Related papers: A Combinatorial Theory of Assembly Systems via Gen…

Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…

We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participate in a mutual endeavor. We present a variety of real-world…

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…

In the paper, frameworks for electronic shopping of composite (modular) products are described: (a) multicriteria selection (product is considered as a whole system, it is a traditional approach), (b) combinatorial synthesis (composition)…

A recent paper of Church, Ellenberg, and Farb uses topology and representation theory of the symmetric group to prove enumerative results about square-free polynomials and F-stable maximal tori of the general linear group over the algebraic…

We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…

Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by…

I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to…

Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…

Performance analysis based on modelling consists of two major steps: model construction and model analysis. Formal modelling techniques significantly aid model construction but can exacerbate model analysis. In particular, here we consider…

For systems that self assemble into finite-sized objects, it is sometimes convenient to compute the thermodynamics for a small system where a single assembly can form. However, we show that in the canonical ensemble the use of small systems…

In this paper we prove a series of matching theorems for two sets of Coxeter generators of a finitely generated Coxeter group that identify common features of the two sets of generators. As an application, we describe an algorithm for…

The biological functions of proteins often depend on dynamic structural ensembles. In this work, we develop a flow-based generative modeling approach for learning and sampling the conformational landscapes of proteins. We repurpose highly…

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a larger system that exhibits their collective behavior in a meaningful way. We propose an automaton-based paradigm for…

Modern generative models exhibit unprecedented capabilities to generate extremely realistic data. However, given the inherent compositionality of the real world, reliable use of these models in practical applications requires that they…

The contribution of this paper is threefold: first, it defines a framework for modelling component-based systems, as well as a formalization of integration rules to combine their behavior. This is based on finite state machines (FSM).…

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…