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.
FGN models networks with fractal structures using Gaussian Multiplicative Chaos.
In this pre-print we explore the multi-fractal properties of 1 minute traded volume of the equities which compose the Dow Jones 30. We also evaluate the weights of linear and non-linear dependences in the multi-fractal structure of the observable. Our results show that the multi-fractal nature of traded volume comes es…
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian processes. Particular focus is on clarity and ease of implementation of the estimator an…
This paper evaluates fractal dimension and persistent homology for neural network generalization.
In the work, a comparative correlation and fractal analysis of time series of Bitcoin crypto currency rate and community activities in social networks associated with Bitcoin was conducted. A significant correlation between the Bitcoin rate and the community activities was detected. Time series fractal analysis indicat…
Study fractal and regular geometry in deep neural networks.
Algorithm identifies fractal system's scaling exponents in high dimensions.
Fractal Flow enhances normalizing flows with interpretable latent space and hierarchical modeling.
Paper introduces quadrilateral labyrinth fractals and their properties.
This work proves generalization bounds for neural networks without Lipschitz assumptions.
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…
Study on heat content for domains with fractal boundaries.
Knots can be embedded into fractals like the Menger Sponge and Sierpinski Tetrahedron.
Two-layer neural networks can approximate functions with fractal singularities.
New framework constructs holographic tensor networks using hyperbolic buildings.
Study links fractal structure to generalization in stochastic optimization.
Labyrinth fractals are self-similar dendrites in the unit square that are defined with the help of a labyrinth set or a labyrinth pattern. In the case when the fractal is generated by a horizontally and vertically blocked pattern, the arc between any two points in the fractal has infinite length [Cristea\&Steinsky 2009…
Paper proves existence of area-minimizing submanifolds on almost any manifold with fractal singular sets.
Cohomology fractals illustrate complex 3-manifold properties.
The paper proves prevalent existence and partially determines moduli space of area-minimizing surfaces with fractal singular sets.
We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with thei…
Labyrinth fractals are dendrites in the unit square. They were introduced and studied in the last decade first in the self-similar case [Cristea & Steinsky (2009,2011)], then in the mixed case [Cristea & Steinsky (2017), Cristea & Leobacher (2017)]. Supermixed fractals constitute a significant generalisation of mixed l…
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in with arbitrary dimension .…
Financial markets are well known examples of multi-fractal complex systems that have garnered much interest in their characterization through complex network theory. The recent studies have used correlation based distance metrics for defining and analyzing financial networks. In this work the singularity strength is em…
Estimates heat kernel gradients on fractal-like cable systems.
Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust m…
In this paper two zero-dimensional compact sets with equal topological and fractal dimensions but embedded in Euclidean space by different ways are under study. Diffraction of plane electromagnetic wave propagated and reflected by fractal surfaces is considered for each of these compact sets placed in vacuum. It is obt…
Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance i…
Study fractal dimension for motion without crossing a subset.
Experimental fractal landscape dynamics observed in emulsions.
Paper develops a fractal dimension-based generalization measure.
Constructs area-minimizing submanifolds with fractal singularities.
Smooth fractal trees via analytic generators, preserving combinatorial and geometric properties.
New framework links fractal complexity to separation dimension.
Fractal learning rate schedules accelerate vanilla gradient descent.
Estimates box dimension of fractal interpolation surfaces using oscillation vectors.
Infinite fractal tree solves shortest connection problem.
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
This study analyzes how the Indian stock market reacts to budget announcements using fractal methods.
Study on topological order on fractal geometries, proving no-go theorem and fault-tolerant gates.
Study generalizes Lebesgue curves to new space-filling and fractal sets.
Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures C_k(F_r,.) from geometric measure theory of parallel sets F_r for small distances…
In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose Dow Jones Industrial Average. The analysis consists about quantification of dependence and non-Gaussianity on the multifractal character of fi…
New fractal spaces not quasisymmetric to Loewner spaces discovered.
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous…
New method estimates deep neural network's intrinsic dimension for better generalization.
FCOC framework improves financial volatility forecasting.
We investigate the local fractal properties of the financial time series based on the evolution of the Warsaw Stock Exchange Index (WIG) connected with the largest developing financial market in Europe. Calculating the local Hurst exponent for the WIG time series we find an interesting dependence between the behavior o…