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Recent conditional image generation methods produce images of remarkable diversity, fidelity and realism. However, the majority of these methods allow conditioning only on labels or text prompts, which limits their level of control over the…
Synthetic generation of three-dimensional cell models from histopathological images aims to enhance understanding of cell mutation, and progression of cancer, necessary for clinical assessment and optimal treatment. Classical reconstruction…
Rendering high-fidelity images from sparse point clouds is still challenging. Existing learning-based approaches suffer from either hole artifacts, missing details, or expensive computations. In this paper, we propose a novel framework to…
Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we…
We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by…
In the paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional energy-based model of fragmentation of rapidly expanding cylinder under plane strain conditions. The model allowed one to estimate the average fragment length and the…
The Rauzy fractal is a domain in the two-dimensional plane constructed by the Rauzy substitution, a substitution rule on three letters. The Rauzy fractal has a fractal-like boundary, and the currently known its constructions is not only for…
The Sierpinski Triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter. Here we look into fractal features in the…
We explore different design choices for injecting noise into generative adversarial networks (GANs) with the goal of disentangling the latent space. Instead of traditional approaches, we propose feeding multiple noise codes through separate…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…
This work proposes to obtain novel fractal descriptors from gray-level texture images by combining information from interior and boundary measures of the Minkowski dilation applied to the texture surface. At first, the image is converted…
Fractal Image Compression (FIC) is a lossy image compression technique that leverages self-similarity within an image to achieve high compression ratios. However, the process of compressing the image is computationally expensive. This paper…
In computer-aided design (CAD), the ability to "reverse engineer" the modeling steps used to create 3D shapes is a long-sought-after goal. This process can be decomposed into two sub-problems: converting an input mesh or point cloud into a…
Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and investigate frames of the form $\{\rho(\xi)…
We present synthetic Doppler maps of gaseous flows in semidetached binaries based on the results of 3D gas dynamical simulations. Using of gas dynamical calculations alongside with Doppler tomography technique permits to identify main…
Deep generative models of 3D shapes have received a great deal of research interest. Yet, almost all of them generate discrete shape representations, such as voxels, point clouds, and polygon meshes. We present the first 3D generative model…
Let $E$ be the Sierpinski gasket, i.e., the self-similar set generated by the IFS $\left \{f_a(x)=\frac{x+a}{q}: a\in \{(0,0), (0,1), (1,0)\}\right \}$. In paper, we provide a description of the following set for $2<q<3$ \begin{equation*}…
A lot of formal and informal recreational study took place in the fields of Meromorphic Maps, since Mandelbrot popularized the map z <- z^2 + c. An immediate generalization of the Mandelbrot z <-z^n + c also known as the Multibrot family…
We present a comprehensive structural characterization of two different highly pure nuclear graphites that compasses all relevant length scales from nanometers to sub-mm. This has been achieved by combining several experiments and neutron…
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar…