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Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random…

We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…

Many real-world networks known as attributed networks contain two types of information: topology information and node attributes. It is a challenging task on how to use these two types of information to explore structural regularities. In…

A growing set of applications consider the process of network formation by using subgraphs as a tool for generating the network topology. One of the pressing research challenges is thus to be able to use these subgraphs to understand the…

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…

We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk…

Using a perturbative expansion for weak synaptic weights and weak sources of randomness, we calculate the correlation structure of neural networks with generic connectivity matrices. In detail, the perturbative parameters are the mean and…

We give two combinatorial proofs of an elegant product formula for the number of spanning trees of the $n$-dimensional hypercube. The first proof is based on the assertion that if one chooses a uniformly random rooted spanning tree of the…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…

While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…

We investigate regression for variable length sequential data containing missing samples and introduce a novel tree architecture based on the Long Short-Term Memory (LSTM) networks. In our architecture, we employ a variable number of LSTM…

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…

Given an ensemble of randomized regression trees, it is possible to restructure them as a collection of multilayered neural networks with particular connection weights. Following this principle, we reformulate the random forest method of…

We analyze the mixing properties of growing networks and find that, in some cases, the assortativity patterns are reversed once links' direction is considered: the disassortative behavior observed in such networks is a spurious effect, and…

In the paper, we present an incremental approach in the construction of scale free networks with hidden variables. The work arises from the necessity to generate that type of networks with a given number of links instead of obtaining a…

Most deep neural networks are trained under fixed network architectures and require retraining when the architecture changes. If expanding the network's size is needed, it is necessary to retrain from scratch, which is expensive. To avoid…