6 citations · 11 across the 11 of their papers we have counts for
13 papers
Quartic Rational Diophantine Quadruples and the Euler Surface
Alen Andrašek, Matija Kazalicki, Domagoj Vlah
We prove that there exist infinitely many quartic rational Diophantine quadruples, that is, sets of four pairwise distinct nonzero rational numbers whose pairwise products increase…
AE-ViT: Stable Long-Horizon Parametric Partial Differential Equations Modeling
Iva Mikuš, Boris Muha, Domagoj Vlah
Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle…
Improving elliptic curve rank classification using multi-value and learned Mestre-Nagao sums
Zvonimir Bujanović, Matija Kazalicki, Domagoj Vlah
Determining the rank of an elliptic curve E/Q remains a central challenge in number theory. Heuristics such as Mestre--Nagao sums are widely used to estimate ranks, but there is co…
Solving Bilevel Optimal Bidding Problems Using Deep Convolutional Neural Networks
Domagoj Vlah, Karlo Šepetanc, Hrvoje Pandžić
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this…
Ranks of elliptic curves and deep neural networks
Matija Kazalicki, Domagoj Vlah
Determining the rank of an elliptic curve E/Q is a hard problem, and in some applications (e.g. when searching for curves of high rank) one has to rely on heuristics aimed at estim…
Reconstruction of Incomplete Wildfire Data using Deep Generative Models
Tomislav Ivek, Domagoj Vlah
We present our submission to the Extreme Value Analysis 2021 Data Challenge in which teams were asked to accurately predict distributions of wildfire frequency and size within spat…
The box dimension of degenerate spiral trajectories of a class of ordinary differential equations
Renato Huzak, Domagoj Vlah, Darko Žubrinić +1
In this paper we initiate the study of the box dimension of degenerate spiral trajectories of a class of ordinary differential equations. A class of singularities of focus type wit…
BlackBox: Generalizable Reconstruction of Extremal Values from Incomplete Spatio-Temporal Data
Tomislav Ivek, Domagoj Vlah
We describe our submission to the Extreme Value Analysis 2019 Data Challenge in which teams were asked to predict extremes of sea surface temperature anomaly within spatio-temporal…
A note on the box dimension of degenerate foci
Domagoj Vlah, Darko Zubrinic, Vesna Zupanovic
We study polynomial planar systems with singularity of focus type without characteristic directions. Simple and natural transformation of weak focus has been used to obtain such de…
Oscillatory Integrals and Fractal Dimension
Jean-Philippe Rolin, Domagoj Vlah, Vesna Zupanovic
We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude with compact support. Geometrical properties of the curves defin…
Fractal properties of Bessel functions
Luka Korkut, Domagoj Vlah, Vesna Zupanovic
A fractal oscillatority of solutions of second-order differential equations near infinity is measured by oscillatory and phase dimensions. The phase dimension is defined as a box d…
Geometrical properties of a class of systems with spiral trajectories in R^3
Luka Korkut, Domagoj Vlah, Vesna Zupanovic
Here we study a class of second-order nonautonomous differential equations, and the corresponding planar and spatial systems, from the point of view of fractal geometry. The fracta…
Wavy spirals and their fractal connection with chirps
Luka Korkut, Domagoj Vlah, Darko Zubrinic +1
We study the fractal oscillatority of a class of real functions near . It is measured by oscillatory and phase dimensions, defined as box dimensions of the…