A Generalisation of an Ostrowski Inequality in Inner Product Spaces

A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given

An Inequality in Metric Spaces

In this note we establish a general inequality valid in metric spaces that is related to the polygonal inequality and admits also a natural geometrical interpretation. Particular instances of interest holding in normed linear spaces and inner product spaces are pointed out as well

SSD: Single Shot MultiBox Detector

We present a method for detecting objects in images using a single deep neural network. Our approach, named SSD, discretizes the output space of bounding boxes into a set of default boxes over different aspect ratios and scales per feature map location. At prediction time, the network generates scores for the presence of each object category in each default box and produces adjustments to the box to better match the object shape. Additionally, the network combines predictions from multiple feature maps with different resolutions to naturally handle objects of various sizes. Our SSD model is simple relative to methods that require object proposals because it completely eliminates proposal generation and subsequent pixel or feature resampling stage and encapsulates all computation in a single network. This makes SSD easy to train and straightforward to integrate into systems that require a detection component. Experimental results on the PASCAL VOC, MS COCO, and ILSVRC datasets confirm that SSD has comparable accuracy to methods that utilize an additional object proposal step and is much faster, while providing a unified framework for both training and inference. Compared to other single stage methods, SSD has much better accuracy, even with a smaller input image size. For $300\times 300$ input, SSD achieves 72.1% mAP on VOC2007 test at 58 FPS on a Nvidia Titan X and for $500\times 500$ input, SSD achieves 75.1% mAP, outperforming a comparable state of the art Faster R-CNN model. Code is available at https://github.com/weiliu89/caffe/tree/ssd .Comment: ECCV 201

Tracing the Origins and Evolution of Small Planets using Their Orbital Obliquities

We recommend an intensive effort to survey and understand the obliquity distribution of small close-in extrasolar planets over the coming decade. The orbital obliquities of exoplanets--i.e., the relative orientation between the planetary orbit and the stellar rotation--is a key tracer of how planets form and migrate. While the orbital obliquities of smaller planets are poorly explored today, a new generation of facilities coming online over the next decade will make such observations possible en masse. Transit spectroscopic observations with the extremely large telescopes will enable us to measure the orbital obliquities of planets as small as $\sim2R_{\oplus}$ around a wide variety of stars, opening a window into the orbital properties of the most common types of planets. This effort will directly contribute to understanding the formation and evolution of planetary systems, a key objective of the National Academy of Sciences' Exoplanet Science Strategies report.Comment: Submitted to the Astro2020 call for science white papers. 7 pages, 2 figure

The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.Comment: 16 page

Inclusion of rapeseed and pumpkin seed cakes in diets for Murciano-Granadina goats alters the fatty acid profile of milk

The objective of this research was to assess the effects of including oil-rich feedstuffs in diets for lactating goats on the fatty acid (FA) profile of their milk. Thirty-six Murciano-Granadina goats were randomly assigned to three treatment groups, namely a control diet (CTRL), a diet based on whole rapeseed (RS), and a diet based on pumpkin seed cake (PSC). The diets were composed of 1 kg hay (70 % Italian ryegrass, 30% alfalfa) and 1.24 kg concentrate, and were formulated to be isoenergetic and isonitrogenous. Milk yield and its contents of protein, fat and lactose did not differ significantly among the groups. However, including oil-rich feeds in the diet altered the fatty acid profile of the milk significantly, decreasing its saturated fatty acid (SFA) content and increasing its content of unsaturated fatty acids (UFAs). Effects on polyunsaturated fatty acids (PUFAs), conjugated linoleic acid (CLA), and the n-6 to n-3 ratio depended on the source of dietary lipids. The PSC augmented diet increased the relative amount of PUFAs and fatty acid methyl esters (FAME) in milk (+25 %) significantly In comparison with CTRL, whereas the RS diet produced a limited and statistically insignificant increase (+7.5%). The concentration of CLA was higher in milk from does fed the PSC diet, whereas the n-6 to n-3 ratio was lower in milk from does fed RS. These preliminary results form the basis for developing premium dairy products that are enriched in fatty acids that are more favourable for human health

Generating indicative-informative summaries with SumUM

We present and evaluate SumUM, a text summarization system that takes a raw technical text as input and produces an indicative informative summary. The indicative part of the summary identifies the topics of the document, and the informative part elaborates on some of these topics according to the reader's interest. SumUM motivates the topics, describes entities, and defines concepts. It is a first step for exploring the issue of dynamic summarization. This is accomplished through a process of shallow syntactic and semantic analysis, concept identification, and text regeneration. Our method was developed through the study of a corpus of abstracts written by professional abstractors. Relying on human judgment, we have evaluated indicativeness, informativeness, and text acceptability of the automatic summaries. The results thus far indicate good performance when compared with other summarization technologies

Abel-type inequalities, complex numbers and Gauss-Pólya type integral inequalities

We obtain inequalities of Abel type but for nondecreasing sequences rather than the usual nonincreasing sequences. Striking complex analogues are presented. The inequalities on the real domain are used to derive new integral inequalities related to those of Gauss-Pólya type

Coherence properties of light propagated through a scattering medium

Partially-coherent, quasi-monochromatic optical fields are fully described by their Mutual Optical Intensity (MOI) or the phase-space equivalent, the Generalised Radiance (GR). This paper reports on the application of a propagation-based phase-space tomographic technique for determining both the MOI and the GR of wavefields. This method is applied to the reconstruction of the MOI and the GR of an optical wavefield propagated through a suspension of \~10micrometre diameter polystyrene spheres.Comment: Photonics 2004, 7th International conference on optoelectronics, fibre optics and photonics, Kochi, Indi