NumPI April 2019

numpi@lists.dm.unipi.it

1 participants
3 discussions

Seminar on 11/04 (Fabio Carrara)
by Leonardo Robol 11 Apr '19

11 Apr '19

Speaker: Fabio Carrara Affiliation: ISTI-CNR, Pisa Time: Thursday, 11 April 2019, h. 14:00 Place: Aula Riunioni, Dipartimento di Matematica Title: Neural networks for image understanding: methods, limitations, and new frontiers Vision is natural and easy for living beings, while it is incredibly complex to be replicated in machines. In the last 40 years, a lot of work in Computer Vision has been spent trying to model and implement visual perception manually, with slow improvements over time. However, in the last decade, deep neural networks revolutionized this field by automatically learning complex models for vision from huge amounts of data, thus relieving the practitioners from defining and extracting complex visual features that would require a lot of manual effort to find. In this talk, we will make a journey into neural networks for computer vision focusing on tasks in which they shine, that is image recognition and understanding. We will cover the most successful neural network formulation for visual data, that is the convolutional neural network, from the basics to recent architectures, while pinpointing current limitations in the field. In conclusion, we will discuss novel neural network architectures, such as continuous ODE-defined models, that have been recently proposed and provide new research directions.

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Seminar on 08/04 (Raf Vandebril)
by Leonardo Robol 08 Apr '19

08 Apr '19

Speaker: Raf Vandebril Affiliation: Department of Computer Science, KU Leuven Time: Monday, 08 April 2019, h. 14:00 Place: Aula Seminari, Dipartimento di Matematica Title: Structures, Gramians, and Krylov Krylov methods are typically used for transforming large scale prolems and matrices to matrices of a manageable size. Krylov inspired algorithms are based on the principle: project - solve - lift. In this talk we will focus on the projection step, the orthogonal bases involved, and the structured of the resulting projection. Two bases are needed for the projection: a basis for a search Krylov subspace, say V, and another basis for the constraint Krylov subspace, name it W. For a matrix A, the projected small to medium sized matrix will be W^*AV. There is now a wide variety of possibilities for constructing the matrices W and V. We could go from classical Krylov to extended and rational Krylov subspaces. But we could also attempt to construct subspaces with variants of the matrix A, such as for instance its inverse, its conjugate transpose, or the inverse of its conjugate transpose. In this lecture we will examine some of these possibilities. A general framework is proposed in which we will touch upon the following aspects: biorthogonal (rational) Krylov, CMV factorizations, non-unitary CMV factorizations, quasiseparable Hessenberg matrices, Hankel and Toeplitz Gramians.

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Seminar on 12/04 (James Nagy)
by Leonardo Robol 04 Apr '19

04 Apr '19

Speaker: James Nagy Affiliation: Department of Mathematics, Emory University Time: Friday, 12 April 2019, h. 11:00 Place: Aula Mancini, SNS Title: MATLAB Tools for Large-Scale Linear Inverse Problems Inverse problems arise in a variety of applications: image processing, finance, mathematical biology, and more. Mathematical models for these applications may involve integral equations, partial differential equations, and dynamical systems, and solution schemes are formulated by applying algorithms that incorporate regularization techniques and/or statistical approaches. In most cases these solutions schemes involve the need to solve a large-scale ill-conditioned linear system that is corrupted by noise and other errors. In this talk we describe and demonstrate capabilities of a new MATLAB software package that consists of state-of-the-art iterative methods for solving such systems, which includes approaches that can automatically estimate regularization parameters, stopping iterations, etc., making them very simple to use. Thus, the package allows users to easily incorporate into their own applications (or simply experiment with) different iterative methods and regularization strategies with very little programming effort. On the other hand, sophisticated users can also easily access various options to tune the algorithms for certain applications. Moreover, the package includes several test problems and examples to illustrate how the iterative methods can be used on a variety of large-scale inverse problems. The talk will begin with a brief introduction to inverse problems, discuss considerations that are needed to compute an approximate solution, and describe some details about new efficient hybrid Krylov subspace methods that are implemented in our package. These methods can guide users in automatically choosing regularization parameters, and can be used to enforce various regularization schemes, such as sparsity. We will use imaging examples that arise in medicine and astronomy to illustrate the performance of the methods. This is joint work with Silvia Gazzola (University of Bath) and Per Christian Hansen (Technical University of Denmark).

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NumPI April 2019