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We investigate the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar Sturm-Liouville operator associated with a fractal self-similar measure…
Generating visible-like face images from thermal images is essential to perform manual and automatic cross-spectrum face recognition. We successfully propose a solution based on cascaded refinement network that, unlike previous works,…
We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.
Image inpainting is the process of taking an image and generating lost or intentionally occluded portions. Inpainting has countless applications including restoring previously damaged pictures, restoring the quality of images that have been…
Following an earthquake, it is vital to quickly evaluate the safety of the impacted areas. Damage detection systems, powered by computer vision and deep learning, can assist experts in this endeavor. However, the lack of extensive, labeled…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
Recent progress in brain-guided image generation has improved the quality of fMRI-based reconstructions; however, fundamental challenges remain in preserving object-level structure and semantic fidelity. Many existing approaches overlook…
Understanding intertrochanteric fracture distribution is an important topic in orthopaedics due to its high morbidity and mortality. The intertrochanteric fracture can contain high-dimensional information including complicated 3D fracture…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
The force fields of interior boundaries of matters are calculated as superposition of fields of modified Sierpinski carpet. The long-range effect interaction in irradiated crystals is introduced as various manifestations of second order…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
Particle-based representations of radiance fields such as 3D Gaussian Splatting have found great success for reconstructing and re-rendering of complex scenes. Most existing methods render particles via rasterization, projecting them to…
Time- and angle-resolved photoelectron spectroscopy with 13 fs temporal resolution is used to follow the different stages in the formation of a Fermi-Dirac distributed electron gas in graphite after absorption of an intense 7 fs laser…
To help understand the underlying mechanisms of neural networks (NNs), several groups have, in recent years, studied the number of linear regions $\ell$ of piecewise linear functions generated by deep neural networks (DNN). In particular,…
This paper studies the concept of power dissipation in infinite graphs and fractals associated with passive linear networks consisting of non-dissipative elements. In particular, we analyze the so-called Feynman-Sierpinski ladder, a fractal…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
Histological images are obtained by transmitting light through a tissue specimen that has been stained in order to produce contrast. This process results in 2D images of the specimen that has a three-dimensional structure. In this paper, we…