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Motivated by children inventing creatively laws on how to add or multiply fractions, we introduce four fraction operations and discover some of their properties.

Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)

We study the problem of adversarially robust self-supervised learning on graphs. In the contrastive learning framework, we introduce a new method that increases the adversarial robustness of the learned representations through i)…

Providing feedback on programming assignments manually is a tedious, error prone, and time-consuming task. In this paper, we motivate and address the problem of generating feedback on performance aspects in introductory programming…

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix…

We show new upper and lower bounds for the complexity of implementation of a sequence of Boolean matrices proposed by Kaski et al. (arXiv:1208.0554) with additive circuits.

Some aspects of the ELectrical EXplicit (ELEX) scheme for using explicit integration schemes in circuit simulation are discussed. It is pointed out that the parallel resistor approach, presented earlier to address singular matrix issues…

In this innovative practice work-in-progress paper, we compare two different methods to teach machine learning concepts to undergraduate students in Electrical Engineering. While machine learning is now being offered as a senior-level…

An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is…

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…

In this paper, we discuss four errors introductory physics students make when attempting to add two inverse-square law vectors. We observe multiple instances in which students 1) add vectors as if they were scalars, 2) project the $r$ (or…

We propose a novel class incremental learning approach by incorporating a feature augmentation technique motivated by adversarial attacks. We employ a classifier learned in the past to complement training examples rather than simply play a…

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…

The construction of attractors of a dissipative difference equation is usually based on compactness assumptions. In this paper, we replace them with contractivity assumptions under which the pullback and forward attractors are identical. As…

In this report, we briefly describe the most recent results from tests on the calculable resistance prototypes from the Electrical Standards Metrology Laboratory from Inmetro (Lampe/Inmetro). These prototypes were built using a different…

In-circuit impedance provides key information for many EMC applications. The inductive coupling approach is a promising method for in-circuit impedance measurement because its measurement setups have no direct electrical contact with the…

A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. Depending on the approach used, the…

While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…

Computation holds great potential for introducing new opportunities for creativity and exploration into the physics curriculum. At the University of Oslo we have begun development of a new class of assignment called computational essays to…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…