Morita equivalence of multidimensional noncommutative tori

One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched.Comment: 13 pages. Minor comment corrected. (To appear in the International Journal of Mathematics.

What is the Role of Recurrent Neural Networks (RNNs) in an Image Caption Generator?

In neural image captioning systems, a recurrent neural network (RNN) is typically viewed as the primary `generation' component. This view suggests that the image features should be `injected' into the RNN. This is in fact the dominant view in the literature. Alternatively, the RNN can instead be viewed as only encoding the previously generated words. This view suggests that the RNN should only be used to encode linguistic features and that only the final representation should be `merged' with the image features at a later stage. This paper compares these two architectures. We find that, in general, late merging outperforms injection, suggesting that RNNs are better viewed as encoders, rather than generators.Comment: Appears in: Proceedings of the 10th International Conference on Natural Language Generation (INLG'17

PEO-Silane Amphiphiles as Surface-Modifying Additives to Improve the Protein Resistance of Silicone

Silicone materials are commonly used for implantable medical devices because of their favorable bulk properties. Unfortunately, due to their hydrophobicity, silicones have a high affinity for protein adsorption which makes them susceptible to thrombosis. In this work, novel PEO-silane amphiphiles [α-(EtO)3Si-(CH2)2-ODMSm-block-PEOn-OCH3] were developed to act as surface-modifying additives (SMAs) for silicone. Based on prior work, the PEO-silane amphiphiles were expected to rapidly migrate to the material surface in response to water exposure and result in a hydrophilic and protein-resistant silicone. These were distinguishable from conventional PEO-silanes due to the hydrophobic oligodimethylsiloxane (ODMS) tether which rendered the SMAs amphiphilic. They were also unique as SMAs due to their diblock structure and crosslinking group (triethoxysilane) to prevent leaching from condensation-cure elastomers. The PEO-silane amphiphiles were prepared with three PEO lengths (n = 3, 8, and 16) and compared to analogous non-amphiphilic PEO-silanes (PEO-controls). When incorporated into silicone via bulk-modification, the PEO-silane amphiphiles exhibited rapid and extensive water-driven restructuring versus silicones modified with the PEO-controls. Multiple concentrations of each PEO-silane amphiphile were evaluated (5, 10, 25, 50, and 100 µmol per 1 g silicone) in terms of their ability to confer hydrophilicity and protein resistance. From these results, it was determined that PEO length dictates restructuring behavior of PEO-silane amphiphiles. Only n = 8 and 16 were able to achieve substantial hydrophilicity and reduce protein adsorption, but the n = 8 length was more effective and maximized protein resistance with concentrations as low as 10 µmol per 1 g silicone (1.68 wt%). Finally, PEO-silane amphiphiles were evaluated in terms of their ability to overcome the limitations associated with SMAs (leaching and poor abrasion recovery). It was found that triethoxysilane did not prevent leaching of PEO-silane amphiphiles (m = 13, n = 8) from silicone in water. However, increasing the ODMS tether length (m = 30) dramatically reduced leaching and water uptake for both the PEO-silane and diblock amphiphiles without impairing restructuring behavior. For all tested SMAs, excellent water-driven surface restructuring behavior persisted on bulk-modified silicones after material abrasion

The Multi-Wavelength Tully-Fisher relation with spatially resolved HI kinematics

In this paper we investigate the statistical properties of the Tully-Fisher relation for a sample of 32 galaxies with measured distances from the Cepheid period-luminosity relation and/or TRGB stars. We take advantage of panchromatic photometry in 12 bands (from FUV to 4.5 $\mu$m) and of spatially resolved HI kinematics. We use these data together with three kinematic measures ($W^{i}_{50}$, $V_{max}$ and $V_{flat}$) extracted from the global HI profiles or HI rotation curves, so as to construct 36 correlations allowing us to select the one with the least scatter. We introduce a tightness parameter $\sigma_{\perp}$ of the TFr, in order to obtain a slope-independent measure of the goodness of fit. We find that the tightest correlation occurs when we select the 3.6 $\mu$m photometric band together with the $V_{flat}$ parameter extracted from the HI rotation curve.Comment: 16 pages, 16 figures, accepted for publication in MNRAS, minor changes due to proof correction

Reconstruction of an in silico metabolic model of _Arabidopsis thaliana_ through database integration

The number of genome-scale metabolic models has been rising quickly in recent years, and the scope of their utilization encompasses a broad range of applications from metabolic engineering to biological discovery. However the reconstruction of such models remains an arduous process requiring a high level of human intervention. Their utilization is further hampered by the absence of standardized data and annotation formats and the lack of recognized quality and validation standards.

Plants provide a particularly rich range of perspectives for applications of metabolic modeling. We here report the first effort to the reconstruction of a genome-scale model of the metabolic network of the plant _Arabidopsis thaliana_, including over 2300 reactions and compounds. Our reconstruction was performed using a semi-automatic methodology based on the integration of two public genome-wide databases, significantly accelerating the process. Database entries were compared and integrated with each other, allowing us to resolve discrepancies and enhance the quality of the reconstruction. This process lead to the construction of three models based on different quality and validation standards, providing users with the possibility to choose the standard that is most appropriate for a given application. First, a _core metabolic model_ containing only consistent data provides a high quality model that was shown to be stoichiometrically consistent. Second, an _intermediate metabolic model_ attempts to fill gaps and provides better continuity. Third, a _complete metabolic model_ contains the full set of known metabolic reactions and compounds in _Arabidopsis thaliana_.

We provide an annotated SBML file of our core model to enable the maximum level of compatibility with existing tools and databases. We eventually discuss a series of principles to raise awareness of the need to develop coordinated efforts and common standards for the reconstruction of genome-scale metabolic models, with the aim of enabling their widespread diffusion, frequent update, maximum compatibility and convenience of use by the wider research community and industry