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Models arising in biology are often written in terms of Ordinary Differential Equations. The celebrated paper of Kermack-McKendrick (19271, founding mathematical epidemiology, showed the necessity to include parameters in order to describe the state of the individuals, as time elapsed after infection. During the 70s, many mathematical studies were developed when equations are structured by age, size, more generally a physiological trait. The renewal, growth-fragmentation are the more standard equations. The talk will present structured equations, show that a universal generalized relative entropy structure is available in the linear case, which imposes relaxation to a steady state under non-degeneracy conditions. In the nonlinear cases, it might be that periodic solutions occur, which can be interpreted in biological terms, e.g., as network activity in the neuroscience. When the equations are conservation laws, a variant of the Monge-Kantorovich distance (called Fortet-Mourier distance) also gives a general non-expansion property of solutions.
Event date: 19/1/2023
Speaker: Prof. Benoît Perthame (Sorbonne University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Biology and Mathematics and Statistics
- Keywords:
- Biomathematics Equations
- Resource Type:
- Video
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Video
This mini-lecture focuses on basic analytical chemistry and the science behind Crime Scene Investigation (CSI). The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Chemistry
- Keywords:
- Forensic sciences Analytical chemistry Crime laboratories
- Resource Type:
- Video
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Video
"We've been promised a future of chrome -- but what if the future is fleshy?" asks biological designer Christina Agapakis. In this awe-inspiring talk, Agapakis details her work in synthetic biology -- a multidisciplinary area of research that pokes holes in the line between what's natural and artificial -- and shares how breaking down the boundaries between science, society, nature and technology can lead us to imagine different possible futures.
- Subjects:
- Technology and Biology
- Keywords:
- Synthetic biology Sci9ence -- Social aspects
- Resource Type:
- Video
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Video
Documentary photographer Olivia Arthur has been exploring a new frontier: the evolution of the blurring line between humanity and technology. In this meditative talk, she shows her work documenting the remarkable ways humans have merged with machines -- from bionics and motorized limbs to synthetic muscles and strikingly realistic robots -- and offers wisdom on the complexity, adaptability and resilience of the human body.
- Subjects:
- Technology and Biomedical Engineering
- Keywords:
- Human body technology
- Resource Type:
- Video
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Video
Designer and architect Neri Oxman is leading the search for ways in which digital fabrication technologies can interact with the biological world. Working at the intersection of computational design, additive manufacturing, materials engineering and synthetic biology, her lab is pioneering a new age of symbiosis between microorganisms, our bodies, our products and even our buildings.
- Subjects:
- Biotechnology and Chemical and Bioprocess Technology
- Keywords:
- Biotechnology Biosynthesis -- Industrial applications
- Resource Type:
- Video
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Video
Irina Kareva translates biology into mathematics and vice versa. She writes mathematical models that describe the dynamics of cancer, with the goal of developing new drugs that target tumors. "The power and beauty of mathematical modeling lies in the fact that it makes you formalize, in a very rigorous way, what we think we know," Kareva says. "It can help guide us to where we should keep looking, and where there may be a dead end." It all comes down to asking the right question and translating it to the right equation, and back.
- Subjects:
- Health Sciences and Mathematics and Statistics
- Keywords:
- Cancer -- Mathematical models Cancer cells -- Mathematical models
- Resource Type:
- Video
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Video
Your mortal enemy has captured you and hooked you up to a bizarre experiment. He's extended your nervous system with one very long neuron to a target about 70 meters away. At some point, he's going to fire an arrow. If you can then think a thought to the target before the arrow hits it, he'll let you go. So who wins that race? Seena Mathew examines the speed of thought.
- Subjects:
- Health Sciences and Biology
- Keywords:
- Neurons -- Physiology Thought thinking Brain -- Physiology
- Resource Type:
- Video
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Video
Physicist Geoffrey West has found that simple, mathematical laws govern the properties of cities -- that wealth, crime rate, walking speed and many other aspects of a city can be deduced from a single number: the city's population. In this mind-bending talk from TEDGlobal he shows how it works and how similar laws hold for organisms and corporations.
- Subjects:
- Environmental Engineering and Mathematics and Statistics
- Keywords:
- Cities towns -- Growth -- Econometric models Sustainable urban development
- Resource Type:
- Video
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Video
Resource inequality is one of our greatest challenges, but it's not unique to humans. Like us, mycorrhizal fungi that live in plant and tree roots strategically trade, steal and withhold resources, displaying remarkable parallels to humans in their capacity to be opportunistic (and sometimes ruthless) -- all in the absence of cognition. In a mind-blowing talk, evolutionary biologist Toby Kiers shares what fungi networks and relationships reveal about human economies, and what they can tell us about inequality.
- Subjects:
- Biology
- Keywords:
- Mycorrhizal fungi -- Ecology
- Resource Type:
- Video
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Video
Traveling is extremely arduous for microscopic sperm -- think of a human trying to swim in a pool made of...other humans. We can compare the journey of a sperm to that of a sperm whale by calculating the Reynolds number, a prediction of how fluid will behave, often fluctuating due to size of the swimmer. Aatish Bhatia explores the great (albeit tiny) sperm's journey.
- Subjects:
- Physics
- Keywords:
- Fluid dynamics Sperm whale Spermatozoa
- Resource Type:
- Video
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