Date/Time : 30 Jul 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Min XU, Carnegie Mellon University

Cryo-electron tomography (cryo-ET) 3D imaging technology captures a 3D image of a single cell’s subcellular structures at sub-molecular resolution and in a near-native state. It provides unprecedented opportunities for systematically studying the native spatial organization of subcellular structures, especially macromolecules. However, cryo-ET has high structural complexity and imaging limits, such as high structural diversity and crowding, low signal-to-noise ratio, and missing values. These have made the automated systematic analysis of such images extremely difficult. I will present our recent efforts to develop methods for automated analysis of cryo-ET data.

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Date/Time : 19 Jun 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Yuan Yancheng, Hong Kong Polytechnic University

Convex clustering model has attracted growing attention in the machine learning community. In this talk, we will introduce some recent progress of convex clustering model on model performance and numerical computation. Moreover, we will introduce a newly developed solver for solving the convex clustering model with GPU acceleration.  

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Date/Time : 18 Jun 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Weng Kee Wong, University of California at Los Angeles

This talk first reviews mathematical techniques for constructing various types of optimal experimental designs before I present applications to design early phase clinical trials. For more complex problems, the methodology is increasingly combined with nature-inspired metaheuristics, which are assumptions free, general-purpose optimization algorithms motivated by nature, like animal behavior. After a quick overview of metaheuristics, I use MATLAB and demonstrate how these algorithms can efficiently find multiple-objective optimal designs for a biomedical problem. E-optimal designs are a minimax type of optimal designs that pose particular mathematical challenges and I discuss some of them, including a continuing effort to find a practically useful algorithm for generating E-optimal designs and has a proof of convergence.

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Date/Time : 29 May 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Renbo Zhao, University of Iowa

We present and analyze a new Frank–Wolfe method for minimizing a -log-homogenous self-concordant barriers, with applications including positron emission tomography, D-optimal design, TV-regularized Poisson image de-blurring, quantum state tomography. The iteration complexity of our method is essentially , which recovers that obtained by Khachiyan (1996) on the D-optimal design problem. In addition, we also present and analyze an away-step variant of our proposed Frank–Wolfe method, and we show the global linear convergence of this method. When specialized to the D-optimal design problem, this settles an open problem in Ahipasaoglu, Sun and Todd (2008).

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Date/Time : 06 Mar 2024 15:40
Venue : S17 #05-12 (SR4)
Speaker : Pierre-Louis Poirion, University of Tokyo

In this talk, we present a randomized subspace regularized Newton method for a non-convex function. We show that our method has global convergence under appropriate assumptions, and its convergence rate is the same as that of the full regularized Newton method. Furthermore, we can obtain a local linear convergence rate, under some additional assumptions, and prove that this rate is the best we can hope, under local strong convexity sumptions, when using random subspace. Finally, we will prove that under rank deficiency conditions, one can obtain super-linear convergence in the subspace setting.

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Date/Time : 06 Mar 2024 15:00
Venue : S17 #05-12 (SR4)
Speaker : Akiko Takeda, University of Tokyo

Random projection techniques based on the Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preserving their optimal values, which leads to smaller-scale optimization problems. In this talk, we show a few applications of random matrix techniques for constructing random subspace algorithms that iteratively solve smaller-scale subproblems and discuss their convergence speed. This talk is based on joint works with Ryota Nozawa, and Pierre-Louis Poirion.

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Date/Time : 28 Feb 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Jiequn Han, Flatiron Institute, USA

Partial differential equations (PDEs) are among the most ubiquitous tools in modeling natural phenomena, and various numerical methods have been developed for decades to solve PDE problems. While deep learning has introduced new techniques to the field, the limited accuracy of deep neural networks hinders their application to scientific problems that require high precision.

This talk will present a warm-start approach that combines the strengths of deep neural networks and classical numerical solvers. The approach uses neural networks to provide an initial guess, enabling classical numerical solvers to achieve a good solution more efficiently. We will demonstrate the advantages of the proposed method through two examples. In the first example, we will demonstrate how the initial guess provided by neural networks helps identify the basin of attraction of the true solution in the inverse scattering problem. In the second example, we will show how the initial guess provided by neural networks leads to faster convergence in solving the Reynolds-averaged Navier-Stokes equations. In both examples, the combination of the classical PDE solver and the neural network outperforms either approach alone. The potential of this approach will be discussed, along with the new challenges that must be tackled to solve challenging scientific problems using this new paradigm

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Date/Time : 20 Feb 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Yin Zhang, Chinese University of Hong Kong, Shenzhen

The Transformer architecture, in which the key innovation is a Self-Attention (SA) mechanism, has revolutionized AI fields since its introduction in 2017. However, it is difficult to extend the original architecture to deeper models with 10 or more layers. In this work, we show that this depth problem is caused by a phenomenon called token similarity escalation (TSE) which is driven by spectral properties of attention matrices in the SA mechanism. Based on the gained insights, we propose a simple de-escalation strategy to surgically removes excessive token similarity without discounting SA as a whole. Empirical evidence is presented to demonstrate the effectiveness of our scheme on small-scale models.

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Date/Time : 11 Jan 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Mathias Weller, Technische Universität Berlin

In this talk, I will give a high-level introduction of some important computational problems in “Phylogenetics”, a branch of Biology that works with evolutionary histories of “taxa” (species, genes, samples, …). We will see some landmark results related to parameterized algorithms that analyze such histories.

In the second part of the talk, I would like to speak about a recently introduced layout-parameter for phylogenetic networks (basically rooted directed acyclic graphs with leaf-labels) called “scanwidth”, which has close ties to the treewidth of the underlying undirected graph. I will give examples for algorithmic results parameterized by the scanwidth and talk about efforts to efficiently compute the parameter itself.

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