The fundamental connection between stochastic differential equations (SDEs) and partial differential equations (PDEs) has found numerous applications in diverse fields. We explore a similar link between stochastic calculus and combinatorial PDEs on graphs with Hodge structure, by showing that...

We study the number of isolated nodes in a soft random geometric graph whose vertices constitute a Poisson process on the torus of length L (the line segment [0 ,L ] with periodic boundary conditions), and where an edge is present between two nodes with a probability which depends on the...

Over the recent years, the study of Sliding Visibility Graph (SVG) algorithm has attracted great interests. The SVG algorithm is an effective method for quickly mapping time series to complex networks. In this paper, we propose the Sliding Horizontal Visibility Graph (SHVG) algorithm, a...

Sustainable energy grids and networks are converging. In recent decades, cost, sustainability, and digitization drivers have caused engineering systems to evolve into systems-of-systems that deliver multiple services across multiple application domains. These engineering systems include...

Load forecasting, especially short-term load forecasting, is of great significance to the safe operation of power grids and power system optimization. Historical data is commonly applied in the most of existing methods of load forecasting to predict the future data in one time step, which is...

Lehman Brothers' failure in 2008 demonstrated the importance of understanding interconnectedness in interbank networks. The interbank market plays a significant role in facilitating market liquidity and providing short-term funding for each other to smooth liquidity shortages. Knowing the...

It is impossible to analyze an asset taken in isolation, without taking into account the wider picture of the market. This fact is behind the extensive use of copulas or vector autoregressive models in finance, which allow to model dependencies between assets. In this paper, we look at the...

Time series forecasting of meteorological variables, such as the hourly air temperature, has multiple benefits for industry, agriculture, and the environment. Due to the high accuracy required for the associated short-term predictions, traditional methods cannot satisfy the requirements and...