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A self-replicator is usually understood to be an object of definite form that promotes the conversion of materials in its environment into a nearly identical copy of itself. The challenge of engineering novel, micro- or nano-scale…
It is a fact of our existence, that no matter where we are, we most often find ourselves either hearing, seeing, talking, or even engaged in design related activities. Despite this reality, the notion of 'design', and in particular…
Repetition, a basic form of artistic creation, appears in most musical works and delivers enthralling aesthetic experiences.
We present a recursive procedure, which is based on the small time expansion of the propagator, in order to generate a semi-classical expansion of the \textit{quantum action} for a quantum mechanical potential in arbitrary dimensions. In…
Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…
Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple…
Inspired by protein folding, we explored the construction of three-dimensional structures and machines from one-dimensional chains of simple building blocks. This approach not only allows us to recreate the self-replication mechanism…
Factorial designs are widely used in agriculture, engineering, and the social sciences to study the causal effects of several factors simultaneously on a response. The objective of such a design is to estimate all factorial effects of…
A novel approach for structure alignment is presented, where the key ingredients are: (1) An error function formulation of the problem simultaneously in terms of binary (Potts) assignment variables and real-valued atomic coordinates. (2)…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
We introduce and investigate binary $(k,k)$-designs -- combinatorial structures which are related to binary orthogonal arrays. We derive general linear programming bound and propose as a consequence a universal bound on the minimum possible…
This paper develops an explicit and implementable framework for constructing spherical designs by lifting point sets from tight fusion frames. By combining existing ingredients, we obtain, in every dimension, explicit spherical $5$-designs…
The choice titration procedure presents a subject with a repeated choice between a standard option that always provides the same reward and an adjusting option for which the reward schedule is adjusted based on the subjects previous…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…
This paper defends an augmented cognitively oriented "generic-design hypothesis": There are both significant similarities between the design activities implemented in different situations and crucial differences between these and other…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
In this paper, we investigate the reconstruction of permutations on {1, 2, ..., n} from betweenness constraints involving the minimum and the maximum element located between t and t+1, for all t=1, 2, ..., n-1. We propose two variants of…
They run our lives, if you believe the hype in the news, but there is no precise definition of "algorithms" which is generally accepted by the mathematicians, logicians and computer scientists who create and study them. My main aims here…
In this paper, a new non-search based synthesis algorithm for reversible circuits is proposed. Compared with the widely used search-based methods, our algorithm is guarantied to produce a result and can lead to a solution with much fewer…