Related papers: Tiling with Boundaries: Dense digital images have …
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and…
The advent of Bell's inequalities provoked the possibility that entangled quantum phenomena is non-local in nature. Since teleportation only requires a finite amount of classical information, i.e. two bits, the author asks whether or not it…
In this paper we provide asymptotic upper bounds on the complexity in two (closely related) situations. We confirm for the total doubling coverings and not only for the chains the expected bounds of the form $$ \kappa({\mathcal U}) \le…
The chosen tool of this thesis is an extremal type approach. The lesson drawn by the theorems proved in the thesis is that surprisingly small compromise is necessary on the efficacy of the solutions to make the approach work. The problems…
Quantum entanglement cannot be unlimitedly shared among arbitrary number of qubits. Larger the number of entangled pairs in an N-qubit system, smaller the degree of bi-partite entanglement is. We analyze a system of N qubits in which an…
Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have non-trivial Gaussian curvature localised at tips, curved interfaces, and…
We present a pixel recursive super resolution model that synthesizes realistic details into images while enhancing their resolution. A low resolution image may correspond to multiple plausible high resolution images, thus modeling the super…
Internal properties of a sample can be observed by medical imaging tools, such as ultrasound devices, magnetic resonance imaging (MRI) and optical coherence tomography (OCT) which are based on relying on changes in material density or…
Thin film interference is integral to modern photonics and optoelectronics, e.g. allowing for precise design of high performance optical filters, efficiency enhancements in photovoltaics and light-emitting devices, as well as the…
We consider image sets of differentially $d$-uniform maps of finite fields. We present a lower bound on the image size of such maps and study their preimage distribution, by extending methods used for planar maps. We apply the results to…
Let L be a link in the 3-sphere that is in thin position but not in bridge position and let P be a thin level sphere. We generalize a result of Wu by giving a bound on the number of disjoint irreducible compressing disks that P can have,…
Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. One extreme of the finite problem is single tile tilings. We develop the algorithm for finding all the single tile tilings and present the…
A geometric form of information theory allows for reasonable, i.e. probabilistic, evidence-ranking based, and generalized noise-level dependent, classifications of the crystallographic and quasicrystallographic symmetries in noisy digital…
We study constrained percolation models on planar lattices including the $[m,4,n,4]$ lattice and the square tilings of the hyperbolic plane, satisfying certain local constraints on faces of degree 4, and investigate the existence of…
Using the complementary wave- and particle-like natures of photons, it is possible to make ``interaction-free'' measurements where the presence of an object can be determined with no photons being absorbed. We investigated several…
Given a set of unit-disks in the plane with union area $A$, what fraction of $A$ can be covered by selecting a pairwise disjoint subset of the disks? Rado conjectured 1/4 and proved $1/4.41$. Motivated by the problem of channel-assignment…
Machine learning methods are changing the way data is analyzed. One of the most powerful and widespread applications of these techniques is in image segmentation wherein disparate objects of a digital image are partitioned and classified.…
This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. The…
For a positive integer $k$, the $k$-recolouring graph of a graph $G$ has as vertex set all proper $k$-colourings of $G$ with two $k$-colourings being adjacent if they differ by the colour of exactly one vertex. A result of Dyer et al.…
Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…