Related papers: Nature's Greatest Puzzles
In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.
We present a comprehensive evaluation of Large Language Models (LLMs) on Computer Science (CS) Data Structure examination questions. Our work introduces a new benchmark dataset comprising exam questions from Tel Aviv University (TAU),…
This article contains a collection of problems contributed during the course of the conference.
Career opportunities are often a matter of chance, but also of willingness to cross interdisciplinary boundaries.
1. The birth of network science. 2. What are random networks? 3. Adjacency matrix. 4. Degree distribution. 5. What are simple networks? Classical random graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated…
This paper contributes to the study of CPAC learnability -- a computable version of PAC learning -- by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class…
The evolving landscape of interinstitutional collaborative research across 15 natural science disciplines is explored using the open data sourced from OpenAlex. This extensive exploration spans the years from 1971 to 2020, facilitating a…
Talk at the 25th Johns Hopkins Workshop "2001: A Relativistic Spacetime Odyssey", Firenze September 2001.
I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…
Technology is increasingly used in Nature Reserves and National Parks around the world to support conservation efforts. Endangered species, such as the Eurasian Lynx (Lynx lynx), are monitored by a network of automatic photo traps. Yet,…
This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…
Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010.
A pedagogical account of entropy and its history.
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and…
These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.
Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is…
One of humanity's earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus exhibit repeated spirals, which appear with an…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…