Related papers: A complementary design theory for doubling
The paper addresses the problem of defining families of ordered sequences $\{x_i\}_{i\in N}$ of elements of a compact subset $X$ of $R^d$ whose prefixes $X_n=\{x_i\}_{i=1}^{n}$, for all orders $n$, have good space-filling properties as…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest…
As an extension of Eisenbud's matrix factorization into the non-commutative realm, X.W. Chen introduced the concept of module factorizations over an arbitrary ring. A theorem of Chen establishes a triangle equivalence between the stable…
The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses…
Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs. Each pair in such a partition is called a nested design pair…
B. Xu characterized rank $4$ self-dual association schemes inducing three partial geometric designs by their character tables. We construct such association schemes as Schur rings over abelian $2$-groups.
The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasi-symmetric 2-$(56,12,9)$ and 2-$(57,12,11)$ designs with intersection numbers 0 and 3, and the…
We introduce systematic methods to create optimal designs for order-of-addition (OofA) experiments, those that study the order in which $m$ components are applied---for example, the order in which chemicals are added to a reaction or layers…
We survey partial geometric designs and investigate their concurrences of points. The concurrence matrix of a design, which encodes the concurrences of pairs of points, can be used in the classification of designs in some extent. An…
Two constructions due to Dr\'apal produce a group by modifying exactly one quarter of the Cayley table of another group. We present these constructions in a compact way, and generalize them to Moufang loops, using loop extensions. Both…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
Olmez, in "Symmetric $1\frac{1}{2}$-Designs and $1\frac{1}{2}$-Difference Sets" (2014), introduced the concept of a partial geometric difference set (also referred to as a $1\frac{1}{2}$-design), and showed that partial geometric difference…
We present a simple yet powerful and applicable quadrature based scheme for constructing optimal iterative methods. According to the, still unproved, Kung-Traub conjecture an optimal iterative method based on $n+1$ evaluations could achieve…
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
A partial affine plane of order $n$ is a point-line incidence structure with $n^2$ points and $n$ points on each line, such that every two lines meet in at most one point. In this paper, we show that a partial affine plane of order $n$, $n$…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
The elementary theory of bivariate linear Diophantine equations over polynomial rings is used to construct causal lifting factorizations (elementary matrix decompositions) for causal two-channel FIR perfect reconstruction transfer matrices…
Inverse design coupled with adjoint optimization is a powerful method to design on-chip nanophotonic devices with multi-wavelength and multi-mode optical functionalities. Although only two simulations are required in each iteration of this…
We clarify the mathematical structure underlying unitary $t$-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any $t$-th order polynomial over the design equals the average over the entire…