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Diffusion models excel at generation, but their latent spaces are high dimensional and not explicitly organized for interpretation or control. We introduce ConDA (Contrastive Diffusion Alignment), a plug-and-play geometry layer that applies…
We address the problem of controlling a dynamical system governing the motion of a 3D weighted shape changing body swimming in a perfect fluid. The rigid displacement of the swimmer results from the exchange of momentum between prescribed…
An electrokinetically-driven deterministic lateral displacement (e-DLD) device is proposed for the continuous, two-dimensional fractionation of suspensions in microfluidic platforms. The suspended species are driven through an array of…
We propose a necessary and sufficient test to determine whether a solution for a general quadratic program with two quadratic constraints (QC2QP) can be computed from that of a specific convex semidefinite relaxation, in which case we say…
In this paper, we compute a conservative approximation of the path-connected components of the free space of a rigid object in a 2D workspace in order to solve two closely related problems: to determine whether there exists a collision-free…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
For a theory with first and second class constraints, we propose a procedure for conversion of second class constraints based on deformation the structure of local symmetries of the Lagrangian formulation. It does not require extension or…
On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…
Directional depinning dynamics of a 2D dusty plasma solid modulated by a 2D square periodic substrate are investigated using Langevin dynamical simulations. We observe prominent directional locking effects when the direction of the external…
Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive…
This paper studies bandit convex optimization with constraints, where the learner aims to generate a sequence of decisions under partial information of loss functions such that the cumulative loss is reduced as well as the cumulative…
We study quantum phase transitions out of the fracton ordered phase of the $\mathbb{Z}_N$ X-cube model. These phase transitions occur when various types of sub-dimensional excitations and their composites are condensed. The condensed phases…
Similar to the notion of h-adaptivity, where the discretization resolution is adaptively changed, I propose the notion of model adaptivity, where the underlying model (the governing equations) is adaptively changed in space and time.…
The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our…
We establish a framework that allows to prove Gamma-converge of functionals of Lagrangian form on spaces of trajectories based on convergence of viscosity solutions of associated Hamilton-Jacobi equations. Gamma convergence follows from a:…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
We derive the quasiconvex relaxation of the Biot-type energy density $\lVert\sqrt{\operatorname{D}\varphi^T \operatorname{D}\varphi}-I_2\rVert^2$ for planar mappings $\varphi\colon\mathbb{R}^2\to \mathbb{R}^2$ in two different scenarios.…