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

Optimization of Transport Capacity for Fodder-Straw in Syria

Rosana G. Moreira, Editor-in-Chief; Texas A&M UniversityThis is a Technical article from International Commission of Agricultural Engineering (CIGR, Commission Internationale du Genie Rural) E-Journal Volume 3 (2001): M. Gebreselassie, O. Kaufman, and J. Hahn. Optimization of Transport Capacity for Fodder-Straw in Syria. Vol. III, December 2001

Aerosol absorption over the clear-sky oceans deduced from POLDER-1 and AERONET observations

We estimate aerosol absorption over the clear-sky oceans using aerosol geophysical products from POLDER-1 space measurements and absorption properties from ground-based AERONET measurements. Our best estimate is 2.5 Wm-2 averaged over the 8-month lifetime of POLDER-1. Low and high absorption estimates are 2.2 and 3.1 Wm-2 based on the variability in aerosol single scattering albedo observed by AERONET. Main sources of uncertainties are the discrimation of the aerosol type from satellite measurements, and potential clear-sky bias induced by the cloud-screening procedure

Succinct Representation of Codes with Applications to Testing

Motivated by questions in property testing, we search for linear error-correcting codes that have the "single local orbit" property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every "sparse" binary code whose coordinates are indexed by elements of F_{2^n} for prime n, and whose symmetry group includes the group of non-singular affine transformations of F_{2^n} has the single local orbit property. (A code is said to be "sparse" if it contains polynomially many codewords in its block length.) In particular this class includes the dual-BCH codes for whose duals (i.e., for BCH codes) simple bases were not known. Our result gives the first short (O(n)-bit, as opposed to the natural exp(n)-bit) description of a low-weight basis for BCH codes. The interest in the "single local orbit" property comes from the recent result of Kaufman and Sudan (STOC 2008) that shows that the duals of codes that have the single local orbit property under the affine symmetry group are locally testable. When combined with our main result, this shows that all sparse affine-invariant codes over the coordinates F_{2^n} for prime n are locally testable. If, in addition to n being prime, if 2^n-1 is also prime (i.e., 2^n-1 is a Mersenne prime), then we get that every sparse cyclic code also has the single local orbit. In particular this implies that BCH codes of Mersenne prime length are generated by a single low-weight codeword and its cyclic shifts

Towards the Formal Reliability Analysis of Oil and Gas Pipelines

It is customary to assess the reliability of underground oil and gas pipelines in the presence of excessive loading and corrosion effects to ensure a leak-free transport of hazardous materials. The main idea behind this reliability analysis is to model the given pipeline system as a Reliability Block Diagram (RBD) of segments such that the reliability of an individual pipeline segment can be represented by a random variable. Traditionally, computer simulation is used to perform this reliability analysis but it provides approximate results and requires an enormous amount of CPU time for attaining reasonable estimates. Due to its approximate nature, simulation is not very suitable for analyzing safety-critical systems like oil and gas pipelines, where even minor analysis flaws may result in catastrophic consequences. As an accurate alternative, we propose to use a higher-order-logic theorem prover (HOL) for the reliability analysis of pipelines. As a first step towards this idea, this paper provides a higher-order-logic formalization of reliability and the series RBD using the HOL theorem prover. For illustration, we present the formal analysis of a simple pipeline that can be modeled as a series RBD of segments with exponentially distributed failure times.Comment: 15 page

Dissolved oxygen dynamics during a phytoplankton bloom in the Ross Sea polynya

The Ross Sea polynya is one of the most productive regions in the Southern Ocean. However, limited access and high spatio-temporal variability of physical and biological processes limit the use of conventional oceanographic methods to measure early season primary productivity. High-resolution observations from two Seagliders provide insights into the timing of a bloom in the southern Ross Sea polynya in December 2010. Changes in chlorophyll and oxygen concentrations are used to assess bloom dynamics. Using a ratio of dissolved oxygen to carbon, net primary production is estimated over the duration of the bloom showing a sensitive balance between net autotrophy and heterotrophy. The two gliders, observing spatially distinct regions during the same period, found net community production rates of -0.9±0.7 and 0.7±0.4 g C m-2 d-1. The difference highlights the spatial variability of biological processes and is probably caused by observing different stages of the bloom. The challenge of obtaining accurate primary productivity estimates highlights the need for increased observational efforts, particularly focusing on subsurface processes not resolved using surface or remote observations. Without an increased observational effort and the involvement of emerging technologies, it will not be possible to determine the seasonal trophic balance of the Ross Sea polynya and quantify the shelf's importance in carbon export

Cluster Winds Blow along Supercluster Axes

Within Abell galaxy clusters containing wide-angle tailed radio sources, there is evidence of a ``prevailing wind'' which directs the WAT jets. We study the alignment of WAT jets and nearby clusters to test the idea that this wind may be a fossil of drainage along large-scale supercluster axes. We also test this idea with a study of the alignment of WAT jets and supercluster axes. Statistical test neighbours indicate no alignment of WAT jets towards nearest clusters, but do indicate approximately 98% confidence in alignment with the long axis of the supercluster in which the cluster lies. We find a preferred scale for such superclusters of order 25 Mpc $h^{-1}$.Comment: Latex, 5 pages, with 5 postscript figures. To be published in MNRAS. Slight revisions to coincide with journal text. Linked to color image at http://kusmos.phsx.ukans.edu/~melott/images/A2634SUW.jp

Racial disparities in treatment patterns and clinical outcomes in patients with HER2-positive metastatic breast cancer.

Data characterizing demographics, treatment patterns, and clinical outcomes in black patients with human epidermal growth factor receptor 2 (HER2)-positive metastatic breast cancer (MBC) are limited. registHER is a large, observational cohort study of patients (n = 1,001) with HER2-positive MBC diagnosed ≤6 months of enrollment and followed until death, disenrollment, or June 2009 (median follow-up of 27 months). Demographics, treatment patterns, and clinical outcomes were described for black (n = 126) and white patients (n = 793). Progression-free survival (PFS) following first-line therapy and overall survival (OS) were examined. Multivariate analyses adjusted for baseline and treatment factors. Black patients were more likely than white patients to be obese (body mass index ≥30), to have diabetes, and to have a history of cardiovascular disease; they were also less likely to have estrogen receptor or progesterone receptor positive disease. In patients treated with trastuzumab, the incidence of cardiac safety events (grade ≥3) was higher in black patients (10.9 %) than in white patients (7.9 %). Unadjusted median OS and PFS (months) were significantly lower in black patients than in white patients (OS: black: 27.1, 95 % confidence interval [CI] 21.3-32.1; white: 37.3, 95 % CI 34.6-41.1; PFS: black: 7.0, 95 % CI 5.7-8.2; white: 10.2, 95 % CI 9.3-11.2). The adjusted OS hazard ratio (HR) for black patients compared with white patients was 1.29 (95 % CI 1.00-1.65); adjusted PFS HR was 1.29 (95 % CI 1.05-1.59). This real-world evaluation of a large cohort of patients with HER2-positive MBC shows poorer prognostic factors and independently worse clinical outcomes in black versus white patients. Further research is needed to identify potential biologic differences that could have predictive impact for black patients or that could explain these differences