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Several older and more recent results on the boundaries of solvability and unsolvability in tag systems are surveyed. Emphasis will be put on the significance of computer experiments in research on very small tag systems.

Computational Complexity · Computer Science 2009-06-22 Liesbeth De Mol

We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.

Functional Analysis · Mathematics 2020-04-09 Sergey Astashkin , Mario Milman

We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…

Computational Complexity · Computer Science 2011-09-27 Manuel Bodirsky , Jan Kara , Barnaby Martin

This note includes an assessment of the partially overlapping samples t-tests in scenarios where elements of the test are at their extremes, including where only one sample contains independent observations

Methodology · Statistics 2019-06-05 Ben Derrick , Deirdre Toher , Paul White

These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.

Soft Condensed Matter · Physics 2017-09-14 John M. Ball

This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.

Artificial Intelligence · Computer Science 2007-05-23 Pierre Albarede

At present a number of current or proposed experiments are directed towards a search for a `new physics' by detecting variations of fundamental physical constants or violations of certain basic symmetries. Various problems related to the…

Atomic Physics · Physics 2015-05-13 Savely G. Karshenboim

We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational…

Computer Science and Game Theory · Computer Science 2021-12-21 Piotr Faliszewski , Krzysztof Sornat , Stanisław Szufa

We study topological properties of the graph topology.

General Topology · Mathematics 2012-07-09 Lubica Hola

Brief review of concepts and unsolved problems in the theory of matrix models.

High Energy Physics - Theory · Physics 2015-06-26 A. Morozov

The paper offers a mathematical formalization of the Turing test. This formalization makes it possible to establish the conditions under which some Turing machine will pass the Turing test and the conditions under which every Turing machine…

Artificial Intelligence · Computer Science 2010-05-28 Evgeny Chutchev

The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…

Probability · Mathematics 2009-09-03 Sergey Foss

The bin-packing problem continues to remain relevant in numerous application areas. This technical report discusses the empirical performance of different bin-packing heuristics for certain test problems.

Optimization and Control · Mathematics 2021-04-27 Bastian Rieck

An overview and classification of software testing models are done. Recommendations on the choice of models are proposed

Software Engineering · Computer Science 2013-06-11 Alexey Markov

This is an update of my problem list.

Logic · Mathematics 2016-09-06 Arnold W. Miller

This review aims to provide a comprehensive update on the progress made on the Sequential Testing problem (STP) in the last 20 years after the review, [1] was published. Many studies have provided new theoretical results, extensions of the…

Data Structures and Algorithms · Computer Science 2025-11-21 Tonguç Ünlüyurt

Today's QCD problems, prospects and achievements are reviewed.

High Energy Physics - Phenomenology · Physics 2007-05-23 Yu. L. Dokshitzer

There are various approaches to the problem of how one is supposed to conduct a statistical analysis. Different analyses can lead to contradictory conclusions in some problems so this is not a satisfactory state of affairs. It seems that…

Statistics Theory · Mathematics 2019-06-25 Michael Evans

Some inequalities for different types of convexity are established.

Classical Analysis and ODEs · Mathematics 2013-09-27 Merve Avci Ardic

This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.

History and Overview · Mathematics 2021-01-06 Melvyn B. Nathanson