Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Bootstrap Percolation and Diﬀusion in Random Graphs with Given Vertex Degrees...
Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài:Coloring the edges of a random graph without a monochromatic giant component...
The most common way in which probabilities are associated with combinatorial
optimization problems is to consider that the data of the problem are deterministic (always
present) and randomness carries over the relation between these data (for example,
randomness on the existence of an edge linking two vertices in the framework of
a random graph theory problem ([BOL 85]) or randomness on the fact that an element
is included to a set or not, when dealing with optimization problems on set-systems or,
even, randomness on the execution time of a task in scheduling problems).
Random matrices are widely and successfully used in physics for almost
60-70 years, beginning with the works of Wigner and Dyson. Initially proposed
to describe statistics of excited levels in complex nuclei, the Random
Matrix Theory has grown far beyond nuclear physics, and also far beyond just
level statistics. It is constantly developing into new areas of physics and mathematics,
and now constitutes a part of the general culture and curriculum of a
Most approaches to topic modeling assume an independence between documents that is frequently violated. We present an topic model that makes use of one or more user-speciﬁed graphs describing relationships between documents. These graph are encoded in the form of a Markov random ﬁeld over topics and serve to encourage related documents to have similar topic structures. Experiments on show upwards of a 10% improvement in modeling performance. of the form of the distance metric used to specify the edge potentials. ...
This interactive presentation describes LexNet, a graphical environment for graph-based NLP developed at the University of Michigan. LexNet includes LexRank (for text summarization), biased LexRank (for passage retrieval), and TUMBL (for binary classiﬁcation). All tools in the collection are based on random walks on lexical graphs, that is graphs where different NLP objects (e.g., sentences or phrases) are represented as nodes linked by edges proportional to the lexical similarity between the two nodes.
We consider the problem of answering complex questions that require inferencing and synthesizing information from multiple documents and can be seen as a kind of topicoriented, informative multi-document summarization. The stochastic, graph-based method for computing the relative importance of textual units (i.e. sentences) is very successful in generic summarization.