Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book
invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy...
In fact, the theory of light interacting with many-electrons systems must adopt a rigorous gauge invariant and Lorentz covariant form to describe both electromagnetic and fermionic degrees of freedom and their interaction simultaneously (1). This chapter aims to describe the theoretical and ...
Evolutionaryalgorithmsfind applications but the theoryalgorithmsis not well developed. 演化算法在工程领域取得了广泛的应用,但是其基础理论尚未完全建立. 互联网 Quantities of comparison experiments showed the effectiveness of above trackingalgorithms. 大量对比实验表明了本文跟踪算法的有效性. ...
Over the past decade, SIM hardware and software have flourished, leading to successful applications in various biological questions. However, unlocking the full potential of SIM system hardware requires the development of advanced reconstruction algorithms. Here, we introduce the basic theory of two SIM...
This leads to the dimension theory introduced by Taylor and Zwicker (1993). Although there has been little interest in m-tier OR-games so far, they are also an interesting type of game to study. First, it is easy to see that every monotonic simple game can be represented by a weighted...
Junge, The Algorithms behind GAIO - Set Oriented Nu- merical Methods for Dynamical Systems. In: B. Fiedler (ed.): Ergodic theory, analysis, and efficient simulation of dynamical systems. Springer (2001).The Algorithms BehindGaio—Set Oriented Numerical Methods for Dynamical Systems - Dellnitz, ...
Computer Science - Information TheoryIn this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such valuations and changing it ...
Each of the algorithms utilizes tools from number theory. The missing details of these algorithms related to the case of large alphabets are provided in the next two sections. In particular, in Section 6 we reduce efficient testing of the proportionality relation to a problem of equality of ...
It was almost the same time when the well-known deep learning technologies started to show great performance in classification and stepped onto the stage of computer vision. Before the explosion of deep learning methods, research works put lots of efforts in designing scale-invariant features (e....