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.
Examines how meridians and parallels help in map drawing.
Mathematical analysis shows Delisle-Euler map methods are optimal.
Euler and Delisle developed a map method for the Russian Empire, which is now outperformed by the Lambert conformal conical projection.
We report on the works of Euler and Chebyshev on the drawing of geographical maps. We point out relations with questions about the fitting of garments that were studied by Chebyshev.
New techniques in Khovanov homology help distinguish exotic surfaces in 4-ball.
We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the context of iteration of a rational map of degree two or more, extends to finitely gene…
New concept of k-holes in simple drawings and convex drawings.
The paper examines isometric timelike surfaces in 4D Minkowski space.
The self-organizing methods were used for the investigation of financial market. As an example we consider data time-series of Dow Jones index for the years 2002-2003 (R. Mantegna, cond-mat/9802256). In order to reveal new structures in stock market behavior of the companies drawing up Dow Jones index we apply SOM (Sel…
VQ-DRAW compresses images and generates realistic samples.
Rotation systems can't always be drawn in surfaces.
New framework models high-Hopf-index hopfions using generalized fold maps.
We present a system for identifying conceptual shifts between visual categories, which will form the basis for a co-creative drawing system to help users draw more creative sketches. The system recognizes human sketches and matches them to structurally similar sketches from categories to which they do not belong. This …
We propose a restricted collapsed draw (RCD) sampler, a general Markov chain Monte Carlo sampler of simultaneous draws from a hierarchical Chinese restaurant process (HCRP) with restriction. Models that require simultaneous draws from a hierarchical Dirichlet process with restriction, such as infinite Hidden markov mod…
We discuss recent results and open questions on the broad theme of (Nielsen) realization problems. Beyond realizing subgroups of mapping class groups, there are many other natural instances where one can ask if a surjection from a group of diffeomorphisms of a manifold to another group admits a section over particular …
Unsupervised image-to-image translation methods learn to map images in a given class to an analogous image in a different class, drawing on unstructured (non-registered) datasets of images. While remarkably successful, current methods require access to many images in both source and destination classes at training time…
Stable blowup profile identified for wave maps in all dimensions.
Criteria found for graph drawings on surfaces.
How can deep learning systems flexibly reuse their knowledge? Toward this goal, we propose a new class of challenges, and a class of architectures that can solve them. The challenges are meta-mappings, which involve systematically transforming task behaviors to adapt to new tasks zero-shot. The key to achieving these c…
Visualizes DNNs using topographic maps for better understanding.
The study characterizes a complex curve of residueless meromorphic differentials on elliptic curves.
We present sketch-rnn, a recurrent neural network (RNN) able to construct stroke-based drawings of common objects. The model is trained on thousands of crude human-drawn images representing hundreds of classes. We outline a framework for conditional and unconditional sketch generation, and describe new robust training …
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates a graph embedding approac…
CoSE models complex drawings by treating strokes as a collection that can be composed.
New method for conditional sampling using M-GANs, likely-free inference.
The Clock Drawing Test (CDT) is a rapid, inexpensive, and popular neuropsychological screening tool for cognitive conditions. The Digital Clock Drawing Test (dCDT) uses novel software to analyze data from a digitizing ballpoint pen that reports its position with considerable spatial and temporal precision, making possi…
There are three main thrusts to this article: a new proof of Levi's Enlargement Lemma for pseudoline arrangements in the real projective plane; a new characterization of pseudolinear drawings of the complete graph; and proofs that pseudolinear and convex drawings of have O and O, respect…
This note provides an elementary proof of the folklore fact that draws from a Dirichlet distribution (with parameters less than 1) are typically sparse (most coordinates are small).
We point out, and draw some consequences of, the fact that the Poisson Lie group G* dual to G=GL_n(C) (with its standard complex Poisson structure) may be identified with a certain moduli space of meromorphic connections on the unit disc having an irregular singularity at the origin. The Riemann-Hilbert map for such co…
Paper finds Dutch Draw optimal baseline for binary classification.
A {\em good drawing\/} of is a drawing of the complete graph with vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than once; and no three edges all cross at the same point. Gioan's Theorem asserts that any two good drawings of that have the same rotations …
In recent years a lot of attention has been paid to topological spaces which are a bit more general than smooth manifolds - orbifolds. Orbifolds are intuitively speaking manifolds with some singularities. The formal definition is also modelled on that of manifolds, an orbifold is a topological space which locally is ho…
This study compares two methods for sampling with transport maps, finding flow-based proposals work better for multimodal distributions.
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric variational family, which adapts its shape to match complex posterior distributions. T…
We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible sheaves on the surface itself. Consequently, our category can be described as cons…
We study a bad arm existing checking problem in which a player's task is to judge whether a positive arm exists or not among given K arms by drawing as small number of arms as possible. Here, an arm is positive if its expected loss suffered by drawing the arm is at least a given threshold. This problem is a formalizati…
In this paper, we explore creative image generation constrained by small data. To partially automate the creation of cartoon sketches consistent with a specific designer's style, where acquiring a very large original image set is impossible or cost prohibitive, we exploit domain specific knowledge for a huge reduction …
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…
Anosov representations give a higher-rank analogue of convex cocompactness in a rank-one Lie group which shares many of its good geometric and dynamical properties; geometric finiteness in rank one may be seen as a controlled weakening of convex cocompactness to allow for isolated failures of hyperbolicity. We introduc…
New method learns high-quality Laplacian representations for reinforcement learning.
We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…
CupNet prunes neural nets for cup-shaped data.
A new method for spotting symbols in CAD images reduces annotation costs and improves accuracy.
New bounds show limitations of sample-wise information-theoretic generalization.
The paper constructs denoisers that recover the Brenier map from higher-order score functions.
We develop a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara in 1991. This class contains as a special case the Möbius energy. For the Möbius energy, due to the celebrated work of Freedman, He, and Wang, we have a relatively good understanding. Their approch is crucially based…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates two graph embedding appro…
Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other criteria. We introduce an optimization framework, Stress-Plus-X (SPX), that sim…