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A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
Most of computer science focuses on automatically solving given computational problems. I focus on automatically inventing or discovering problems in a way inspired by the playful behavior of animals and humans, to train a more and more…
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
I postulate that human or other intelligent agents function or should function as follows. They store all sensory observations as they come - the data is holy. At any time, given some agent's current coding capabilities, part of the data is…
Textbooks in applied mathematics often use graphs to explain the meaning of formulae, even though their benefit is still not fully explored. To test processes underlying this assumed multimedia effect we collected performance scores, eye…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
For many practical applications of ASP, for instance data integration or planning, query answering is important, and therefore query optimization techniques for ASP are of great interest. Magic Sets are one of these techniques, originally…
We discuss some seemingly paradoxical yet valid effects of quantum physics in information processing. Firstly, we argue that the act of ``doing nothing'' on part of an entangled quantum system is a highly non-trivial operation and that it…
Video motion magnification techniques allow us to see small motions previously invisible to the naked eyes, such as those of vibrating airplane wings, or swaying buildings under the influence of the wind. Because the motion is small, the…
Current approaches to video analysis of human motion focus on raw pixels or keypoints as the basic units of reasoning. We posit that adding higher-level motion primitives, which can capture natural coarser units of motion such as backswing…
Dynamic programming is an important optimization technique, but designing efficient dynamic programming algorithms can be difficult for even professional programmers. Thinning, a technique developed for systematically deriving efficient…
It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
In this article, I present recent methods for the numerical simulation of fluid dynamics and the associated computational algorithms. The goal of this article is to explain how to model an incompressible fluid, and how to write a computer…
We formulate Dempster Shafer Belief functions in terms of Propositional Logic using the implicit notion of provability underlying Dempster Shafer Theory. Given a set of propositional clauses, assigning weights to certain propositional…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility.…
In this paper, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method can be applied to real diagonalizable matrices, is provably…
We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…
Existing approaches to learning to prove theorems focus on particular logics and datasets. In this work, we propose Monte-Carlo simulations guided by reinforcement learning that can work in an arbitrarily specified logic, without any human…