This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

PURPOSE The purpose of this study was to use 4-dimensional-computed tomography (4D-CT) to evaluate respiration-induced liver motion magnitude and influencing factors in patients with intrahepatic tumors undergoing abdominal compression. METHODS From January 2012 to April 2016, 99 patients with intrahepatic tumors were included in this study. They all underwent 4D-CT to assess respiratory live...

Both regularization and compression are important issues in image processing and have been widely approached in the literature. The usual procedure to obtain the compression of an image given through a noisy blur requires two steps: first a deblurring step of the image and then a factorization step of the regularized image to get an approximation in terms of low rank nonnegative factors. We exa...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

Metamagnetic transitions are analogs of a pressure-driven gas-liquid transition in water. In insulators, they marked by superlinear increase the magnetization that occurs at field strength set spin exchange interactions. Here we study topological metamagnets, which is itself quantity and for find single line two materials with substantially different magnetic interactions: ices ${\mathrm{Dy}}_{...

We investigate the phase behavior and kinetics of a monodisperse mixture of active (i.e., self-propelled) and passive isometric Brownian particles through Brownian dynamics simulations and theory. As in a purely active system, motility of the active component triggers phase separation into a dense and a dilute phase; in the dense phase, we further find active-passive segregation, with "rafts" o...

For minimal Z2-topological dynamical systems, we introduce a cube structure and a variation of the regionally proximal relation for Z2 actions, which allow us to characterize product systems and their factors. We also introduce the concept of topological magic systems, which is the topological counterpart of measure theoretic magic systems introduced by Host in his study of multiple averages fo...

In this paper, new methods to improve the encoding of connectivity and geometry of the topological surgery scheme are proposed. In connectivity compression, after obtaining the vertex and triangle spanning trees by decomposing a threedimensional object, bits are adaptively allocated to each run of two spanning trees on a threshold basis. The threshold is the length of a binary number of the max...

GUNDUZ, AYSEGUL. Compression and Transmission of Facial Images Over Very Narrowband Wireless Channels. (Under the direction of Dr. Hamid Krim.) Law enforcement officers on mobile duty are often confronted with ID authentication of subjects, requiring the transmission of a driver’s license picture over wireless channels with very narrow bandwidths. To access mug shots in a reliable and timely ma...