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In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
The current status of BESII is reported. Some published results based on the data collected by BESI and some new preliminary results based on the BESII data are reviewed in this paper.
In this paper, we discuss a potential agenda for future work in the theory of random sets and belief functions, touching upon a number of focal issues: the development of a fully-fledged theory of statistical reasoning with random sets,…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
Deep Learning is one of the newest trends in Machine Learning and Artificial Intelligence research. It is also one of the most popular scientific research trends now-a-days. Deep learning methods have brought revolutionary advances in…
We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…
This work provides a starting point for researchers interested in gaining a deeper understanding of the big picture of artificial intelligence (AI). To this end, a narrative is conveyed that allows the reader to develop an objective view on…
Several open problems in algebraic logic are solved.
With the explosive growth of textual information, summarization systems have become increasingly important. This work aims to concisely indicate the current state of the art in abstractive text summarization. As part of this, we outline the…
Participants in recent discussions of AI-related issues ranging from intelligence explosion to technological unemployment have made diverse claims about the nature, pace, and drivers of progress in AI. However, these theories are rarely…
We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are…
There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given…
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
Track and field world records have risen and fallen throughout the history of the sport. A recent rash of record-breaking performances has prompted the question: "How good can we get?". This article offers a review of several attempts to…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
Generating value from data requires the ability to find, access and make sense of datasets. There are many efforts underway to encourage data sharing and reuse, from scientific publishers asking authors to submit data alongside manuscripts…
We examine properties of achievement sets of series in $\mathbb{R}^2$. We show several examples of unusual sets of subsums on the plane. We prove that we can obtain any set of P-sums as a cut of an achievement set in $\mathbb{R}^2.$ We…
Contemporary debates on "open science" mostly focus on the pub- lic accessibility of the products of scientific and academic work. In contrast, this paper presents arguments for "opening" the ongoing work of science. That is, this paper is…
The way science is currently practiced shows conclusions but hides how they were reached. Researchers work privately, polish their results, publish a finished paper, and defend it. Errors are punished by retraction rather than corrected by…