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

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

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

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

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

Astro2020 Science White Paper: Toward Finding Earth 2.0: Masses and Orbits of Small Planets with Extreme Radial Velocity Precision

Having discovered that Earth-sized planets are common, we are now embarking on a journey to determine if Earth-like planets are also common. Finding Earth-like planets is one of the most compelling endeavors of the 21st century - leading us toward finally answering the question: Are we alone? To achieve this forward-looking goal, we must determine the masses of the planets; the sizes of the planets, by themselves, are not sufficient for the determination of the bulk and atmospheric compositions. Masses, coupled with the radii, are crucial constraints on the bulk composition and interior structure of the planets and the composition of their atmospheres, including the search for biosignatures. Precision radial velocity is the most viable technique for providing essential mass and orbit information for spectroscopy of other Earths. The development of high quality precision radial velocity instruments coupled to the building of the large telescope facilities like TMT and GMT or space-based platforms like EarthFinder can enable very high spectral resolution observations with extremely precise radial velocities on minute timescales to allow for the modeling and removal of radial velocity jitter. Over the next decade, the legacy of exoplanet astrophysics can be cemented firmly as part of humankind's quest in finding the next Earth - but only if we can measure the masses and orbits of Earth-sized planets in habitable zone orbits around Sun-like stars.Comment: Science White Paper Submitted to the Astro2020 Decadal Survey (35 co-signers in addition to co-authors

Reduced-symmetry two-dimensional solitons in photonic lattices

We demonstrate theoretically and experimentally a novel type of localized beams supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.Comment: 5 pages, 4 figure