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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
Before the advent of computers around 1950, optimization centered either on small-dimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinite-dimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving large-scale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Convex sets Mathematical optimization Computer science -- Mathematics
- Resource Type:
- Video
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Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Sampling (Statistics) Differential equations Partial -- Numerical solutions Mathematical models Adaptive computing systems
- Resource Type:
- Video
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Video
We introduce a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only Hessian-vector products in two directions. Moreover; the computational overhead remains comparable to the first-order such as the gradient descent method. We show that the method has a local super-linear convergence and a global convergence rate of 0(∈-3/2) to satisfy the first-order and second-order conditions under a commonly used approximated Hessian assumption. We further show that this assumption can be removed if we perform one step of the Krylov subspace method at the end of the algorithm, which makes DRSOM the first first-order-type algorithm to achieve this complexity bound. The applicability and performance of DRSOM are exhibited by various computational experiments in logistic regression, L2-Lp minimization, sensor network localization, neural network training, and policy optimization in reinforcement learning. For neural networks, our preliminary implementation seems to gain computational advantages in terms of training accuracy and iteration complexity over state-of-the-art first-order methods including SGD and ADAM. For policy optimization, our experiments show that DRSOM compares favorably with popular policy gradient methods in terms of the effectiveness and robustness.
Event date: 19/09/2022
Speaker: Prof. Yinyu Ye (Stanford University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex programming Nonconvex programming Mathematical optimization
- Resource Type:
- Video
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Video
Convex Matrix Optimization (MOP) arises in a wide variety of applications. The last three decades have seen dramatic advances in the theory and practice of matrix optimization because of its extremely powerful modeling capability. In particular, semidefinite programming (SP) and its generalizations have been widely used to model problems in applications such as combinatorial and polynomial optimization, covariance matrix estimation, matrix completion and sensor network localization. The first part of the talk will describe the primal-dual interior-point methods (IPMs) implemented in SDPT3 for solving medium scale SP, followed by inexact IPMs (with linear systems solved by iterative solvers) for large scale SDP and discussions on their inherent limitations. The second part will present algorithmic advances for solving large scale SDP based on the proximal-point or augmented Lagrangian framework In particular, we describe the design and implementation of an augmented Lagrangian based method (called SDPNAL+) for solving SDP problems with large number of linear constraints. The last part of the talk will focus on recent advances on using a combination of local search methods and convex lifting to solve low-rank factorization models of SP problems.
Event date: 11/10/2022
Speaker: Prof. Kim-Chuan Toh (National University of Singapore)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex programming Semidefinite programming
- Resource Type:
- Video
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Video
The notion of expertise is integral to all forms of institutional and professional practice in many domains – in education, healthcare, social welfare, law, journalism, banking, information technology, marketing, translating and interpreting services etc. It is a concept addressed by scholars across many disciplines – cognitive science, sociology, anthropology, psychology, language/communication studies, among others. There are, however, enduring problems of definition, description and measurement of expertise. Some scholars draw attention to the ongoing ‘crisis in expertise’ and others pronounce the ‘death of expertise’ in contemporary society.
More humbly, I begin with a characterisation of professional expertise very broadly to include scientific, experiential, technological, organisational, legal, ethical and communicative knowledge. This then leads me to the notion of ‘distributed expertise’, which extends beyond the individual remit and the conventional lay-expert divide. For instance, in the healthcare domain, a significant development afforded by internet-based technology is the increased level of patients’ e-health literacy and, consequently, democratisation of expertise. This amounts not only to accessing health information digitally, but also the phenomenon of patients ‘doctoring’ themselves in ‘the now of its presence’, i.e., ‘expert patients’ becoming instrumental in self-diagnosis and even self-treatment.
Additionally, ‘distributed expertise’ is also constitutive of ‘expert systems’, e.g., diagnostic and interventionist technologies as well as decision aids mediated by algorithms and templates. This is what I refer to as the technologization of expertise. I suggest that there is overreliance on ‘expert systems’ by both experts and lay persons in everyday decision making. Access to and use of ‘expert systems’ in optimal ways inevitably necessitates a reconfiguration of the very conditions and consequences of professional expertise.
Event Date: 25/11/2022
Speaker: Prof. Srikant Sarangi (Hong Kong Polytechnic University)
Hosted by: Faculty of Humanities
- Keywords:
- Information technology -- Social aspects Democratization Expertise
- Resource Type:
- Video
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Video
As a recent New York Times editorial proclaimed, "The Global Order Isn't Working. It's Time for Something Different." To teach environmental history and environmental ethics is to reacquaint ourselves with the facts that we need to try to build, while there is still time, a new cooperative order that understands this: simple fact: that other people and other countries are quite literally "the air we breathe." Moreover, all who claim to be ethical persons must take seriously the notion of inter-generational equity and try to act upon it. This notion should, in theory, come more easily to countries whose traditions have built upon classical/ Confucian learning, for those traditions say that the most important marker of human behavior is working toward common ends (qun 群) while "learning what is enough" (zhi zu 知足). Put another way, many resources within the Chinese tradition may strengthen our resolve to act more constructively in less short-sighted ways.
Event Date: 14/11/2022
Speaker: Prof. Michael Nylan (University of California, Berkeley)
Hosted by: Faculty of Humanities
- Keywords:
- Environmental ethics Intergenerational relations Philosophy Confucian Confucian ethics
- Resource Type:
- Video
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Video
The lecture commenced with a warm welcome address by Prof. CHEN Qingyan, Director of PAIR, followed by a brief speaker introduction by Prof. WANG Zuankai, Associate Vice President (Research and Innovation) of PolyU. In his presentation, Prof. Yang highlighted that urgent need for tissue/organ biomanufacturing owing to the shortage of donation for organ transplantation. He pointed out some challenges in the in vitro manufacturing of tissues/organs, particularly in relation to accurate design, precise fabrication, and functional induction, which underscore the imperative need for new methods for tissue/organ manufacturing. Next, Prof. Yang outlined the development roadmap of biomanufacturing and shared specific examples demonstrating the research progress in 3D bioprinting. In concluding his presentation, Prof. Yang shared his insights on the future direction for biomanufacturing, as well as some significant accomplishments by him and his team at Zhejiang University in the field.
A question-and-answer session moderated by Prof. Wang was followed. Both the online and on-site audience had a fruitful discussion with Prof. Yang.
Even date: 2/1/2024
Speaker: Prof. Huayong Yang (Zhejiang University)
Moderator: Prof. Zuankai Wang (Hong Kong Polytechnic University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Biology and Biomedical Engineering
- Keywords:
- Tissue engineering Biomedical engineering Three-dimensional printing Regenerative medicine
- Resource Type:
- Video
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Video
PAIR distinguished lecture series: an overview of high performance computing and future requirements
In this talk, we examine how high performance computing has changed over the last ten years and look toward the future in terms of trends. These changes have had and will continue to impact our numerical scientific software significantly. A new generation of software libraries and algorithms are needed for the effective and reliable use of (wide area) dynamic, distributed, and parallel environments. Some of the software and algorithm challenges have already been encountered, such as the management of communication and memory hierarchies through a combination of compile-time and run-time techniques, but the increased scale of computation, depth of memory hierarchies, range of latencies, and increased run-time environment variability will make these problems much harder.
Even date: 6/12/2023
Speaker: Prof. Jack Dongarra
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Computing
- Keywords:
- High performance computing
- Resource Type:
- Video
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Video
The lecture commenced with a welcome speech by Prof. CHEN Qingyan, Director of PAIR, followed by a brief speaker introduction by Prof. Christopher CHAO, Vice President (Research and Innovation).
In his presentation, Prof. Brilakis first gave a brief introduction to digital twins (DT), pointing out that DT plays a central role in digital transformation. Next, he elaborated on the application of DT in the construction industry and explained how DT is involved in the planning, design, construction, maintenance and operation processes. He introduced research conducted at the University of Cambridge on inexpensive methods for generating object-oriented infrastructure geometry, detecting, and mapping visible defects on the resulting DT, automatically extracting defect spatial measurements, and sensor and sensor data modelling. Prof. Brilakis also provided examples of how these resulting DT are further exploited in design for manufacturing and assembly (DfMA), mixed-reality-enabled mobile inspection, and proactive asset protection from accidental damage. To conclude, Prof. Brilakis stated that DT, smart materials, data science, and automation & bobotics, constitute important digital assets for driving sustainability, and pointed out the future development directions in these areas.
A question-and-answer session moderated by Prof. DING Xiaoli, Director of the Research Institute for Land and Space (RILS), and Prof. WANG Yuhong, Member of RILS, followed. This session provided both the online and on-site audience with an opportunity to engage in a fruitful discussion with Prof. Brilakis.
Even date: 08/03/2024
Speaker: Prof. Ioannis BRILAKIS (University of Cambridge)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Technology
- Keywords:
- Buildings -- Computer-aided design Digital twins (Computer simulation) Construction industry
- Resource Type:
- Video
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