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On the Separability of Functions and Games

Abstract

We study the notion of (additive) separability of a function of several variables with respect to a hypergraph (H-graph). We prove the existence of a unique minimal H-graph with respect to which a function is separable and show that the corresponding minimal decomposition of the function can be obtained through a recursive algorithm. We then focus on (strategic form) games and propose a concept of separability for a game with respect to a forward directed hypergraph (FDH-graph). This notion refines and generalizes that of the graphical game and is invariant with respect to strategic equivalence. We show that every game is separable with respect to a minimal FDH-graph. Moreover, for exact potential games, such minimal FDH-graph reduces to the minimal H-graph of the potential function. Our results imply and refine known results on graphical potential games and yield a new proof of the celebrated Hammersely-Clifford theorem on Markov random fields.

article Article

date_range 2024

language English

link Link of the paper

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Arditti Laura

Como Giacomo

Fagnani Fabio

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Hammersley-Clifford theorem

hypergraphical games

network games

potential games

separable functions

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Assessment of reinforced concrete building damages following the Kahramanmaraş earthquakes in Malatya, Turkey (February 6, 2023)

Abstract

Earthquakes of magnitude Mw = 7.7 and Mw = 7.6 hit the city of Kahramanmaraş (Turkey) on 6 February 2023. These earthquakes caused serious damage in 11 provinces in Turkey resulting in over 50,000 deaths and huge economic losses with the collapse of thousands of buildings. Two consecutive devastating earthquakes have severely damaged the reinforced concrete building stock located in Malatya. There are many reasons reinforced concrete structures suffer damage under the influence of seismic loads. These reasons can be listed as material and section properties that do not comply with earthquake codes, workmanship defects, ground parameters that are not considered and design errors, as seen in field investigations after earthquakes in Turkey in the past. In this research, a field study was conducted on reinforced concrete buildings damaged after the earthquakes in Malatya province. The causes of structural damages in reinforced concrete buildings between 6–26 years of age were assessed in terms of design and material defects. The structural damages were mainly caused due to insufficient stirrups in structural members, short column, strong beam–weak column, failures of infill walls, soft story type collapse, poor concrete quality, and reinforcement corrosion. In addition to the field investigation, the spectrum relationships created using raw acceleration data obtained from DEMP (Disaster and Emergency Management Presidency) stations in Malatya province were compared with the design response spectra.

article Article

date_range 2024

language English

link Link of the paper

Collapsed buildings

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