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Diffusion models offer a powerful means of capturing the manifold of realistic protein structures, enabling rapid design for protein engineering tasks. However, existing approaches observe critical failure modes when precise constraints are…
Symmetrization of topologically ordered wavefunctions is a powerful method for constructing new topological models. Here, we study wavefunctions obtained by symmetrizing quantum double models of a group $G$ in the Projected Entangled Pair…
The cycleGAN is becoming an influential method in medical image synthesis. However, due to a lack of direct constraints between input and synthetic images, the cycleGAN cannot guarantee structural consistency between these two images, and…
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…
Controllable molecular graph generation is essential for material and drug discovery, where generated molecules must satisfy diverse property constraints. While recent advances in graph diffusion models have improved generation quality,…
In this paper, we propose a method to build molecular cages designed to capture a specific substrate. We model a cage as a graph of atoms with coordinates in space, and several constraints on their edges (degree, length and angle). We use a…
Most earlier 3D structure-based molecular generation approaches follow an atom-wise paradigm, incrementally adding atoms to a partially built molecular fragment within protein pockets. These methods, while effective in designing tightly…
We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric…
Recent advances in coarse-grained lattice and off-lattice protein models are reviewed. The sequence dependence of thermodynamical folding properties are investigated and evidence for non-randomness of the binary sequences of good folders…
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…
Parametric CAD models encode entire families of shapes that should, in principle, be easy for designers to explore. However, in practice, parametric CAD models can be difficult to manipulate due to implicit semantic constraints among…
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
In this paper we propose a heuristic technique for distributing points on the surface of a unit n-dimensional Euclidean sphere, generated as the orbit of a finite cyclic subgroup of orthogonal matrices, the so called cyclic group codes.…
A central problem in systems biology is to identify parameter values such that a biological model satisfies some behavioral constraints (\eg, time series). In this paper we focus on parameter synthesis for hybrid (continuous/discrete)…
Designing complex engineered systems requires managing tightly coupled trade-offs between subsystem capabilities and resource requirements. Monotone co-design provides a compositional language for such problems, but its generality does not…
We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…
The paper presents a novel approach to synthesize robust controllers for nonlinear systems along perturbed trajectories. The approach linearizes the system with respect to a reference trajectory. In contrast to existing methods rooted in…
A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property, where design of novel drugs is an important topic in bioinformatics and chemo-informatics. The…
Topologies of large deformation Contact-aided Compliant Mechanisms (CCMs), with self and mutual contact, exemplified via path generation applications, are designed using the continuum synthesis approach. Design domains are parameterized…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…