Mathematical Model Drives Demand-Responsive Transport Shift in Barcelona
A CRM-developed mathematical model has enabled Barcelona to replace fixed bus routes with demand-responsive transport (DRT) zones, reducing risk for TMB. By 2024, five routes have been converted, enhancing passenger comfort and lowering environmental impact.
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Estimation of Extreme Earthquakes and Other Natural Disasters
The Complex Systems Group found that natural disasters follow a power-law distribution, meaning extreme events are more frequent than Gaussian models suggest. Their work enables robust probability estimates for disasters, with applications such as assessing earthquake risks in projects like the CASTOR gas platform.
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Enhanced Encoder Resolution through Mathematical Innovation
Researchers at CRM, in partnership with Hohner Automáticos S.L., developed a patented algorithm that improves encoder resolution cost-effectively, strengthening Hohner’s market position and reputation. This innovation supports job creation and boosts sales.
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A mathematical model conceived and computationally implemented by CRM has guided the decision on which areas of Barcelona should replace the local, fixed-bus routes, known as “Bus del Barri,” with a demand-responsive transport (DRT) service. Following exploratory research by the Dynamical Systems group UAB-CRM, a project was commissioned by Transportes Metropolitans de Barcelona (TMB) and carried out with the crucial participation of the Knowledge Transfer Unit. Thanks to the use of a genetic algorithm as the core method for optimizing routes, TMB was able to make a costly decision with significantly reduced risk.
This work has led to the replacement of five local bus routes with fixed stops (lines 118, 135, 128, 120, and 121) with five DRT zones (El Farró-Galvany, Montbau-la Vall d’Hebron, Torre Baró Nord, Torre Baró Sud, and Vallbona) by 2024, through a service called “El Meu Bus.” An additional 15 routes are being considered for such a transformation.
Five thousand passengers have already joined the app that provides access to the service, benefiting from more comfortable travel, reduced waiting times, and a lower average number of kilometres travelled, thereby encouraging greater use of public transport. The optimization of routes also results in decreased environmental impact and lower maintenance costs.
The Complex Systems Group has characterized the statistical distribution that governs various natural disaster-causing phenomena, confirming that their behavior follows a power law. This insight implies “expect the unexpected”: extreme natural catastrophes are more frequent than what a normal (Gaussian) distribution would predict.
This robust statistical approach allows reliable estimation of the likelihood of such events. For instance, the group has calculated that an extreme geomagnetic storm has a 2% chance of occurring in the next decade (down from a previous estimate of 12%), which could trigger a global collapse of electrical systems. Rigorous data analysis makes it possible to estimate the probabilities of earthquakes and other potentially hazardous events, although practical earthquake prediction remains beyond reach due to the lack of tools to accurately forecast when they might occur in a specific region.
However, robust probabilistic laws offer a promising alternative. One notable application of this approach was a study, involving a group member as a collaborator, used in the scientific report that ultimately closed the CASTOR submarine gas injection project off the Castellón-Tarragona coast. It was estimated that the platform’s operation would lead to a high probability of earthquakes exceeding 6 on the Richter scale, potentially resulting in hundreds of fatalities and over €1 million in material damages.
Encoders are crucial tools in industrial automation, enabling precise measurement and control of motion and position within machinery across various sectors, including packaging, energy, automotive, and textile industries. These optical sensors convert mechanical motion into electrical signals, which are then interpreted by control systems to accurately determine position, velocity, and direction of movement.
Researchers at the Complex Analysis Group at CRM, in collaboration with the innovative Catalan SME, Hohner Automáticos S.L., utilized a creative combination of discrete mathematics and harmonic analysis techniques. They implemented these techniques into an algorithm to overcome the well-known limitations of the most traditional and affordable type of encoder. This approach enabled them to increase the resolution of the encoders while maintaining low manufacturing costs.
The exclusive, patent-protected method has helped Hohner strengthen its position as a market leader in Spain, contributing to high-skilled job creation and increasing sales during the impact period (2019 onwards). This advancement has raised Hohner’s profile as an innovative and agile company in the eyes of competitors and customers.