Title: Breaking Time Invariance: Assorted-Time Normalization for RNNs

Abstract: ... (not provided due to the conference reviewing policy)

Collaboration: Cole Pospisil, M.S. and Qiang Ye, Ph.D.

Publication: Submitted to a conference proceedings.

Title: Symmetry Structured ConvolutionalNeural Networks

Abstract: ... (not provided due to the journal reviewing policy)

Collaboration: Kehelwala Dewage Gayan Maduranga, Ph.D. and Qiang Ye, Ph.D.

Publication: Submitted to a journal.

Title: Adaptive Weighted Discriminator for Training Generative Adversarial Networks

Abstract: Generative adversarial network (GAN) has become one of the most important neural network models for classical unsupervised machine learning. A variety of discriminator loss functions have been developed to train GAN's discriminators and they all have a common structure: a sum of real and fake losses that only depends on the actual and generated data respectively. One challenge associated with an equally weighted sum of two losses is that the training may benefit one loss but harm the other, which we show causes instability and mode collapse. In this paper, we introduce a new family of discriminator loss functions that adopts a weighted sum of real and fake parts, which we call adaptive weighted loss functions or aw-loss functions. Using the gradients of the real and fake parts of the loss, we can adaptively choose weights to train a discriminator in the direction that benefits the GAN's stability. Our method can be potentially applied to any discriminator model with a loss that is a sum of the real and fake parts. Experiments validated the effectiveness of our loss functions on unconditional and conditional image generation tasks, improving the baseline results by a significant margin on CIFAR-10, STL-10, and CIFAR-100 datasets in Inception Scores (IS) and Frechet Inception Distance (FID) metrics.

Collaboration: Qiang Cheng, Ph.D. and Qiang Ye, Ph.D.

Publication: arXiv; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, pp. 4781-4790

Code: Available at GitHub.

Title: Recurrence Relation for Rook Placement on Genocchi Boards in Four and Five Dimensions

Abstract: The two-dimensional rook theory can be generalized to three and higher dimensions by assuming that rooks attack along hyperplanes. Using this generalization, Alayont and Krzywonos defined two families of boards in any dimension generalizing the triangular boards of two dimensions whose rook numbers correspond to Stirling numbers of the second kind. One of these families of boards is the family of Genocchi boards whose rook numbers are the Genocchi numbers. This combinatorial interpretation of the Genocchi numbers provides a new triangle generation of the Genocchi numbers. In our project, we investigate whether such a similar triangle generation exists for the generalized Genocchi numbers in four and five dimensions.

Collaboration: Feryal Alayont, Ph.D. and Stephanie Loewen, M.S.

Publication: Submitted to the Minnesota Journal of Undergraduate Mathematics.

Title: A Group Theory Version of the Lights Out Game

Abstract: The original Lights Out game has a 5x5 grid of buttons/vertices that can be toggled and can either be turned on or off. When a player starts a game, some of the lights are on and some are off. When player toggles a vertex, that vertex changes the state of every adjacent vertex and itself. The goal of the game is to toggle vertices in a way such that all lights are off. We are studying a different version of the Lights Out game. All vertices are labeled with elements of Z_n and when we toggle a vertex, we add the number that is currently on it to every adjacent vertex and itself. For example, when a particular vertex has a label of 4 in Z_8 and we toggle it, it adds 4 to itself and every adjacent vertex, and the label becomes 0. The game gives the set of all possible labelings a digraph structure, where arc of a digraph corresponds to the toggling of a vertex that changes the graph from one labeling to another. In our research we are focusing on connected components of this digraph, and how they are related to some issues of whether or not the game can be won. Such as: how many winnable labelings are there? And if we are in the winnable connected component, are there labelings that are unwinnable? Is there a function that maps a labeling from one connected component to another and how is it defined?

Collaboration: Darren Parker, Ph.D.

Publication: Accepted to Involve - A Journal of Mathematics, soon to appear in print.

Title: Calculations of the Optimal Parameters for Technological Process of Penocarbides Manufacturing

Abstract: Research of mathematical planning for optimization of parameters for technological process of penocarbides manufacturing. (translated from Russian)

Collaboration: Valentina Kuzurman, Ph.D.

Publication: Available at Youth Forum: Technical and Mathematical Science (translated from Russian) | PDF

Title: Evaluation of nitrate content in food and methods of its reduction

Abstract: This paper deals with comparative analysis of the nitrate content in foods. The methods were developed for reducing the nitrate content in vegetable foods, the level of which exceeds the norm.

Collaboration: Valentina Kuzurman, Ph.D. and Raisa Mamanova, M.S.

Publication: Available at Materials of the Scientific and Practical Conference in the framework of the Days of Science of Students and Postgraduates of Vladimir State University named after Alexander Grigoryevich and Nikolai Grigoryevich Stoletov (translated from Russian)