Related papers: A new and flexible method for constructing designs…
The Handbook of Combinatorial Designs catalogs many types of combinatorial designs, together with lists of open instances for which existence has not yet been determined. We develop a constructive protocol CPro1, which uses Large Language…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Quantifying the effect of uncertainties in systems where only point evaluations in the stochastic domain but no regularity conditions are available is limited to sampling-based techniques. This work presents an adaptive sequential…
In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of…
Text embeddings are essential for many tasks, such as document retrieval, clustering, and semantic similarity assessment. In this paper, we study how to contrastively train text embedding models in a compute-optimal fashion, given a suite…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
We introduce CODS (Computational Optimization in Design Space), a theoretical model that frames computational design as a constrained optimization problem over a structured, multi-dimensional design space. Unlike existing methods that rely…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
Do you want to know what an anti-chiece Latin square is? Or what a non-consecutive toroidal modular Latin square is? We invented a ton of new types of Latin squares, some inspired by existing Sudoku variations. We can't wait to introduce…
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…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
In order to obtain a metasurface structure capable of filtering the light of a specific wavelength in the visible band, traditional method usually traverses the space consisting of possible designs, searching for a potentially satisfying…
The rapidly growing ecosystem of Large Language Models (LLMs) makes it increasingly challenging to manage and utilize the vast and dynamic pool of models effectively. We propose LOCUS, a method that produces low-dimensional vector…
It is well-known that many famous pooling designs are constructed from mathematical structures by the "containment matrix" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree…
Optimal design of experiments for correlated processes is an increasingly relevant and active research topic. Present methods have restricted possibilities to judge their quality. To fill this gap, we complement the virtual noise approach…
To understand the universe and to interpret the cosmological parameters governing its evolution it is necessary to contrast the data from galaxy surveys with simulation. Typically it entails using computationally expensive N -body…
We report a method to convert discrete representations of molecules to and from a multidimensional continuous representation. This model allows us to generate new molecules for efficient exploration and optimization through open-ended…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
In order to be applicable in real-world scenario, Boundary Attacks (BAs) were proposed and ensured one hundred percent attack success rate with only decision information. However, existing BA methods craft adversarial examples by leveraging…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…