Materials property prediction for limited datasets enabled by feature selection and joint learning with MODNet

In order to make accurate predictions of material properties, current machine-learning approaches generally require large amounts of data, which are often not available in practice. In this work, MODNet, an all-round framework, is presented which relies on a feedforward neural network, the selection of physically meaningful features, and when applicable, joint-learning. Next to being faster in terms of training time, this approach is shown to outperform current graph-network models on small datasets. In particular, the vibrational entropy at 305 K of crystals is predicted with a mean absolute test error of 0.009 meV/K/atom (four times lower than previous studies). Furthermore, joint learning reduces the test error compared to single-target learning and enables the prediction of multiple properties at once, such as temperature functions. Finally, the selection algorithm highlights the most important features and thus helps to understand the underlying physics.

Metric properties of the canonical defining pair for determined graphs

The aim of this paper is to study the representation of deterministic graphs (D-graphs) by sets of words over the vertex labels alphabet and to find metric properties of this representation. Vertex-labeled graphs are widely used in various computational processes modeling in programming, robotics, model checking, etc. In such models graphs playing the role of an information environment of single or several mobile agents. Walks of agents on a graph determines the sequence of vertices labels or words in the alphabet of labels. A vertex-labeled graph is said to be D-graph if all vertices in the neighborhood of every its vertex have different labels. For D-graphs in case when the graph as a whole and the initial vertex (i.e. the vertex from which the agent started walking) are known there exists the one-to-one correspondence between the sequence of vertices visited by the agent and the trajectory of its walks on the graph. In case when the D-graph is not known as a whole, agent walks on it can be arranged in such way that an observer obtains information about the structure of the graph sufficient to solve the problems of graph recognizing, finding optimal path between vertices, comparison between current graph and etalon graph etc. This paper specifies the representation of D-graphs by the defining pair of sets of words (the first describes cycles of the graph and the second -- all its vertices of degree 1). This representation is an analogue of the system of defining relations for everywhere defined automata. The structure of the so-called canonical defining pair, which is minimal in terms of the number of words, is also considered. An algorithm for building such pair is developed and described in detail. For D-graphs with a given number of vertices and edges, the exact number of words in the first component of its canonical defining pair and the minimum and maximum attainable bounds for the the number of words in the second component of this pair are obtained. This representation allows us to use new methods and algorithms to solve the problems of analyzing vertex-labeled graphs.

SkipGNN: predicting molecular interactions with skip-graph networks

Molecular interaction networks are powerful resources for molecular discovery. They are increasingly used with machine learning methods to predict biologically meaningful interactions. While deep learning on graphs has dramatically advanced the prediction prowess, current graph neural network (GNN) methods are mainly optimized for prediction on the basis of direct similarity between interacting nodes. In biological networks, however, similarity between nodes that do not directly interact has proved incredibly useful in the last decade across a variety of interaction networks. Here, we present SkipGNN, a graph neural network approach for the prediction of molecular interactions. SkipGNN predicts molecular interactions by not only aggregating information from direct interactions but also from second-order interactions, which we call skip similarity. In contrast to existing GNNs, SkipGNN receives neural messages from two-hop neighbors as well as immediate neighbors in the interaction network and non-linearly transforms the messages to obtain useful information for prediction. To inject skip similarity into a GNN, we construct a modified version of the original network, called the skip graph. We then develop an iterative fusion scheme that optimizes a GNN using both the skip graph and the original graph. Experiments on four interaction networks, including drug–drug, drug–target, protein–protein, and gene–disease interactions, show that SkipGNN achieves superior and robust performance. Furthermore, we show that unlike popular GNNs, SkipGNN learns biologically meaningful embeddings and performs especially well on noisy, incomplete interaction networks.

The Model of Secure Social Networks Activity Based on Graph Theory

The article deals with social networks parameters that describe individuals within network. The basic idea is based on an assumption that individuals with common characteristics are likely to communicate with each other. This is a kind of epidemical model with the chance of sending some information, as a functions of distance between source and potential destination. The main approach in the article is based on clustering of local characteristics of network. They characterize degree of interaction between the closest neighbors of current graph node. For the most networks if a node A is connected to node B and node B – to node C, then, there is a big chance of the fact, that node A is connected to node C (friends of our friends are also our friends). Depending on the graph structure, between two nodes there are often a few different paths. Distribution of nodes degree is a distribution with “long tail” and is modelled with degree distribution. It means, that in such networks, there are a lot of nodes, that has 1-3 neighbors, but a little of nodes, which has thousands of neighbors. A modelling of parameters (possible quantity of graph edges, clustering coefficient, connection of new node, shortest and average path, residual lifetime of chain, node interactions, average degree of node etc.) of social networks is taken. Calculations are illustrated with graphical materials. Relevant equations are represented.

Transactional Model of Graph Transformations in Computer Aided Design

Different types of graphs have successfully been used to represent different objects in design problems. Graph transformations are often used as a way to generate, update and modify such graphs. Typical use of graph productions assumes that change of a graph is done by applying a single transformation or a sequence of independent productions. Yet, in many real life design tasks the application of a production may depend on the possibility of applying other productions. Moreover the productions required to be applied usually only depend on the current graph so the set of productions cannot be defined apriori. In this paper we present a novel approach, called a transactional model, where a set of productions is dynamically chosen in a way that it is possible to fulfill a common goal.. Only if all of the productions can be applied the whole transaction is carried out. The approach is illustrated with the problem from the domain of architectural design.

PARALLEL MACHINE SCHEDULING WITH A SIMULTANEITY CONSTRAINT AND UNIT-LENGTH JOBS TO MINIMIZE THE MAKESPAN

In this paper, we consider the parallel machine scheduling with a simultaneity constraint and unit-length jobs. The problem can be described as follows. There are given m parallel machines and a graph G, whose vertices represent jobs. Simultaneity constraint means that we can process a vertex job v if and only if there exists at least dG(v) idle machines, where dG(v) is the degree of vertex v in graph G. Once a vertex job is completed, we delete the vertex and its incident edges from the graph. The number of machines that a vertex job needing depends on its degree in current graph. Changes of graph result in changes of vertex degree. Here, we consider a special case that all jobs in the original graph are unit-length. Let pv denote the processing time of vertex job v, we define pv = 0 if d(v) = 0, and pv = 1, otherwise. The objective is to minimize the time by which each vertex job is completed, i.e., the time by which the graph becomes an empty graph. We show that this problem is strongly NP-hard and provide a [Formula: see text]-approximation algorithm.

Online Ramsey Games in Random Graphs

Consider the following one-player game. Starting with the empty graph onnvertices, in every step a new edge is drawn uniformly at random and inserted into the current graph. This edge has to be coloured immediately with one ofravailable colours. The player's goal is to avoid creating a monochromatic copy of some fixed graphFfor as long as possible. We prove a lower bound ofnβ(F,r)on the typical duration of this game, where β(F,r) is a function that is strictly increasing inrand satisfies limr→∞β(F,r) = 2 − 1/m2(F), wheren2−1/m2(F)is the threshold of the corresponding offline colouring problem.