Rationality of fields of invariants for some representations of SL(2)\timesSL(2)

We prove that the quotient by SL(2)\timesSL(2) of the space of bidegree (a, b) curves on P^1\timesP^1 is rational when ab is even and a\not=b.Comment: added Section 2.1 in which a general method is explained. to appear in Compositio Mat

Improvement of adhesive toughness measurement

The double cantilever beam (DCB) method for adhesive toughness measurement was improved by incorporating a sufficiently sharp crack made by a wedge-tapping method. A known route to producing cracks via loading–unloading cycles was proved unreliable because the cycles produced plastic deformation in the adhesive where new cracks propagated. Abnormally high toughness values with large standard deviations were obtained with cracks made by embedding a non-sticky insert. Only instantly propagated cracks made by tapping were sufficiently sharp to produce reproducible, accurate tough-ness measurements. However, toughened resin was insensit

Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

Low-order equal-time statistics of a barotropic flow on a rotating sphere are investigated. The flow is driven by linear relaxation toward an unstable zonal jet. For relatively short relaxation times, the flow is dominated by critical-layer waves. For sufficiently long relaxation times, the flow is turbulent. Statistics obtained from a second-order cumulant expansion are compared to those accumulated in direct numerical simulations, revealing the strengths and limitations of the expansion for different relaxation times.Comment: 23 pages, 8 figures. Version to appear in J. Atmos. Sc

A Precise Distance to IRAS 00420+5530 via H2O Maser Parallax with the VLBA

We have used the VLBA to measure the annual parallax of the H2O masers in the star-forming region IRAS 00420+5530. This measurement yields a direct distance estimate of 2.17 +/- 0.05 kpc (<3%), which disagrees substantially with the standard kinematic distance estimate of ~4.6 kpc (according to the rotation curve of Brand and Blitz 1993), as well as most of the broad range of distances (1.7-7.7 kpc) used in various astrophysical analyses in the literature. The 3-dimensional space velocity of IRAS 00420+5530 at this new, more accurate distance implies a substantial non-circular and anomalously slow Galactic orbit, consistent with similar observations of W3(OH) (Xu et al., 2006; Hachisuka et al. 2006), as well as line-of-sight velocity residuals in the rotation curve analysis of Brand and Blitz (1993). The Perseus spiral arm of the Galaxy is thus more than a factor of two closer than previously presumed, and exhibits motions substantially at odds with axisymmetric models of the rotating Galaxy.Comment: 33 pages, 12 figures; Accepted by ApJ (to appear March 2009

Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy

With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations. The obtained results can be reduced to the classical Hamilton hierachy of ordinary calculus.Comment: 12 p

Deep learning networks find unique mammographic differences in previous negative mammograms between interval and screen-detected cancers: a case-case study.

BackgroundTo determine if mammographic features from deep learning networks can be applied in breast cancer to identify groups at interval invasive cancer risk due to masking beyond using traditional breast density measures.MethodsFull-field digital screening mammograms acquired in our clinics between 2006 and 2015 were reviewed. Transfer learning of a deep learning network with weights initialized from ImageNet was performed to classify mammograms that were followed by an invasive interval or screen-detected cancer within 12 months of the mammogram. Hyperparameter optimization was performed and the network was visualized through saliency maps. Prediction loss and accuracy were calculated using this deep learning network. Receiver operating characteristic (ROC) curves and area under the curve (AUC) values were generated with the outcome of interval cancer using the deep learning network and compared to predictions from conditional logistic regression with errors quantified through contingency tables.ResultsPre-cancer mammograms of 182 interval and 173 screen-detected cancers were split into training/test cases at an 80/20 ratio. Using Breast Imaging-Reporting and Data System (BI-RADS) density alone, the ability to correctly classify interval cancers was moderate (AUC = 0.65). The optimized deep learning model achieved an AUC of 0.82. Contingency table analysis showed the network was correctly classifying 75.2% of the mammograms and that incorrect classifications were slightly more common for the interval cancer mammograms. Saliency maps of each cancer case found that local information could highly drive classification of cases more than global image information.ConclusionsPre-cancerous mammograms contain imaging information beyond breast density that can be identified with deep learning networks to predict the probability of breast cancer detection

Replication of LDL SWAs hits in PROSPER/PHASE as validation for future (pharmaco)genetic analyses

&lt;p&gt;&lt;b&gt;Background:&lt;/b&gt; The PHArmacogenetic study of Statins in the Elderly at risk (PHASE) is a genome wide association study in the PROspective Study of Pravastatin in the Elderly at risk for vascular disease (PROSPER) that investigates the genetic variation responsible for the individual variation in drug response to pravastatin. Statins lower LDL-cholesterol in general by 30%, however not in all subjects. Moreover, clinical response is highly variable and adverse effects occur in a minority of patients. In this report we first describe the rationale of the PROSPER/PHASE project and second show that the PROSPER/PHASE study can be used to study pharmacogenetics in the elderly.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; The genome wide association study (GWAS) was conducted using the Illumina 660K-Quad beadchips following manufacturer's instructions. After a stringent quality control 557,192 SNPs in 5,244 subjects were available for analysis. To maximize the availability of genetic data and coverage of the genome, imputation up to 2.5 million autosomal CEPH HapMap SNPs was performed with MACH imputation software. The GWAS for LDL-cholesterol is assessed with an additive linear regression model in PROBABEL software, adjusted for age, sex, and country of origin to account for population stratification.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; Forty-two SNPs reached the GWAS significant threshold of p = 5.0e-08 in 5 genomic loci (APOE/APOC1; LDLR; FADS2/FEN1; HMGCR; PSRC1/CELSR5). The top SNP (rs445925, chromosome 19) with a p-value of p = 2.8e-30 is located within the APOC1 gene and near the APOE gene. The second top SNP (rs6511720, chromosome 19) with a p-value of p = 5.22e-15 is located within the LDLR gene. All 5 genomic loci were previously associated with LDL-cholesterol levels, no novel loci were identified. Replication in WOSCOPS and CARE confirmed our results.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusion:&lt;/b&gt; With the GWAS in the PROSPER/PHASE study we confirm the previously found genetic associations with LDL-cholesterol levels. With this proof-of-principle study we show that the PROSPER/PHASE study can be used to investigate genetic associations in a similar way to population based studies. The next step of the PROSPER/PHASE study is to identify the genetic variation responsible for the variation in LDL-cholesterol lowering in response to statin treatment in collaboration with other large trials.&lt;/p&gt

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD and aura symptoms on the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value [sigma]=1 at the instability point. We predict that human cortex is only weakly susceptible to SD ([sigma]&#x3c;1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. We discuss the increased dynamical repertoire of cortical tissue close to [sigma]=1, in particular, the resulting implications on migraine pharmacology that is hitherto tested in the regime ([sigma]&#x3e;&#x3e;1), and potentially silent aura occurring below a second bifurcation point at [sigma]=0 on the susceptible scale

Intermittent maser flare around the high mass young stellar object G353.273+0.641 I: data & overview

We have performed VLBI and single-dish monitoring of 22 GHz H$_{2}$O maser emission from the high mass young stellar object G353.273+0.641 with VERA (VLBI Exploration of Radio Astrometry) and Tomakamai 11-m radio telescope. Two maser flares have been detected, separated almost two years. Frequent VLBI monitoring has revealed that these flare activities have been accompanied by structural change of the prominent shock front traced by H2O maser alignments. We have detected only blue-shifted emissions and all maser features have been distributed within very small area of 200 $\times$ 200 au$^{2}$ in spite of wide velocity range (> 100 km s$^{-1}$). The light curve shows notably intermittent variation and suggests that the H$_{2}$O masers in G353.273+0.641 are excited by episodic radio jet. The time-scale of \sim2 yr and characteristic velocity of \sim500 km s$^{-1}$ also support this interpretation. Two isolated velocity components of C50 (-53 \pm 7 km s$^{-1}$) and C70 (-73 \pm 7 km s$^{-1}$) have shown synchronised linear acceleration of the flux weighted V_{\rmn{LSR}} values (\sim-5 km s$^{-1}$ yr$^{-1}$) during the flare phase. This can be converted to the lower-limit momentum rate of 1.1 \times 10$^{-3}$ M_{\sun} km s$^{-1}$ yr$^{-1}$. Maser properties are quite similar to that of IRAS 20126+4104 especially. This corroborates the previous suggestion that G353.273+0.641 is a candidate of high mass protostellar object. The possible pole-on geometry of disc-jet system can be suitable for direct imaging of the accretion disc in this case.Comment: 13 pages, 5 figures accepted for publication in MNRA

Nitrogen and sulphur management: challenges for organic sources in temperate agricultural systems

A current global trend towards intensification or specialization of agricultural enterprises has been accompanied by increasing public awareness of associated environmental consequences. Air and water pollution from losses of nutrients, such as nitrogen (N) and sulphur (S), are a major concern. Governments have initiated extensive regulatory frameworks, including various land use policies, in an attempt to control or reduce the losses. This paper presents an overview of critical input and loss processes affecting N and S for temperate climates, and provides some background to the discussion in subsequent papers evaluating specific farming systems. Management effects on potential gaseous and leaching losses, the lack of synchrony between supply of nutrients and plant demand, and options for optimizing the efficiency of N and S use are reviewed. Integration of inorganic and organic fertilizer inputs and the equitable re-distribution of nutrients from manure are discussed. The paper concludes by highlighting a need for innovative research that is also targeted to practical approaches for reducing N and S losses, and improving the overall synchrony between supply and demand