BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Ä¢¹½ÊÓÆµ//NONSGML v1.0//EN NAME:PhD defence D. Sclosa METHOD:PUBLISH BEGIN:VEVENT DTSTART:20250219T134500 DTEND:20250219T151500 DTSTAMP:20250219T134500 UID:2025/phd-defence-d-sclosa@8F96275E-9F55-4B3F-A143-836282E12573 CREATED:20250508T000027 LOCATION:(1st floor) Auditorium, Main building De Boelelaan 1105 1081 HV Amsterdam SUMMARY:PhD defence D. Sclosa X-ALT-DESC;FMTTYPE=text/html:

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Dynamical Systems on Gr aphs

Surprising patterns in networks revealed

Dynamical systems on a graph
A group of people exchanging op inions. An artificial neural network making predictions. A virus spre ading through a population. A server distributing tasks across multip le computers. A network evolving randomly with connections switching on and off. Each of these phenomena represents a dynamical system on a graph: a mathematical structure that illustrates the interconnectio ns between different points. Sclosa focused his research on these dif ferent types of networks, such as social networks, artificial neural networks, electricity networks, and even viruses spreading through a population.

Influence of network structure on dyn amics
It turns out that the structure of a network has a major influence on how information, opinions or even electricit y spread. For example, social networks with many recurring connection s â€“ loops â€“ ensure that information frequently returns to its sta rting point. This ensures that multiple opinions can coexist stably, making the network more democratic. For example, imagine a group of p eople standing in a line, where each person only speaks to their imme diate neighbours. The opinion models suggest that after a while, a co nsensus is reached among them, for example that everyone becomes poli tically moderate. In contrast, for a group of people arranged in a ci rcle, a different stable configuration can emerge, with a spectrum of different opinions coexisting. For example, from far left to far rig ht, and looping back again.

Practical appl ications
The findings of this study are not limited to social networks. As the findings are mathematical theorems about general networks, they can be applied to a wide range of systems. Whe ther it concerns a neural network, an electricity grid or a server di stributing tasks across computers, if the network meets the study's h ypotheses, its dynamics can be predicted. For instance, network analy sis can determine which connections should be reinforced or severed i n a power grid to prevent blackouts. Similarly, it can identify which roads should be widened or closed to improve traffic flow.

Theoretical and computer-based methods
T he research was largely conducted using theoretical mathematical meth ods. However, in one specific case the predicted dynamics turned out to be so surprising that a practical test was needed. Python code was used to simulate a network where an infinite number of stable equili bria were possible. This illustrates how mathematics and computer sci ence can go hand in hand to explain complex phenomena.

M ore information on the

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Surprising patterns in networks revealed

T he shape of a network has an unexpected but predictable effect on its dynamics, mathematician Davide Sclosa shows in new research. This pr ovides new insights into how networks function and could contribute t o a better understanding of social dynamics, information distribution and even technological infrastructures. Dynamical syst ems on a graph
A group of people exchanging opinion s. An artificial neural network making predictions. A virus spreading through a population. A server distributing tasks across multiple co mputers. A network evolving randomly with connections switching on an d off. Each of these phenomena represents a dynamical system on a gra ph: a mathematical structure that illustrates the interconnections be tween different points. Sclosa focused his research on these differen t types of networks, such as social networks, artificial neural netwo rks, electricity networks, and even viruses spreading through a popul ation. Influence of network structure on dynamics
It turns out that the structure of a network has a major influence on how information, opinions or even electricity spread. F or example, social networks with many recurring connections â€“ loops â€“ ensure that information frequently returns to its starting point . This ensures that multiple opinions can coexist stably, making the network more democratic. For example, imagine a group of people stand ing in a line, where each person only speaks to their immediate neigh bours. The opinion models suggest that after a while, a consensus is reached among them, for example that everyone becomes politically mod erate. In contrast, for a group of people arranged in a circle, a dif ferent stable configuration can emerge, with a spectrum of different opinions coexisting. For example, from far left to far right, and loo ping back again. Practical applications
The findings of this study are not limited to social networ ks. As the findings are mathematical theorems about general networks, they can be applied to a wide range of systems. Whether it concerns a neural network, an electricity grid or a server distributing tasks across computers, if the network meets the study's hypotheses, its dy namics can be predicted. For instance, network analysis can determine which connections should be reinforced or severed in a power grid to prevent blackouts. Similarly, it can identify which roads should be widened or closed to improve traffic flow. Theoretical and computer-based methods
The research was largely conducted using theoretical mathematical methods. However, in one sp ecific case the predicted dynamics turned out to be so surprising tha t a practical test was needed. Python code was used to simulate a net work where an infinite number of stable equilibria were possible. Thi s illustrates how mathematics and computer science can go hand in han d to explain complex phenomena. More information on the th esis Dynamical Systems on Graphs END:VEVENT END:VCALENDAR