Projective duality and K-energy asymptotics

Let X be a smooth, linearly normal n dimensional complex projective variety. Assume that the projective dual of X has codimension one with defining polynomial D(X). In this paper the log of the norm of D(X) is expressed as the restriction to the Bergman metrics of an energy functional on X. We show how, for smooth plane curves, this energy functional reduces to the standard action functionals of Kahler geometry.Comment: 27 page

Metadynamics with Discriminants: a Tool for Understanding Chemistry

We introduce an extension of a recently published method\cite{Mendels2018} to obtain low-dimensional collective variables for studying multiple states free energy processes in chemical reactions. The only information needed is a collection of simple statistics of the equilibrium properties of the reactants and product states. No information on the reaction mechanism has to be given. The method allows studying a large variety of chemical reactivity problems including multiple reaction pathways, isomerization, stereo- and regiospecificity. We applied the method to two fundamental organic chemical reactions. First we study the \ce{S_N2} nucleophilic substitution reaction of a \ce{Cl} in \ce{CH_2 Cl_2} leading to an understanding of the kinetic origin of the chirality inversion in such processes. Subsequently, we tackle the problem of regioselectivity in the hydrobromination of propene revealing that the nature of empirical observations such as the Markovinikov's rules lies in the chemical kinetics rather than the thermodynamic stability of the products

Stabilizing Training of Generative Adversarial Networks through Regularization

Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of hyper-parameters. This fragility is in part due to a dimensional mismatch or non-overlapping support between the model distribution and the data distribution, causing their density ratio and the associated f-divergence to be undefined. We overcome this fundamental limitation and propose a new regularization approach with low computational cost that yields a stable GAN training procedure. We demonstrate the effectiveness of this regularizer across several architectures trained on common benchmark image generation tasks. Our regularization turns GAN models into reliable building blocks for deep learning

Implicitization of curves and (hyper)surfaces using predicted support

We reduce implicitization of rational planar parametric curves and (hyper)surfaces to linear algebra, by interpolating the coefficients of the implicit equation. For predicting the implicit support, we focus on methods that exploit input and output structure in the sense of sparse (or toric) elimination theory, namely by computing the Newton polytope of the implicit polynomial, via sparse resultant theory. Our algorithm works even in the presence of base points but, in this case, the implicit equation shall be obtained as a factor of the produced polynomial. We implement our methods on Maple, and some on Matlab as well, and study their numerical stability and efficiency on several classes of curves and surfaces. We apply our approach to approximate implicitization, and quantify the accuracy of the approximate output, which turns out to be satisfactory on all tested examples; we also relate our measures to Hausdorff distance. In building a square or rectangular matrix, an important issue is (over)sampling the given curve or surface: we conclude that unitary complexes offer the best tradeoff between speed and accuracy when numerical methods are employed, namely SVD, whereas for exact kernel computation random integers is the method of choice. We compare our prototype to existing software and find that it is rather competitive

Historical Document Image Segmentation with LDA-Initialized Deep Neural Networks

In this paper, we present a novel approach to perform deep neural networks layer-wise weight initialization using Linear Discriminant Analysis (LDA). Typically, the weights of a deep neural network are initialized with: random values, greedy layer-wise pre-training (usually as Deep Belief Network or as auto-encoder) or by re-using the layers from another network (transfer learning). Hence, many training epochs are needed before meaningful weights are learned, or a rather similar dataset is required for seeding a fine-tuning of transfer learning. In this paper, we describe how to turn an LDA into either a neural layer or a classification layer. We analyze the initialization technique on historical documents. First, we show that an LDA-based initialization is quick and leads to a very stable initialization. Furthermore, for the task of layout analysis at pixel level, we investigate the effectiveness of LDA-based initialization and show that it outperforms state-of-the-art random weight initialization methods.Comment: 5 page

Automated identification of Fos expression

The concentration of Fos, a protein encoded by the immediate-early gene c-fos, provides a measure of synaptic activity that may not parallel the electrical activity of neurons. Such a measure is important for the difficult problem of identifying dynamic properties of neuronal circuitries activated by a variety of stimuli and behaviours. We employ two-stage statistical pattern recognition to identify cellular nuclei that express Fos in two-dimensional sections of rat forebrain after administration of antipsychotic drugs. In stage one, we distinguish dark-stained candidate nuclei from image background by a thresholding algorithm and record size and shape measurements of these objects. In stage two, we compare performance of linear and quadratic discriminants, nearest-neighbour and artificial neural network classifiers that employ functions of these measurements to label candidate objects as either Fos nuclei, two touching Fos nuclei or irrelevant background material. New images of neighbouring brain tissue serve as test sets to assess generalizability of the best derived classification rule, as determined by lowest cross-validation misclassification rate. Three experts, two internal and one external, compare manual and automated results for accuracy assessment. Analyses of a subset of images on two separate occasions provide quantitative measures of inter- and intra-expert consistency. We conclude that our automated procedure yields results that compare favourably with those of the experts and thus has potential to remove much of the tedium, subjectivity and irreproducibility of current Fos identification methods in digital microscopy

Automatic recognition of fingerspelled words in British Sign Language

We investigate the problem of recognizing words from video, fingerspelled using the British Sign Language (BSL) fingerspelling alphabet. This is a challenging task since the BSL alphabet involves both hands occluding each other, and contains signs which are ambiguous from the observer’s viewpoint. The main contributions of our work include: (i) recognition based on hand shape alone, not requiring motion cues; (ii) robust visual features for hand shape recognition; (iii) scalability to large lexicon recognition with no re-training. We report results on a dataset of 1,000 low quality webcam videos of 100 words. The proposed method achieves a word recognition accuracy of 98.9%

The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: selecting emission line galaxies using the Fisher discriminant

We present a new selection technique of producing spectroscopic target catalogues for massive spectroscopic surveys for cosmology. This work was conducted in the context of the extended Baryon Oscillation Spectroscopic Survey (eBOSS), which will use ~200 000 emission line galaxies (ELGs) at 0.6<zspec<1.0 to obtain a precise baryon acoustic oscillation measurement. Our proposed selection technique is based on optical and near-infrared broad-band filter photometry. We used a training sample to define a quantity, the Fisher discriminant (linear combination of colours), which correlates best with the desired properties of the target: redshift and [OII] flux. The proposed selections are simply done by applying a cut on magnitudes and this Fisher discriminant. We used public data and dedicated SDSS spectroscopy to quantify the redshift distribution and [OII] flux of our ELG target selections. We demonstrate that two of our selections fulfil the initial eBOSS/ELG redshift requirements: for a target density of 180 deg^2, ~70% of the selected objects have 0.6<zspec<1.0 and only ~1% of those galaxies in the range 0.6<zspec<1.0 are expected to have a catastrophic zspec estimate. Additionally, the stacked spectra and stacked deep images for those two selections show characteristic features of star-forming galaxies. The proposed approach using the Fisher discriminant could, however, be used to efficiently select other galaxy populations, based on multi-band photometry, providing that spectroscopic information is available. This technique could thus be useful for other future massive spectroscopic surveys such as PFS, DESI, and 4MOST.Comment: Version published in A&

Norwegian Sea Herring Stock Discrimination phase I (NORDISI)

There is growing concern among fishermen about the migration of North Sea herring into the Norwegian Sea. The Pelagic Freezer-trawler Association therefore commissioned IMARES to develop a technique to monitor possible catches of North Sea herring in the Norwegian Sea. This technique will use morphometric (shape) differences in herring to distinguish between Norwegian Sea spawning herring and North Sea herring. The results show that the model is able to distinguish Norwegian spring spawning herring from North Sea autumn or winter spawning herring. Overall we can conclude that even though we still have to overcome some methodological problems we are confident that this research constitutes a first step towards developing a technique to monitor catches of herring from the Norwegian Sea for Norwegian Spring spawning or other herring