Related papers: Achievement sets -- current results and open probl…
In the paper we develop the method of higher energies. New upper bounds for the additive energies of convex sets, sets A with small |AA| and |A(A+1)| are obtained. We prove new structural results, including higher sumsets, and develop the…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems. This has resulted in an algorithmic toolbox that is by now…
We survey the state of the union-closed sets conjecture.
I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.
Recent machine learning techniques can be modified to produce creative results. Those results did not exist before; it is not a trivial combination of the data which was fed into the machine learning system. The obtained results come in…
The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…
Nuclear theory today aims for a comprehensive theoretical framework that can describe all nuclei. I discuss recent progress in this pursuit and the associated challenges as we move forward.
An achievement set of a series is a set of all its subsums. We study the properties of achievement sets of conditionally convergent series in finite dimensional spaces. The purpose of the paper is to answer some of the open problems…
We present our view of what is necessary to build an engaging open-domain conversational agent: covering the qualities of such an agent, the pieces of the puzzle that have been built so far, and the gaping holes we have not filled yet. We…
The development of IT and WWW provides different teaching strategies, which are chosen by teachers. Students can acquire knowledge through different learning models. The problem based learning is a popular teaching strategy for teachers.…
The present status of Unified Theories is summarized with special emphasis on their possible experimental tests. Outline: i) Unification of couplings; ii) Where can a positive signal come from? iii) HERA anomaly and Unification; iv) Recent…
In this paper, we study some properties of $*-$open and $*-$closed subsets of a space. The collection of all $*-$open subsets of a space $X$ form a topology on $X$ which is denoted by $^{*}O(X)$. We investigate the relations between…
We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and proper chains of solution sets of those. We recall the basic…
This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The main goal of this paper is to investigate relations between topologies obtained by: $\theta$-open sets, $\omega$-open sets, $\theta_\omega$-open sets, local function, and local closure function with ideal of the countable sets. As the…
This paper describes some of the ideas used in the development of our work on small gaps between primes.
With the development of recommender systems (RS), several promising systems have emerged, such as context-aware RS, multi-criteria RS, and group RS. However, the education domain may not benefit from these developments due to missing…