Date/Time : 13 Jan 2020 15:00
Venue : S17 #04-06 SR1
Speaker : Zhu Wei, Duke University

Date/Time:13 Jan 2020 15:00 Venue: S17 #04-06 SR1 Speaker: Zhu Wei, Duke University Applied differential geometry and harmonic analysis in deep learning regularization With the explosive production of digital data and information, data-driven methods, deep neural networks (DNNs) in particular, have revolutionized machine learning and scientific computing by gradually outperforming traditional hand-craft model-based algorithms. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of over parameterized DNNs still remains a mystery despite many recent efforts. In this talk, I will discuss two recent works to inject” the “modelling” flavour back into deep learning to improve the generalization performance and interpretability of DNNs. This is accomplished by deep learning regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by imposing a “smoothness” inductive bias over the DNN model. This is achieved by solving a variation problem with a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivalent representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients. Add to calendar: 

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Date/Time : 10 Jan 2020 15:00
Venue : S17 #04-05 SR2
Speaker : Seung-Hyeok Kye, Seoul National University, South Korea

Date/Time:10 Jan 2020 15:00 Venue: S17 #04-05 SR2 Speaker: Seung-Hyeok Kye, Seoul National University, South Korea A lattice arising from quantum information theory The notion of separability/entanglement is one of the central themes in the current quantum information theory, and it is known to be NP hard in general to determine if a given state is separable or entangled. In multipartite systems, the notions of separability depend on partitions of systems to yield the notions of partial separability and partial entanglement. In the simplest multipartite case of the three qubit system, there are three kinds of basic partial separability which give rise to corresponding convex sets. Intersections and convex hulls of them also have been considered by researchers to get more kinds of separability and entanglement. In this talk, we consider the lattice generated by these three convex sets, with respect to two operations: convex hull and intersection. We will discuss mathematical properties of this lattice. This talk is based on three papers: arXiv 1812.01227 (with Kyung Hoon Han), arXiv 1905.07678 (with Kyung Hoon Han) and arXiv 1911.06496 (with Kyung Hoon Han and Szilard Szalay). Add to calendar: 

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Date/Time : 03 Jan 2020 15:00
Venue : S17 #04-05 SR2
Speaker : Paul Van Dooren, Catholic University of Louvain, Belgium

Date/Time:03 Jan 2020 15:00 Venue: S17 #04-05 SR2 Speaker: Paul Van Dooren, Catholic University of Louvain, Belgium Detecting roles in very large graphs Computing meaningful clusters of nodes is crucial to analyze very large networks, but since this is a combinatorial optimization problem, its complexity can be prohibitive. In this talk, we present a pairwise node similarity measure that allows to extract roles, i.e. group of nodes sharing similar flow patterns within a network. We then propose a low rank iterative scheme to approximate the similarity measure for very large networks and we show that our low rank similarity score successfully extracts the different roles in random graphs of Erdös-Renyi type. We then argue that when projecting our similarity measure onto a low rank manifold (say, of rank r), the role models can be recovered using classical clustering techniques in an r-dimensional space, which reduces the complexity significantly. We illustrate these ideas with a number of real world applications including coral spawning in the great barrier reef. Add to calendar: 

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Date/Time : 21 Dec 2019 15:00
Venue : S17 #04-06 SR1
Speaker : Oleg Evnin , Chulalongkorn University

Date/Time:21 Dec 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Oleg Evnin, Chulalongkorn University Large structured matrices and quantum chaos in resonant systems Resonant systems emerge as weakly nonlinear approximations to problems of mathematical physics with highly resonant linearized perturbations, including Bose-Einstein condensates in harmonic traps and dynamics in AdS spacetimes. The classical dynamics within this class of systems can be very rich, ranging from fully integrable to chaotic as one changes the values of the mode coupling coefficients. Despite the complexity of the corresponding classical dynamics, the quantum version turns out to be remarkably simple: the Hamiltonian is block-diagonal in the Fock basis, with all blocks of varying finite sizes. One thus deals with the systematics of eigenvalues of highly structured finite matrices, including limits when these matrices become very large. I’ll report on a recent study of both numerical patterns emerging for the integrable cases, and the spectral statistics, which efficiently distinguishes the special integrable cases from generic (chaotic) points in the parameter space, and discuss a range of potential applications.

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Date/Time : 13 Nov 2019 14:00
Venue : S17 #04-05 SR2
Speaker : Li Zimu,

Date/Time:13 Nov 2019 14:00 Venue: S17 #04-05 SR2 Speaker: Li Zimu A Global Geometric Approach to Parallel Transport of Strings in Gauge Theory In this talk, we will introduce a global geometric method to formulate the concept of parallel transport on surfaces, which first is studied in the context of higher gauge theory as an extension of the classical notion of parallel transport along paths. We will discuss a generalized 3-dimensional non-abelian Stokes’ theorem related to parallel transport on surfaces. After that, we will extend this theorem to four dimension by replacing the underlying algebraic structure: crossed module with crossed 2-module. This 4-dimensional Stokes’ theorem further yields a global formula for parallel transport on volumes, and guarantees its gauge invariance with other important properties which have been seen in the case of surfaces. Add to calendar: 

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Date/Time : 09 Oct 2019 15:00
Venue : S17 #04-06 SR1
Speaker : Cai Tianxin, Zhejiang University

Date/Time:09 Oct 2019 15:00 Venue: S17 #04-06 SR1 Speaker: Cai Tianxin, Zhejiang University From Seeing to Discovering Our civiliza􀀁on has been developed based on modern knowledge and tradi􀀁on, oriental or occidental, but there is an important third source which has o􀀂en been largely neglected: interdisciplinary and intercultural inference and exchange. In this lecture, Professor Cai will focus on the interplay between science and humanity and in par􀀁cular the similarity among mathema􀀁cs, art, poetry, and daily life. He will explain why math is everywhere. Professor Cai believes that there is a process from seeing to discovering in any field of study or career, and he will demonstrate it through classical or modern pain􀀁ng together with some photographs that he took from all around the world. Add to calendar: 

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Date/Time : 28 Aug 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Michael Rockner, Bielefeld University

Date/Time:28 Aug 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Michael Rockner, Bielefeld University Solutions of SPDE as zeros of maps on scaled path spaces It has been recently shown that the solutions of a large class of stochastic partial differential equations (SPDE) can be obtained as zeros of properly defined map on a path space equipped with a norm which is “scaled” by the exponential of a function-valued Brownian motion. In the talk this result will be reviewed and connected to current developments about the case where the underlying SPDE is a gradient flow, perturbed by linear multiplicative noise. In this case it follows from the above result and by applying methods from the calculus of variations that the solution minimizes a certain explicit convex functional on the path space. Applications include stochastic porous media equations, stochastic nonlinear parabolic equations (as e.g. the stochastic Cauchy problem for the p-Laplacian)and in the non-gradient case also stochastic nonlinear transport equations. Add to calendar: 

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Date/Time : 08 Aug 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Yu Weichuan, Hong Kong University of Science and Technology

Date/Time:08 Aug 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Yu Weichuan, Hong Kong University of Science and Technology PTM-Invariant Peptide Identification Using Coding Method In computational proteomics, the identification of peptides with an unlimited number of post-translational modification (PTM) types is a challenging task. The computational cost associated with database search increases exponentially with respect to the number of modified amino acids and linearly with respect to the number of potential PTM types at each amino acid. The problem becomes intractable very quickly if we want to enumerate all possible PTM patterns. We proposed a novel method named PIPI to achieve PTM-invariant peptide identification. It first codes peptide sequences into Boolean vectors and codes experimental spectra into real-valued vectors. For each coded spectrum, it then searches the coded sequence database to find the top scored peptide sequences as candidates. After that, PIPI uses dynamic programming to localize and characterize modified amino acids in each candidate. We used simulation experiments and real data experiments to evaluate the performance in comparison with restricted tools (i.e., Mascot, Comet, and MS-GF+) and unrestricted tools (i.e., Mascot with error tolerant search, MS-Alignment, ProteinProspector, and MODa). Comparison with restricted tools shows that PIPI has a close sensitivity and running speed. Comparison with unrestricted tools shows that PIPI has the highest sensitivity except for Mascot with error tolerant search and ProteinProspector. The simulation experiments also show that PIPI has the lowest false discovery proportion and the highest PTM characterization accuracy among the unrestricted tools. This is a joint work with Fengchao Yu and Ning Li. Add to calendar: 

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Date/Time : 13 Feb 2019 15:00
Venue : S17 #04-06 SR1
Speaker : Marko Hans Weber, Columbia University

Date/Time:13 Feb 2019 15:00 Venue: S17 #04-06 SR1 Speaker: Marko Hans Weber, Columbia University Systemic Portfolio Diversification: Equilibrium Holdings and Policy Implications We study the implications of fire-sale externalities on optimal portfolio selection. Banks select their asset holdings to minimize expected execution costs triggered by the need to comply with regulatory leverage requirements. We show that if banks disregard the price impact caused by other banks’ liquidation actions, they hold an excessively diversified portfolio. Instead, banks seek systemic diversification when they account for other banks’ asset holdings: They reduce portfolio overlapping to decrease the likelihood of simultaneous deleveraging, sacrificing diversification benefits at the individual level. The bank’s equilibrium allocation is not socially efficient. A benevolent social planner aiming for minimum fire-sale externalities should provide incentives to increase banks’ diversity. A tax on portfolio overlaps aligns the private and social optimum. Social costs can be reduced by enforcing policies which mandate the split of a bank into smaller institutions with heterogeneous leverage ratios. Add to calendar: 

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