### Book chapter

## Differences in Structural Connectomes between Typically Developing and Autism Groups

We study dierences in structural connectomes between typically developing and autism spectrum disorders individuals with machine learning techniques using connection weights and network metrics as features. We build linear SVM classier with accuracy score 0:64 and report 16 features (seven connection weights and nine network node centralities) best distinguishing these two groups.

### In book

We prove existence and uniqueness of a solution to the problem of minimizing the logarithmic energy of vector potentials associated to a d-tuple of positive measures supported on closed subsets of the complex plane. The assumptions we make on the interaction matrix are weaker than the usual ones, and we also let the masses of the measures vary in a compact subset of ℝ+ d. The solution is characterized in terms of variational inequalities. Finally, we review a few examples taken from the recent literature that are related to our results.

In this paper, we tackle a problem of predicting phenotypes from structural connectomes. We propose that normalized Laplacian spectra can capture structural properties of brain networks, and hence graph spectral distributions are useful for a task of connectome-based classication. We introduce a kernel that is based on earth mover's distance (EMD) between spectral distributions of brain networks. We access performance of an SVM classier with the proposed kernel for a task of classication of autism spectrum disorder versus typical development based on a publicly available dataset. Classication quality (area under the ROC-curve) obtained with the EMD-based kernel on spectral distributions is 0.71, which is higher than that based on simpler graph embedding methods.

This article introduces a new measure of linguistic complexity which is based on the dual nature of the linguistic sign. Complexity is analyzed as consisting of three components, namely the conceptual complexity (complexity of the signified), the formal complexity (complexity of the signifier) and the form-meaning correspondence complexity. I describe a way of plotting the form-meaning relationship on a graph with two tiers (the form tier and the meaning tier) and apply a complexity measure from graph theory (average vertex degree) to assess the complexity of such graphs. The proposed method is illustrated by estimating the complexity of full noun phrases (determiner + adjective + noun) in English, Swedish, and German. I also mention the limitations and the problems which might arise when using this method.

The collection represents proceedings of the nineth international conference "Discrete Models in Control Systems Theory" that is held by Lomonosov Moscow State Uneversity and is dedicated in 90th anniversary of Sergey Vsevolodovich Yablonsky's birth. The conference subject are includes: discrete functional systems; discrete functions properties; control systems synthesis, complexity, reliability, and diagnostics; automata; graph theory; combinatorics; coding theory; mathematical methods of information security; theory of pattern recognition; mathematical theory of intellegence systems; applied mathematical logic. The conference is sponsored by Russian Foundation for Basic Research (project N 15-01-20193-г).

The application opportunities to the supply chain management of such scientific branches as the Graph theory, Social Network Analysis are shown. Using simulations, it is shown how supply chain characteristics can influence of the results of the product on the market.

Proceedings include extended abstracts of reports presented at the III International Conference on Optimization Methods and Applications “Optimization and application” (OPTIMA-2012) held in Costa da Caparica, Portugal, September 23—30, 2012.