Related papers: Nature's Greatest Puzzles
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…
In 2007 an international conference engaged a reflection on the present conditions for sciences and scientific practice, to initiate a dialogue between science, philosophy, epistemology and sociology. Starting from many examples taken from…
Rich clusters of galaxies are the most massive virialized systems known. Even though they contain only a small fraction of all galaxies, rich clusters provide a powerful tool for the study of galaxy formation, dark matter, large-scale…
In May 2015, a conference entitled "Groups, Geometry, and 3-manifolds" was held at the University of California, Berkeley. The organizers asked participants to suggest problems and open questions, related in some way to the subject of the…
The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop on Convex and Abstract Polytopes at the Banff International…
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry"…
Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global…
In this short report the first attempt of a new approach to the still mysterious phenomenon of the life, and its peak, the human being, is presented from the view point of the natural sciences, i.e. of the physics in the broad sense of the…
Not only did Turing help found one of the most exciting areas of modern science (computer science), but it may be that his contribution to our understanding of our physical reality is greater than we had hitherto supposed. Here I explore…
Nature's many varied complex systems (including galaxies, stars, planets, life, and society) are islands of order within the increasingly disordered universe. All organized systems are subject to physical, biological or cultural evolution,…
Origins of contemporary $B$-physics. Mesons with beauty and charm. Stable tetraquarks? Flavor and the problem of identity. Top matters. Electroweak symmetry breaking and the Higgs sector. Future instruments.
Of all the issues discussed at {\em Alife VII: Looking Forward, Looking Backward}, the issue of whether it was possible to create an artificial life system that exhibits {\em open-ended evolution} of novelty is by far the biggest. Of the 14…
A survey article for AMS Summer Institute at Seattle in 2005.
We provide a brief summary of the history of galaxy structure studies. We also introduce several large-scale redshift surveys and summarize the most commonly used methods to identify the groups and clusters of galaxies. We present several…
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
The main purpose of these lectures is to give a pedagogical overview on the possibility to classify and relate off-shell linear supermultiplets in the context of supersymmetric mechanics. A special emphasis is given to a recent graphical…
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
This introductory paper is structured in the form of an "interview", where the author answers the following questions: Why did you begin working with complex systems? How would you define complexity? What is your favourite aspect/concept of…
The problems concerning a possible discovery of the mini block holes at earthly accelerators are discussed.