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A topological interlocking assembly is an arrangement of blocks, where all blocks are kinematically constrained by their neighboring blocks and a fixed frame. This concept has been known for a long time, attracting recent interest due to…
Ternary logic is expected to increase the area efficiency of VLSI due to its expressiveness compared to the traditional binary logic. This paper proposes a new symmetric ternary logic and a systematic logic composition methodology that…
Over the past decade a large family of spintronic devices have been proposed as candidates for replacing CMOS for future digital logic circuits. Using the recently developed Modular Approach framework, we investigate and identify the…
Kinematics of mechanisms is intricately coupled to their geometry and their utility often arises out of the ability to perform reproducible motion with fewer actuating degrees of freedom. In this article, we explore the assembly of…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
The space of elliptic modular forms of fixed weight and level can be identfied with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying…
In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues,…
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…
Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Geometric lattice has widely used in diverse fields, especially search algorithm design which plays important role…
It is well known that knots are countable in ordinary knot theory. Recently, knots {\it with intersections} have raised a certain interest, and have been found to have physical applications. We point out that such knots --equivalence…
We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…
This paper introduces the chain lattice, a hierarchical truss structure comprising two interpenetrating lattices. One lattice toughens the material and prevents catastrophic localized failure while the other lattice serves as a porous…
Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…
In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set. Further we describe a biordered subset satisfying certain…
Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
Inverse design can be a useful strategy for discovering interactions that drive particles to spontaneously self-assemble into a desired structure. Here, we extend an inverse design methodology--relative entropy optimization--to determine…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…