arXiv research

(NOTE: per referee comments, this article has been split; it is now superseded by "Existence of thread-wire minimizers" and "Near-wire thread-wire minimizers"; please see http://www.bkstephens.net.) Alt's thread problem asks for least-area surfaces bounding a fixed "wire" curve and a movable "thread" curve of length L.…

Serenity optimizes neural network execution for edge devices by scheduling with optimal memory footprint.

Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature $k$ in $\mathbb{R}^n$ (a wire). For a class of curves, that we call nice wires, the wire billiard map is area preserving twist map of the cylinder. In this paper we are investigating whether the basic features of conventional planar b…

Decussation improves robustness of 3D neural networks.

There are several types of equation of motion of elastic wires. In this paper, we treat an equation taking account of the thickness of wire. The equation was introduced by Caflisch and Maddocks on plane curves, and they proved the existence of solutions. Koiso and Sugimoto generalized the result to any dimensional Eucl…

Theoretical comparison of three invariance approaches in deep linear networks.

Researchers use Gaussian Process Regression to improve accuracy of a low-cost hot-wire anemometer.

Differentiable NAS frameworks grow networks wider and deeper, revealing biases in wiring evolution.

Enneper's wire, the image of the circle of radius $R$ under Enneper's surface, bounds exactly three minimal surfaces for $R$ between 1 and $\sqrt 3$, and these three surfaces depend continuously on $R$. The other two surfaces (besides Enneper's surface) are absolute minima of area among disk-type surfaces bounded by En…

Unbraided wiring diagrams for Stein fillings of lens spaces are described.

RicciNets prunes neural networks by removing edges of low importance based on Ricci curvature, reducing FLOPs by 35%.

Generative model for morphisms in free categories learns from wiring diagrams.

In-vivo examination of the physical connectivity of axonal projections through the white matter of the human brain is made possible by diffusion weighted magnetic resonance imaging (dMRI) Analysis of dMRI commonly considers derived scalar metrics such as fractional anisotrophy as proxies for "white matter integrity," a…

Soap films hanging from a wire frame are studied in the framework of capillarity theory. Minimizers in the corresponding variational problem are known to consist of positive volume regions with boundaries of constant mean curvature/pressure, possibly connected by "collapsed" minimal surfaces. We prove here that collaps…

EM-GAN uses GANs for fast stress analysis of multi-segment interconnects.

We study association between macroeconomic news and stock market returns using the statistical theory of copulas, and a new comprehensive measure of news based on the indexing of news wires. We find the impact of economic news on equity returns to be nonlinear and asymmetric. In particular, controlling for economic con…

Estimates for graph embeddings into symmetric spaces derived from coarse geometry.

We study a novel economic network (supply chain) comprised of wire transfers (electronic payment transactions) among the universe of firms in Brazil (6.2 million firms). We construct a directed and weighted network in which vertices represent cities and edges connote pairwise economic dependence between cities. Cities …

We give an upper bound on the z-degree of the Kauffman polynomial of a link, using bridges of length greater than one which are separated in some tangle decomposition of a link diagram. We construct some examples by wiring together rational tangles.

Current algorithms for deep learning probably cannot run in the brain because they rely on weight transport, where forward-path neurons transmit their synaptic weights to a feedback path, in a way that is likely impossible biologically. An algorithm called feedback alignment achieves deep learning without weight transp…

Transfer learning is a popular practice in deep neural networks, but fine-tuning of large number of parameters is a hard task due to the complex wiring of neurons between splitting layers and imbalance distributions of data in pretrained and transferred domains. The reconstruction of the original wiring for the target …

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…

Paper uses CNN to predict process parameters from molten pool data in WLAM.

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 …

Survey of integrable billiard models and inequalities.

The paper explores knots with equal bridge and braid index, conjecturing they have a unique equilibrium state.

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…

We introduce a new neural network model, together with a tractable and monotone online learning algorithm. Our model describes feed-forward networks for classification, with one output node for each class. The only nonlinear operation is rectification using a ReLU function with a bias. However, there is a rectifier on …

New neural net learns time-reversible symplectic dynamics.

Study on dynamic curves with elastic energy and spontaneous curvature.

Method finds differential equations for integrable billiard tables.

Low-density parity-check codes, a class of capacity-approaching linear codes, are particularly recognized for their efficient decoding scheme. The decoding scheme, known as the sum-product, is an iterative algorithm consisting of passing messages between variable and check nodes of the factor graph. The sum-product alg…

Generative AI agents improve ERP systems by automating complex financial tasks.

Study on evolving interfaces with complex curvature and density effects.

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational memory. In this paper, we propose to separate the storage of individual experience…

Bayesian method reconstructs neural network memories from connectivity.

The introduction of automated flight control and management systems have made possible aircraft designs that sacrifice arodynamic stability in order to incorporate stealth technology intro their shape, operate more efficiently, and are highly maneuverable. Therefore, modern flight management systems are reliant on mult…

Estimating arbitrary quantities of interest (QoIs) that are non-linear operators of complex, expensive-to-evaluate, black-box functions is a challenging problem due to missing domain knowledge and finite budgets. Bayesian optimal design of experiments (BODE) is a family of methods that identify an optimal design of exp…

Many transformations in deep learning architectures are sparsely connected. When such transformations cannot be designed by hand, they can be learned, even through plain backpropagation, for instance in attention mechanisms. However, during learning, such sparse structures are often represented in a dense form, as we d…

We investigate the elastic behavior of knotted loops of springy wire. To this end we minimize the classic bending energy $E_{\text{bend}}=\intκ^2$ together with a small multiple of ropelength $\mathcal R=\text{length}/\text{thickness}$ in order to penalize selfintersection. Our main objective is to characterize elastic…

Study on elastic curves with variable stiffness, derived from bending energy.

We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the fundamental group of their complements. It is derived from the peripheral struct…

Optimizes QoS in FSO links over South Africa using ensemble learning.

A quantum state generation method that respects physical constraints.

Deep reinforcement learning has obtained significant breakthroughs in recent years. Most methods in deep-RL achieve good results via the maximization of the reward signal provided by the environment, typically in the form of discounted cumulative returns. Such reward signals represent the immediate feedback of a partic…

Many systems of interest in science and engineering are made up of interacting subsystems. These subsystems, in turn, could be made up of collections of smaller interacting subsystems and so on. In a series of papers David Spivak with collaborators formalized these kinds of structures (systems of systems) as algebras o…

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…

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis, Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan, January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give, respectively,…