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Events

• Nov

  6

  Appl Math: Leonid Berlyand on "Introduction to Mathematics of Artificial Neural Networks (ANNs)"

  McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  11:15 AM M416, Technological Institute

  EVENT DETAILS

  Title: Introduction to Mathematics of Artificial Neural Networks (ANNs)

  Speaker: Leonid Berlyand, The Pennsylvania State University

  Abstract: We begin by addressing the image classification problem, where the goal is to map images x to classes α using an exact classifier Φ(x,α). Since an exact classifier is often unfeasible, Artificial Neural Networks (ANNs) F(x,α) are used to approximate Φ(x,α), with α representing tunable parameters. Unlike classical methods that use coefficients in expansions, ANN parameters are inspired by the structure of the human brain. The process of optimizing these parameters is called training.

  We highlight two advancements: First, a pruning technique using the Marchenko-Pastur spectral approach from Random Matrix Theory (RMT), which reduces computational complexity without sacrificing accuracy. Second, we examine autoencoders, a special type of ANN used for image-to-image transformations. The focus is on the fixed points of the autoencoder function F(x,α), crucial for distinguishing real images from fakes. Using the Banach Fixed Point Theorem, we show that with light-tailed distributions (e.g. Gaussian), there is a unique stable fixed point, while with heavy-tailed distributions (e.g. Cauchy), there are multiple fixed points N. The number of fixed points N depends non-monotonically on the number of layers L, suggesting an optimal number of layers L_0 for best performance. These results are vital for improving autoencoder design.

  Zoom: https://northwestern.zoom.us/j/92383067097

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  TIME Thursday, November 6, 2025 at 11:15 AM - 12:15 PM

  LOCATION M416, Technological Institute    map it

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  CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

  CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

• Nov

  20

  Appl Math: Ed Lyman on "Elastic and Dynamic Response of Membranes Across Scales"

  McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  11:15 AM M416, Technological Institute

  EVENT DETAILS

  Title: Elastic and Dynamic Response of Membranes Across Scales

  Speaker: Ed Lyman, University of Delaware

  Abstract: Cell membranes are quasi-2D soft materials, about 5 nm thick but with hundreds of square microns of surface area. They are a bilayer structure, assembled from amphiphilic molecules (lipids) and proteins. The function of membranes imposes challenging design constraints: impermeable yet fluid, mechanically robust yet deformable. Across the tree of life, cells meet these challenges by synthesizing a diverse array of lipids, whose chemistry and interactions determine the key continuum properties, like stiffness against bending and the viscosity which controls diffusion and encounter of membrane bound signaling partners. In this talk I will present our group's work using simulations to connect lipid chemistry and membrane properties, focusing on two applications. The first project considers the membranes of a family of marine invertebrates called ctenophores, which synthesize a specialized lipid chemistry to maintain membrane deformability at high pressure. The second project focuses on how lipid chemistry is used to control the viscosity of the membrane, and the challenges that come with trying to measure the viscosity of soft, thin, not-quite two dimensional fluids.

  Zoom: https://northwestern.zoom.us/j/95131921396

  -----

  To subscribe to the Applied Mathematics Colloquia List send a message to LISTSERV@LISTSERV.IT.NORTHWESTERN.EDU with the command:

  SUBSCRIBE esam-seminar FirstName LastName

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  TIME Thursday, November 20, 2025 at 11:15 AM - 12:15 PM

  LOCATION M416, Technological Institute    map it

  ADD TO CALENDAR

  CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

  CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

• Dec

  13

  Northwestern Engineering PhD Hooding and Master's Recognition Ceremony

  McCormick School of Engineering and Applied Science

  4:00 PM Pick-Staiger Concert Hall

  EVENT DETAILS

  The ceremony will take place on Saturday, December 13 in Pick-Staiger Concert Hall, 50 Arts Circle Drive.

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  TIME Saturday, December 13, 2025 at 4:00 PM - 6:00 PM

  LOCATION Pick-Staiger Concert Hall    map it

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  CONTACT Andi Joppie    andi.joppie@northwestern.edu EMAIL

  CALENDAR McCormick School of Engineering and Applied Science