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A fundamental issue in causal inference for Big Observational Data is confounding due to covariate imbalances between treatment groups. This can be addressed by designing the data prior to analysis. Existing design methods, developed for…
A relatively simple and accurate analytical model for studying the reflectivity of neutron multilayer monochromators and supermirrors is proposed. Design conditions that must be fulfilled in order to reach the maximum reflectivity are…
Motivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank $r$ and with bounded subdeterminants. In particular, we study the…
A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in…
This paper considers the estimation of treatment effects in randomized experiments with complex experimental designs, including cases with interference between units. We develop a design-based estimation theory for arbitrary experimental…
An RNA secondary structure is designable if there is an RNA sequence which can attain its maximum number of base pairs only by adopting that structure. The combinatorial RNA design problem, introduced by Hale\v{s} et al. in 2016, is to…
We introduce a novel LLM based solution design approach that utilizes combinatorial optimization and sampling. Specifically, a set of factors that influence the quality of the solution are identified. They typically include factors that…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
From self-assembly and protein folding to combinatorial metamaterials, a key challenge in material design is finding the right combination of interacting building blocks that yield targeted properties. Such structures are fiendishly…
Decision trees are an extremely popular machine learning technique. Unfortunately, overfitting in decision trees still remains an open issue that sometimes prevents achieving good performance. In this work, we present a novel approach for…
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…
A $t$-$(n,d,\lambda)$ design over ${\mathbb F}_q$, or a subspace design, is a collection of $d$-dimensional subspaces of ${\mathbb F}_q^n$, called blocks, with the property that every $t$-dimensional subspace of ${\mathbb F}_q^n$ is…
We have established the association matrix that expresses the estimator of effects under baseline parameterization, which has been considered in some recent literature, in an equivalent form as a linear combination of estimators of effects…
In this paper, we provide a criterion for determining whether multiple shells support a $t$-design. We construct as a corollary an infinite series of $2$-designs using power residue codes.
A residual design ${\cal{D}}_B$ with respect to a block $B$ of a given design $\cal{D}$ is defined to be linearly embeddable over $GF(p)$ if the $p$-ranks of the incidence matrices of ${\cal{D}}_B$ and $\cal{D}$ differ by one. A sufficient…
Designing a multi-layer optical system with designated optical characteristics is an inverse design problem in which the resulting design is determined by several discrete and continuous parameters. In particular, we consider three design…
We construct validation designs $Z_m$ aimed at estimating the integrated squared prediction error of a given design $X_n$. Our approach is based on the minimization of a maximum mean discrepancy for a particular kernel, conditional on…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…
Topological descriptors, such as the Euler characteristic function and the persistence diagram, have grown increasingly popular for representing complex data. Recent work showed that a carefully chosen set of these descriptors encodes all…