Related papers: Generating derivative superstructures for systems …

This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…

We present an algorithm for generating all derivative superstructures--for arbitrary parent structures and for any number of atom types. This algorithm enumerates superlattices and atomic configurations in a geometry-independent way. The…

We considered the problem how to handle the exploding number of possibilities to be sorted into irreducible classes by using a clustering tool when its input capacity cannot accommodate the total number of the possibility. Concrete…

Finite temperature disordered solid solutions and magnetic materials are difficult to study directly using first principles calculations, due to the large unit cells and many independent samples that are required. In this work, we develop a…

We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give an explicit sufficient…

The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…

Generating irreducible site-occupancy configurations by taking advantage of crystal symmetry is a ubiquitous method for accelerating of disordered structure prediction, which plays an important role in condensed matter physics and material…

In this paper, we study the construction of structural models for the description of substitutional defects in crystalline materials. Predicting and designing the atomic structures in such systems is highly challenging due to the…

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…

One of the great challenges of modern science is to faithfully model, and understand, matter at a wide range of scales. Starting with atoms, the vastness of the space of possible configurations poses a formidable challenge to any simulation…

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…

In this paper I propose a new model for representing the formation energies of multicomponent crystalline alloys as a function of atom types. In the cases when displacements of atoms from their equilibrium positions are not large, the…

We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…

This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…

A general method is presented for modeling high entropy alloys as ensembles of randomly sampled, ordered configurations on a given lattice. Statistical mechanics is applied post hoc to derive the ensemble properties as a function of…

We propose approximate and accurate formulas for the number of electron configurations in hot plasmas. Such a quantity is an ingredient of algorithms devoted to the generation of configurations or superconfigurations, which is a…

A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose…

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…