A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unbraided wiring diagrams for Stein fillings of lens spaces are described.
Generative model for morphisms in free categories learns from wiring diagrams.
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.
(NOTE: per referee comments, this article has been split; it is now superseded by "Existence of thread-wire minimizers" and "Near-wire thread-wire minimizers"; please see http://www.bkstephens.net.)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.…
Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature in (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 under Enneper's surface, bounds exactly three minimal surfaces for between 1 and , and these three surfaces depend continuously on . The other two surfaces (besides Enneper's surface) are absolute minima of area among disk-type surfaces bounded by En…
RicciNets prunes neural networks by removing edges of low importance based on Ricci curvature, reducing FLOPs by 35%.
Study on supply chain networks using wire transfers in Brazil.
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…
Bayesian method reconstructs neural network memories from connectivity.
EM-GAN uses GANs for fast stress analysis of multi-segment interconnects.
Serenity optimizes neural network execution for edge devices by scheduling with optimal memory footprint.
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…
Soap films collapse only if their bulk has negative pressure, forming convex shapes.
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…
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…
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,…
Unified 3D R-matrices from quantum cluster algebra.
Estimates for graph embeddings into symmetric spaces derived from coarse geometry.
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.
The paper refines transformations of lattice diagrams and introduces dotted diagrams.
This note explains how to transform Heegaard diagrams into framed link diagrams.
New minimal link diagrams found, including torus links and homogeneous ones.
Algorithm converts Kirby diagrams to trisection diagrams for 4-manifolds.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering …
Study categorizes knots and links as rigid or shaky based on Reidemeister moves.
Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Problems on region choices for knot and link diagrams solved using Alexander numbering.