相关论文: A new threshold model based on tropical mathematic…

Models for cross-sectional network data have become increasingly well-developed in recent decades, and are widely used. This has led to a growing interest in the connection between such cross-sectional models and the behavioral processes…

This paper introduces a new method to train recurrent neural networks using dynamical trajectory-based optimization. The optimization method utilizes a projected gradient system (PGS) and a quotient gradient system (QGS) to determine the…

We prove that the Transformer self-attention mechanism in the high-confidence regime ($\beta \to \infty$, where $\beta$ is an inverse temperature) operates in the tropical semiring (max-plus algebra). In particular, we show that taking the…

Structural balance theory is an established framework for studying social relationships of friendship and enmity. These relationships are modeled by a signed network whose energy potential measures the level of imbalance, while stochastic…

Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…

Temporal higher-order networks, where each hyperlink involving a group of nodes are activated or deactivated over time, are recently used to represent complex systems such as social contacts, interactions or collaborations that occur at…

Many networked systems such as electric networks, the brain, and social networks of opinion dynamics are known to obey conservation laws. Examples of this phenomenon include the Kirchoff laws in electric networks and opinion consensus in…

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix…

In this work we consider \emph{temporal networks}, i.e. networks defined by a \emph{labeling} $\lambda$ assigning to each edge of an \emph{underlying graph} $G$ a set of \emph{discrete} time-labels. The labels of an edge, which are natural…

We present a continuous threshold model (CTM) of cascade dynamics for a network of agents with real-valued activity levels that change continuously in time. The model generalizes the linear threshold model (LTM) from the literature, where…

Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks…

Revealing how a biological network is organized to realize its function is one of the main topics in systems biology. The functional backbone network, defined as the primary structure of the biological network, is of great importance in…

Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…

We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize social networks for which adoption of a product by the whole network is…

Motivated by extreme value theory, max-linear Bayesian networks have been recently introduced and studied as an alternative to linear structural equation models. However, for max-linear systems the classical independence results for…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…

Recurrent-attention hybrids aim to combine the efficiency of recurrence with the expressivity of attention, but existing approaches typically apply attention uniformly across all positions, even when the recurrent state alone is sufficient…

Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new…