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Video
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
Universities conduct research for three reasons: to educate students, to contribute to society, and to understand the world. While society often holds a view of the scholar as a solitary and singular genius, in reality scholars today participate in a highly collaborative, worldwide search for shared understandings that stand the test of time and the scrutiny of others. The problems in the 21st century often demand effort by teams of researchers with resources at scale: laboratories and equipment, compute resources, and expert staffing. Working with faculty, students, and other stakeholders to identify the greatest opportunities and the resources needed to address them is both a privilege and a challenge for modern academic administrators. In this talk, I will share three examples: fostering collaborative proposal-writing; planning for shared capabilities in experimental facilities, data, and computation; and transforming academic structures.
Event date: 12/4/2023
Speaker: Prof. Kathryn Ann Moler
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Statistics and Research Methods
- Keywords:
- Research Science
- Resource Type:
- Video
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Video
More than one hundred years ago, Albert Einstein published his Theory of General Relativity (GR). One year later, Karl Schwarzschild solved the GR equations for a non-rotating, spherical mass distribution; if this mass is sufficiently compact, even light cannot escape from within the so-called event horizon, and there is a mass singularity at the center. The theoretical concept of a 'black hole' was born, and was refined in the next decades by work of Penrose, Wheeler, Kerr, Hawking and many others. First indirect evidence for the existence of such black holes in our Universe came from observations of compact X-ray binaries and distant luminous quasars. I will discuss the forty-year journey, which my colleagues and I have been undertaking to study the mass distribution in the Center of our Milky Way from ever more precise, long-term studies of the motions of gas and stars as test particles of the space time. These studies show the existence of a four million solar mass object, which must be a single massive black hole, beyond any reasonable doubt.
Event date: 09/02/2023
Speaker: Prof. Reinhard GENZEL
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Cosmology and Astronomy and Physics
- Keywords:
- Astrophysics Astronomy Deep space -- Milky Way Nobel Prize winners General relativity (Physics) Black holes (Astronomy)
- Resource Type:
- Video
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Courseware
This course provides a thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis is placed on problem solving and quantitative reasoning. This course covers Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves.
- Course related:
- AP10005 Physics I
- Subjects:
- Physics
- Keywords:
- Physics
- Resource Type:
- Courseware
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Video
In this lesson, we'll be looking at the cell cycle. This is the lifespan of a eukaryotic somatic cell. A somatic cell is any cell in the body of an organism, except for sex cells such as sperm and egg cells. The cell cycle describes the sequence of cell growth and division. A cell spends most of its life a state called interphase. Interphase has three phases, the G1, S, and G2 phases. Interphase is followed by cell division, which has one phase, the M phase. Together these four phases make up the entire cell cycle. G1 of interphase is sometimes called growth 1 or gap phase 1. In G1, a cell is busy growing and carrying out whatever function it's supposed to do. Note that some cells, such as muscle and nerve cells, exit the cell cycle after G1 because they do not divide again. A cell enters the S phase after it grows to the point where it's no longer able to function well and needs to divide. The S stands for synthesis, which means to make, because a copy of DNA is being made during this phase. Once DNA replication is complete, the cell enters the shortest and the last part of interphase called G2, also known as growth 2 or gap phase 2. Right now, it's enough to know that further preparations for cell division take place in the G2 phase. Now that interphase is over, the cell is ready for cell division, which happens in the M phase. The M phase has two events. The main one is mitosis, which is division of the cell's nucleus, followed by cytokinesis, a division of the cytoplasm. So, at the end of M phase, you have two daughter cells identical to each other and identical to the original cell. Let's review. The cell cycle describes the life cycle of an individual cell. It has four phases, three in interphase and one for cell division. Most cell growth and function happen during G1. The cell enters the S phase when it needs to divide. In this phase the cell replicates its DNA. Replication just means the cell makes a copy of its DNA. In G2, the cell undergoes further preparations for cell division. Finally, we have cell division in the M phase. The M phase consists of mitosis, which is nuclear division, and cytokinesis, or division of the cytoplasm. We'll explore the details of mitosis and cytokinesis separately
- Subjects:
- Biology
- Keywords:
- Cell cycle
- Resource Type:
- Video
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Video
Stanford Electrical Engineering Course on Convex Optimization.
- Course related:
- AMA4850 Optimization Methods
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical optimization Convex functions
- Resource Type:
- Video
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Others
Welcome to the Coding Train with Daniel Shiffman! A community dedicated to learning creative coding with beginner-friendly tutorials and projects on YouTube and more.
- Subjects:
- Computing
- Keywords:
- Coding theory Computer programming
- Resource Type:
- Others
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Others
Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints. This technique has been useful for guiding quantitative decisions in business planning, in industrial engineering, and—to a lesser extent—in the social and physical sciences.
- Course related:
- AAE3009 Operations Research and Computational Analytics in Air Transport Operations
- Subjects:
- Mathematics and Statistics
- Keywords:
- Linear programming
- Resource Type:
- Others
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Others
MyScope was developed by Microscopy Australia to provide an online learning environment for those who want to learn about microscopy. The platform provides insights into the fundamental science behind different microscopes, explores what can and cannot be measured by different systems and provides a realistic operating experience on high end microscopes.
We sincerely hope you find the website an enjoyable environment where you can explore the microscopy space and leave ready to undertake your own exciting experiments.
- Course related:
- CE620 Research Methods
- Subjects:
- Laboratory Techniques and Safety
- Keywords:
- Microscopy
- Resource Type:
- Others
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Others
Learn to code, design, and more—all on your own time
- Subjects:
- Computing
- Keywords:
- Coding theory Mobile apps Computer programming
- Resource Type:
- Others