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.
Paper introduces quadrilateral labyrinth fractals and their properties.
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.
FGN models networks with fractal structures using Gaussian Multiplicative Chaos.
Knots can be embedded into fractals like the Menger Sponge and Sierpinski Tetrahedron.
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.
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 .…
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…
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…
Study fractal dimension for motion without crossing a subset.
This paper evaluates fractal dimension and persistent homology for neural network generalization.
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 Flow enhances normalizing flows with interpretable latent space and hierarchical modeling.
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…
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…
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…
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…
The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The dependence of this homology class on the direction can have a rather rich structure, leading in special cases to a fractal. In th…
Novikov's problem of semiclassical orbits of quasi-electrons in a normal metal leads to a correspondance between 3-ply periodic functions in R and fractals in R P^2. These fractals are the complement of infinitely many open sets labeled by integer 2-cycles of T^3. Here we present a characterization of the fractal point…
While developing their software, professional object-oriented (OO) software developers keep in their minds an image of the subtyping relation between types in their software. The goal of this paper is to present an observation about the graph of the subtyping relation in Java, namely the observation that, after the add…
We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hy…
New framework captures non-autonomous IFS limit set topology.
Floating geodesic planes in Hitchin manifolds have fractal closures with non-integer dimensions.
In this paper we study BSE Index financial time series for fractal and multifractal behaviour. We show that Bombay stock Exchange (BSE)Index time series is mono-fractal and can be represented by a fractional Brownian motion.
Gradient descent with large steps leads to chaotic parameter space and unpredictable outcomes.
Using the moving frame and invariants, any discrete curve in could be uniquely identified by its centroaffine curvatures and torsions. In this paper, depending on the affine curvatures of the fractal curves, such as Koch curve and Hilbert curve, we can clearly describe their iterative regularities. Interestingly…
It is proved that for every fractal continuous mapping F: I\to I^2 of the unit interval onto the unit square there is a pair of points x,y\in I, such that |F(x)-F(y)|^2\ge 5|x-y|.
Study fractal and regular geometry in deep neural networks.
We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across …