelium and ovarian cancer cell cells (OVCAR-3) expressed beta-catenin, APC, GSK3beta and Lef-1. Nuclear staining of beta-catenin and Lef-1 were demonstrated only in OVCAR-3 cells. There were significant increases of beta-catenin and GSK3beta, while APC was reduced in ovarian cancer compared to the normal ovary. Beta-catenin and Lef-1 were coimmunoprecipitated in ovarian tumours, but not in the normal ovary. Nuclear localisation of beta-catenin or Lef-1 could not be demonstrated in the normal ovary or in the ovarian tumours. The absence of nuclear localisation of beta-catenin could be due to an increased binding to the cadherin-alpha-catenin cell adhesion complex. In fact, we have earlier reported an increased expression of E-cadherin in ovarian adenocarcinomas. In summary, this study demonstrates an increase in the expression of components of the Wingless/Wnt pathway in malignant ovarian tumours. The increase suggests a role for this signalling pathway in cell transformation and in tumour progression. However, it remains to be demonstrated whether it is an increased participation of beta-catenin in transcriptional regulation, or in the stabilisation of cellular integrity, or both, that is the crucial event in ovarian tumorigenesis