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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
Tech that can decode your brain activity and reveal what you're thinking and feeling is on the horizon, says legal scholar and ethicist Nita Farahany. What will it mean for our already violated sense of privacy? In a cautionary talk, Farahany warns of a society where people are arrested for merely thinking about committing a crime (like in "Minority Report") and private interests sell our brain data -- and makes the case for a right to cognitive liberty that protects our freedom of thought and self-determination.
- Subjects:
- Technology and Computing
- Keywords:
- Privacy Thought thinking -- Data processing Technological innovations -- Social aspects
- Resource Type:
- Video
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Video
What if we looked at Parkinson's as an neurological electrical problem? Brain researcher Eleftheria Pissadaki and her team study dopamine neurons, the neurons that selectively die during Parkinson's. They discovered that the bigger a neuron is, the more vulnerable it becomes because it simply requires more energy. This new insight is reframing the disease -- and by "finding the fuse box for each neuron" and figuring out how much energy it needs, may help us neuroprotect our brain cells.
- Subjects:
- Health Sciences and Mathematics and Statistics
- Keywords:
- Brain -- Diseases -- Research Brain -- Mathematical models
- Resource Type:
- Video
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Video
Can the way you speak and write today predict your future mental state, even the onset of psychosis? In this fascinating talk, neuroscientist Mariano Sigman reflects on ancient Greece and the origins of introspection to investigate how our words hint at our inner lives and details a word-mapping algorithm that could predict the development of schizophrenia. "We may be seeing in the future a very different form of mental health," Sigman says, "based on objective, quantitative and automated analysis of the words we write, of the words we say."
- Subjects:
- Health Sciences
- Keywords:
- Mental health Mental illness
- Resource Type:
- Video
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Video
Neuroscientist Kay M. Tye investigates how your brain gives rise to complex emotional states like depression, anxiety or loneliness. From the cutting edge of science, she shares her latest findings -- including the development of a tool that uses light to activate specific neurons and create dramatic behavioral changes in mice. Learn how these discoveries could change the way you think about your mind -- and possibly uncover effective treatments for mental disorders.
- Subjects:
- Health Sciences
- Keywords:
- Mental illness -- Physiological aspects
- Resource Type:
- Video