Summary of Public Lecture - Goriely

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00:00:00 - 01:00:00

This video discusses the progression of Alzheimer's disease and how it affects different areas of the brain. It also highlights the importance of early diagnosis and explains the different stages of the disease.

  • 00:00:00 The speaker introduces Ellen E&L, the chair of the mathematics department at Stanford, and speaks about her dedication to mathematics and its application to modern scientific and technological society. She also mentions the importance of mathematics in soul-building, and goes on to say that Allah is one of the many applications of mathematics.
  • 00:05:00 Dr. Tadashi Goriely will speak about mathematics versus dementia, the former being an example of an intellectual activity that can be impaired by disease, and how brain imaging technology has helped researchers study the disease. He will also discuss the origins of the disease and its symptoms.
  • 00:10:00 The video discusses the progression of Alzheimer's disease and its associated symptoms. It highlights the importance of early diagnosis and explains the different stages of the disease.
  • 00:15:00 Public Lecture - Goriely discusses how apraxia not being able to do some movement even though there is no motor problem, agnosia problem in recognizing faces, aphasia problem in recognizing words and speech, and recognition eventually leads to psycho behavioral problems, such as psychosis. She also discusses the process of neurodegenerative diseases, and how they all share certain common traits, such as a progressive loss of self-identity and a systematic progression.
  • 00:20:00 According to the speaker, a disease called Aldama is characterized by dramatic physical changes in the brain within a few years. Additionally, brain versus enzyme theory suggests that a diseased brain exhibits characteristics similar to those of a walnut-shaped brain. The speaker points out that while this concept is useful as a conceptual tool, it is not a realistic model for understanding the disease's progression. Mathematical models are used to attempt to predict the spatial progression of the disease and to understand the role of biomarkers.
  • 00:25:00 The video discusses the idea that diffusion of toxic proteins through the brain can be modeled using a network diffusion model. This model can be used to extract information about which nodes are the most likely to be affected by the diffusion, as well as the degree of diffusion. This information can be used to better understand the progression of a disease.
  • 00:30:00 This lecture covers the basics of linear algebra, and explains the concept of an eigenmode. The lecture also covers the importance of symmetric matrices and the relationship between the network and atrophy in the brain.
  • 00:35:00 The Public Lecture by Dr. Goriely discusses the Windy Hill model, which is a model that explains how a protein can become toxic and cause neuron damage. The model is based on concentration and rate equations, and it is able to predict how aggregates and fragments will form.
  • 00:40:00 This lecture discusses the Fisher equation, which is a fundamental equation in mathematical biology. The equation describes the spread of gene through a population, and is useful for understanding the properties of systems. It is important to note that the equation is only applicable in one dimension, and that additional information must be provided in order to apply it to the brain.
  • 00:45:00 The speaker discusses how they used a computer simulation to study the progression of neurodegenerative diseases in the brain. They found that the disease affects different areas at different stages, and that the color of the inversion map matched what was known from post-mortem analysis.
  • 00:50:00 The video discusses how the brain is highly interconnected, and how a discrete model can be used to study this connectivity. The video also introduces a new model called the "continuum model," which is based on the idea that the brain is a continuum.
  • 00:55:00 Goriely discusses the importance of spatial progression of a disease being heavily influenced by the underlying mechanism and structure of the network, as well as the functional network. She explains how this information can be used to test different hypotheses and assumptions about the disease.

01:00:00 - 01:15:00

This video provides an introduction to the field of applied mathematics, with a focus on how the brain's symmetry can lead to the generation of proteins in both halves. The speaker also discusses how mathematicians can use degree distributions to analyze networks and determine the shortest equation connecting nodes.

  • 01:00:00 Public Lecture Goriely provides a brief overview of research on the impact of physical activity on dementia, with a focus on dancing. He notes that while dancing was found to be the most effective form of physical activity in reducing symptoms of dementia, there are still many unanswered questions about the impact of physical activity on the brain.
  • 01:05:00 The speaker discusses the idea that there is no definite effect of cognitive activities like crossword puzzles and Dukes on the progression of dementia, and points out that the clearance rate of the toxin protein may be influenced by the size of the aggregate.
  • 01:10:00 Public Lecture - Goriely discusses how the brain is symmetrical, with two halves that act independently. He explains how the brain's symmetry leads to spontaneous generation of proteins in both halves, and how this explains the brain's efficiency in processing information. He also talks about a problem with correlating network topology with propagation, and how mathematicians can use degree distributions to analyze networks and determine the shortest equation connecting nodes.
  • 01:15:00 This YouTube video provides a brief introduction to Applied Mathematics, which is written at a lower level than most other mathematics texts. The video is aimed at people who are looking for a shorter introduction to the subject.

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