arXiv research

New AI algorithm improves multi-layer optical film design efficiency.

In this paper we first review the covering space method with constrained BV functions for solving the classical Plateau's problem. Next, we carefully analyze some interesting examples of soap films compatible with the covering space method: in particular, the case of a soap film only partially wetting a space curve, a …

Solves the film scheduling and staggered showtimes problem for movie theaters.

In this paper we provide the first examples of non-flat soap films proven to span tetrahedra. These are members of a continuous two parameter family of soap films with tetrahedral boundaries. Of particular interest is a two parameter subfamily where each spanning soap film has the property that two minimal surfaces mee…

Soap films collapse only if their bulk has negative pressure, forming convex shapes.

Derives equilibrium law for Plateau borders in wet soap films and foams.

Recent breakthroughs in computer vision and natural language processing have spurred interest in challenging multi-modal tasks such as visual question-answering and visual dialogue. For such tasks, one successful approach is to condition image-based convolutional network computation on language via Feature-wise Linear …

We introduce a general-purpose conditioning method for neural networks called FiLM: Feature-wise Linear Modulation. FiLM layers influence neural network computation via a simple, feature-wise affine transformation based on conditioning information. We show that FiLM layers are highly effective for visual reasoning - an…

Extends symmetry and rigidity to surfaces with soap film-like singularities.

We prove existence and a.e. regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in R^3. The energy of a film is defined to be the sum of its surface area and the length of its singular branched set. The class of surfaces over which area is minimized includes images of disks, …

A soap film is actually a thin solid fluid bounded by two surfaces of opposite orientation. It is natural to model the film using one polyhedron for each side. Two problems are to get the polyhedra for both sides to be in the same place without canceling each other out and to model triple junctions without introducing …

Develops a geometric framework for soap film instabilities.

GNN-FiLM uses feature-wise linear modulation to improve graph neural networks.

What are the possible shapes of various things and why? For instance, when a closed wire or a frame is dipped into a soap solution and is raised up from the solution, the surface spanning the wire is a soap film. What are the possible shapes of soap films and why? Or, for instance, why is DNA like a double spiral stair…

Smoothness of collapsed regions in soap films is proven, indicating wetted singularities.

Classifies soap film surfaces with vertical potentials.

For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surface spanning the boundary.

A deep learning algorithm designs low-cost SPP films.

FiLM improves deep learning for long-term time series forecasting.

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoi…

Plateau's soap film problem is to find a surface of least area spanning a given boundary. We begin with a compact orientable $(n-2)$-dimensional submanifold $M$ of $\R^n$. If $M$ is connected, we say a compact set $X$ "spans" $M$ if $X$ intersects every Jordan curve whose linking number with $M$ is 1. Picture a soap fi…

Automated malaria diagnosis from field slides achieves accurate results.

Improved continual learning method using variational inference and FiLM layers.

Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-κ^2$. Using the cone total curvature $TC(Γ)$ of a graph $Γ$ which was introduced by Gulliver and Yamada Math. Z. 2006, we prove that the density at any point of a soap film-like…

Motivated by the study of the equilibrium equations for a soap film hanging from a wire frame, we prove a compactness theorem for surfaces with asymptotically vanishing mean curvature and fixed or converging boundaries. In particular, we obtain sufficient geometric conditions for the minimal surfaces spanned by a given…

New method finds all thin film structures from reflectometry data.

Open problems in billiards and optics from a workshop.

New method generates optical vortices in any knot shape.

Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow as an inverse problem is ill-posed. Standard approaches to determine optical flow…

Paper tackles depth estimation and optic disc-cup segmentation from color fundus images.

Method detects and locates eavesdropping in optical links.

Optical ESNs enable flexible, efficient machine learning with reduced energy.

GANPOP uses deep learning to estimate optical properties from single images, improving accuracy over existing methods.

Paper develops a deforestation detection system using optical and SAR data.

Study of optical geometries with intrinsic torsion in general relativity.

Optical DNNet boosts accuracy with multiple frequency-channels.

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution …

Paper develops machine learning to translate SAR to optical images for easier interpretation.

Glaucoma is the second leading cause of blindness all over the world, with approximately 60 million cases reported worldwide in 2010. If undiagnosed in time, glaucoma causes irreversible damage to the optic nerve leading to blindness. The optic nerve head examination, which involves measurement of cup-to-disc ratio, is…

We describe two applications of machine learning in the context of IP/Optical networks. The first one allows agile management of resources at a core IP/Optical network by using machine learning for short-term and long-term prediction of traffic flows and joint global optimization of IP and optical layers using colorles…

Express Wavenet reduces neural network parameters to 1% of standard networks.

The paper solves the isoperimetric problem in Riemannian optical geometry, proving circles minimize lengths with area constraints.

Derives Levi-Civita connection formulas for specific geometries.

Designs chiral photonic structures using machine learning for efficient optical properties.

Novel approach localizes optic disc and fovea centers efficiently.

This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4πmust be smoothly embedded. Related results are proved for varifolds and for soap film surfaces.

New methods for constructing null fluid metrics and solving optical lift conjectures.

We discuss recently emerging applications of the state-of-art deep learning methods on optical microscopy and microscopic image reconstruction, which enable new transformations among different modes and modalities of microscopic imaging, driven entirely by image data. We believe that deep learning will fundamentally ch…