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## Dual network embedding for representing research interests in the link prediction problem on co-authorship networks

We present a study on co-authorship network representation based on network embedding together with additional information on topic modeling of research papers and new edge embedding operator. We use the link prediction (LP) model for constructing a recommender system for searching collaborators with similar research interests. Extracting topics for each paper, we construct keywords co-occurrence network and use its embedding for further generalizing author attributes. Standard graph feature engineering and network embedding methods were combined for constructing co-author recommender system formulated as LP problem and prediction of future graph structure. We evaluate our survey on the dataset containing temporal information on National Research University Higher School of Economics over 25 years of research articles indexed in Russian Science Citation Index and Scopus. Our model of network representation shows better performance for stated binary classification tasks on several co-authorship networks.

In this paper we show that for a given co-authorship network we could construct a recommender system for searching collaborators with similar research interests defined via keywords and topic modelling. We suggest new link embedding method and evaluate our model on National Research University Higher School of Economics (NRU HSE) co-authorship network.

The problem of link prediction gathered a lot of attention in the last few years, arising in dierent applications ranging from recommendation systems to social networks. In this paper, we will describe the most popular similarity indices, compare their performance in their ability to show links with the highest probability of being removed from initial network and describe the approach that allows to use them to predict missing links using supervised machine learning. We will show the accuracy of prediction of this method on examples of real networks.

Nowadays, increased attention is drawn towards Network Representation Learning, a technique that maps nodes of a network into vectors of a low-dimensional embedding space. Thus constructed graph embedding aims to preserve nodes similarity and other specific network properties. The embedding vectors can later be used for downstream machine learning problems, such as node classification, link prediction and graph visualization. Naturally, some networks have text information associated with them. For instance, in a citation network, each node is a scientific paper associated with its abstract or title; in a social network, all users might be viewed as nodes of a network and posts of each user as textual attributes. This work studies how combining existing methods of text and graph embeddings can increase accuracy on the downstream tasks and propose modifications to popular architectures to better capture textual information in graph embedding and fusion frameworks.

Dealing with relational data always required significant computational resources, domain expertise and task-dependent feature engineering in order to incorporate structural information into predictive model. Nowadays, a family of automated graph feature engineering techniques have been proposed in different streams of literature. So-called graph embeddings provide a powerful tool to construct vectorized feature spaces for graphs and their components, such as nodes, edges and subgraphs under preserving inner graph properties. Using the constructed feature spaces, many machine learning problems on graphs can be solved via standard frameworks suitable for vectorized feature representation.

Our survey aims to describe the core concepts of graph embeddings, and provide several taxonomies for their description. First, we start with methodological approach, and extract three types of graph embedding models based on matrix factorization, random-walks and deep learning approaches. Next, we describe how different types of networks impact the ability to of models to incorporate structural and attributed data into a unified embedding. Going further, we perform a thorough evaluation of graph embedding applications to machine learning problems on graphs, among which are node classification, link prediction, clustering, visualization, compression, and a family of the whole graph embedding algorithms suitable for graph classification, similarity and alignment problems. Finally, we overview the existing applications of graph embeddings to computer science domains, formulate open problems and provide experiment results, explaining how different embedding and graph properties are connected to the four classic machine learning problems on graphs, such as node classification, link prediction, clustering and graph visualization.

As a result, our survey covers a new rapidly growing field of network feature engineering, presents an in-depth analysis of models based on network types, and overviews a wide range of applications to machine learning problems on graphs.

In this paper, we study network feature engineering for the problem of future co-author recommendation, also called collaborator recommender system. We present a system, which uses authors' research interests and existing collaboration information to predict missing and most probable in the future links in the co-authorship network. The recommender system is stated as a link prediction problem for the current network and for new edges that appear next year. From machine learning point of view, both problems are treated as binary classification. We evaluate our research on our University researchers co-authorship network, while also mentioning results on sub-network of publications indexed in Scopus. Our approach has high accuracy and provides scalable solution for any significantly large co-authorship network.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.

For a class of optimal control problems and Hamiltonian systems generated by these problems in the space *l *2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space *l *2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.

The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.