Related papers: A small collection of open problems
After the recent experimental results on neutrino oscillations, some shape starts to emerge from the puzzle. However, the situation is still far from being clarified. First of all, accommodating all experimental results in a single and…
100 prisoners and a light bulb is a long standing mathematical puzzle. The problem was studied mostly in 2002 [5], 2003 [1], and 2004 [3]. Solutions in published articles had average number of visits above 3850, but best solutions on forums…
Scientists pursue collective knowledge, but they also seek personal recognition from their peers. When scientists decide whether or not to work on a big new problem, they weigh the potential rewards of a major discovery against the costs of…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
The origins of life stands among the great open scientific questions of our time. While a number of proposals exist for possible starting points in the pathway from non-living to living matter, these have so far not achieved states of…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
We present five open problems in quantum gravity which one might reasonably hope to solve in the next decade. Hints appearing in the literature are summarized for each one.
Readability assessment is the task of evaluating the reading difficulty of a given piece of text. Although research on computational approaches to readability assessment is now two decades old, there is not much work on synthesizing this…
The last 30 years have seen the creation of a variety of electronic collaboration tools for science and business. Some of the best-known collaboration tools support text editing (e.g., wikis). Wikipedia's success shows that large-scale…
In a series of papers in the last ten years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations…
The COVID-19 pandemic has posed a unique challenge for the world to find solutions, ranging from vaccines to ICT solutions to slow down the virus spreading. Due to the highly contagious nature of the virus, social distancing is one…
This paper first describes, from a high level viewpoint, the main challenges that had to be solved in order to develop a theory of spin glasses in the last fifty years. It then explains how important inference problems, notably those…
The Linked Data Paradigm is one of the most promising technologies for publishing, sharing, and connecting data on the Web, and offers a new way for data integration and interoperability. However, the proliferation of distributed,…
We know anything because we learn about it, there is anything we ever share about it, but now a lot of media that can represent how it happened as infrastructure of the knowledge sharing. This paper aims to introduce a model for…
In the very large debates on ethics of algorithms, this paper proposes an analysis on human responsibility. On one hand, algorithms are designed by some humans, who bear a part of responsibility in the results and unexpected impacts.…
At the frontier of most areas in science, computer simulations play a central role. The traditional division of natural science into experimental and theoretical investigations is now completely outdated. Instead, theory, simulation, and…
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…
An attempt to seek out and understand emerging trends and some of the challenges we face when dealing with an increasing amount and complexity of entertainment technologies in our homes, particularly in spaces that are both private and…
The multi-answer phenomenon, where a question may have multiple answers scattered in the document, can be well handled by humans but is challenging enough for machine reading comprehension (MRC) systems. Despite recent progress in…