M. M. Postnikov: his life, work and legacy
Machine calculations in Weyl groups.
MacMahon's theorem for a set of permutations with given descent indices and right-maximal records.
Maintaining the Minimal Distance of a Point Set in Poly-logarithmic Time.
Majority multiplicative ordered weighting geometric operators and their use in the aggregation of multiplicative preference relations.
In this paper, we introduced the majority multiplicative ordered weighted geometric (MM-OWG) operator and its properties. This is a general type of the aggregate dependent weights which we have applied in geometric environment. The MM-OWG operator is based on the OWG operators and on the majority operators. We provide the MM-OWG operators to aggregate in a multiplicative environment, i.e. when it's necessary to aggregate information given on a ratio scale. Therefore, it allows us to incorporate...
Man and computer
Manifold indexed fractional fields
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
Manifold indexed fractional fields∗
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
Marches sur les arbres homogènes suivant une suite substitutive
Ce travail consiste à étudier les comportements des marches sur les arbres homogènes suivant la suite engendrée par une substitution. Dans la première partie, on étudie d’abord les marches sans orientation sur et on détermine complètement, d’après les propriétés combinatoires de la substitution, les conditions assurant que les marches sont bornées, récurrentes ou transientes. Comme corollaire, on obtient le comportement asymptotique des sommes partielles des coefficients de la suite substitutive....
Marginalization in models generated by compositional expressions
In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.
Marginalization in multidimensional compositional models
Efficient computational algorithms are what made graphical Markov models so popular and successful. Similar algorithms can also be developed for computation with compositional models, which form an alternative to graphical Markov models. In this paper we present a theoretical basis as well as a scheme of an algorithm enabling computation of marginals for multidimensional distributions represented in the form of compositional models.
Marginalization like a projection.
This paper studies the problem of marginalizing convex polytopes of probabilities represented by a set of constraints. This marginalization is obtained as a special case of projection on a specific subspace. An algorithm that projects a convex polytope on any subspace has been built and the expression of the subspace, where the projection must be made for obtaining the marginalization, has been calculated.
Markov chain comparison.
Markov Chains Connected to the Process of Generation of the Words by a Generative System
Matematický popis přirozených jazyků
Mathematical Communication and Representation in a Virtual Learning Environment
Abstract. At an exclusively online university such as the UOC the necessity for communicating mathematics in the web is pressing. In an environment that does not allow for face to face communication, things implicitly communicated when using a blackboard, such as the canonical verbalization or handwriting of formulae, are lost and become a big obstacle. Also, the editorial process for the creation of learning/teaching resources is suited for a generalist approach and, consequently, needs such as...
Mathematical description of program diagram
Mathematical Document Classification via Symbol Frequency Analysis
Earlier work has examined the frequency of symbol and expression use in mathematical documents for various purposes including mathematical handwriting recognition and forming the most natural output from computer algebra systems. This work has found, unsurprisingly, that the particulars of symbol and expression vary from area to area and, in particular, between different top-level subjects of the 2000 Mathematical Subject Classification. If the area of mathematics is known in advance, then an area-specific...
Mathematical Formulae Recognition
We present a summary of our work in progress related to mathematical formulae recognition. Our approach is based on the structural construction paradigm and two-dimensional grammars. It is a general framework and can be successfully used in the analysis of images containing objects exhibiting rich structural relations. In contrast to most of all other known approaches, the method does not treat symbols segmentation and structural analysis as two separate processes. This allows the system to solve...
Mathematical Formulae Recognition and Logical Structure Analysis of Mathematical Papers
In most cases the current on-line journals in mathematics are supplied in the form of PDF with print images of papers in the front and OCR’ed hidden texts behind to provide with search facilily using key words. The embedded hidden texts usually does not include good information about mathematical formulae in the papers. We can say that, for the future development of DML, it is desirable to include, in the digitised journals, more structured information of the content of mathematical papers, e.g....