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We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self…
Judging scholarly posters creates a challenge to assign the judges efficiently. If there are many posters and few reviews per judge, the commonly used Balanced Incomplete Block Design is not a feasible option. An additional challenge is an…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
This is the first paper that provides a systematic treatment of the $r$-dimensional PTE problem in additive number theory, abbreviated by PTE$_r$, through its connection with combinatorial design theory, the branch of combinatorial…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using…
Designing 3D objects from scratch is difficult, especially when the user intent is fuzzy without a clear target form. In the spirit of modeling-by-example, we facilitate design by providing reference and inspiration from existing model…
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…
The intersection problem for a pair of 2-(v, 3, 1) directed designs and 2-(v, 4, 1) directed designs is solved by Fu in 1983 and by Mahmoodian and Soltankhah in 1996, respectively. In this paper we determine the intersection problem for…
Design erosion is a persistent problem within the software engineering discipline. Software designs tend to deteriorate over time and there is a need for tools and techniques that support software architects when dealing with legacy…
Major advancements in the capabilities of computer vision models have been primarily fueled by rapid expansion of datasets, model parameters, and computational budgets, leading to ever-increasing demands on computational infrastructure.…
Recently multi-access coded caching schemes with number of users different from the number of caches obtained from a special case of resolvable designs called Cross Resolvable Designs (CRDs) have been reported and a new performance metric…
The construction of Superintegrable models with rotational symmetry and two integrals of any integer degree greater than 3 was completed in [9] only for the so called simple case. It is extended here to a more general situation and several…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
We study $T$-designs in the nonbinary Johnson scheme. This scheme generalizes both the Johnson and Hamming schemes and admits a bivariate $Q$-polynomial structure. Zhu (2021) provided a combinatorial characterization of $T$-designs in this…
In this paper, we introduce a model of a single-failure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the well-studied index coding problem. The relation between the…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
In this article, we show the existence of large sets $\operatorname{LS}_2[3](2,k,v)$ for infinitely many values of $k$ and $v$. The exact condition is $v \geq 8$ and $0 \leq k \leq v$ such that for the remainders $\bar{v}$ and $\bar{k}$ of…
A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…