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Image-generation models are changing how we express ourselves in visual art. However, what people think of AI-generated art is still largely unexplored, especially compared to traditional art. In this paper, we present the design of an…
Nowadays, technological advances have influenced all human activities, creating new dynamics and ways of communication. In this context, some artists have incorporated these advances in their creative process, giving rise to unique…
The diversity of painting styles represents a rich visual vocabulary for the construction of an image. The degree to which one may learn and parsimoniously capture this visual vocabulary measures our understanding of the higher level…
Synthetic polymers are versatile and widely used materials. Similar to small organic molecules, a large chemical space of such materials is hypothetically accessible. Computational property prediction and virtual screening can accelerate…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Data-driven generative modeling has made remarkable progress by leveraging the power of deep neural networks. A reoccurring challenge is how to enable a model to generate a rich variety of samples from the entire target distribution, rather…
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that…
In this work, we propose a complete framework that generates visual art. Unlike previous stylization methods that are not flexible with style parameters (i.e., they allow stylization with only one style image, a single stylization text or…
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…
In creative design, where aesthetics play a crucial role in determining the quality of outcomes, there are often multiple worthwhile possibilities, rather than a single ``best'' design. This challenge is compounded in the use of…
We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy based solvers in terms of decorated graphs. Under the…
We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the Bernstein basis; it can be seen as generalization of the…
We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies…
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight spans of finite metric spaces…
Modern image generative models show remarkable sample quality when trained on a single domain or class of objects. In this work, we introduce a generative adversarial network that can simultaneously generate aligned image samples from…
We present a framework for automating generative deep learning with a specific focus on artistic applications. The framework provides opportunities to hand over creative responsibilities to a generative system as targets for automation. For…
Graph motif, defined as the microstructure that appears repeatedly in a large graph, reveals important topological characteristics of the large graph and has gained increasing attention in power system analysis regarding reliability,…
Multi-omics data offer unprecedented insights into complex biological systems, yet their high dimensionality, sparsity, and intricate interactions pose significant analytical challenges. Network-based approaches have advanced multi-omics…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…