arXiv subjects

Roza Aceska

Publications and source records attributed to Roza Aceska.

7 recordsLinked to original sources

arXiv2026

Ornaments and Difference Distance Magic Oriented Graphs

One way to construct Difference Distance Magic Oriented Graphs (DDMOGs) is via a recently introduced technique called weighted sum. We explore the quality of said construction further by introducing the notion of an ornament. An ornament is an oriented graph that, when used in a weighted sum with an existing DDMOG, creates a new DDMOG. We provide results on the construction of a specific type of ornaments, called s-nodes ornaments. We conclude the paper with a list of open questions related to DDMOGs and ornaments.

math.CO↗

arXiv2026

New Results on Difference Distance Magic Labelings

A graph labeling assigns values to the components of a graph (vertices, edges, etc.). In particular, distance magic labelings have been widely studied in undirected graphs. In such a labeling, the vertices are labeled with unique values from one up to the number of vertices so that the sum of labels on the neighbors of any vertex is the same across all vertices. For oriented graphs, a related concept of distance difference magic has been studied. In a distance difference magic labeling, each vertex is given a unique value from one up to the number of vertices such that for each vertex the sums of the labels of vertices in the in-neighborhood minus the sums of the labels of vertices in the out-neighborhood equals zero. In this paper, we expand on this concept by showing a connected difference distance magic oriented graph on $n$ vertices exists for each integer $n \geq 5$. We also construct arbitrarily large difference distance magic oriented graphs from smaller ones using a new graph sum and exhibit a connection between linear algebra and this type of labeling.

math.CO↗

arXiv2025

Dual Frame Completion Problem

In this paper we present the construction of an exact dual frame under specific structural assumptions posed on the dual frame. When given a frame $F$ for a finite dimensional Hilbert space, and a set of vectors $H$ that is assumed to be a subset of a dual frame of $F$, we answer the following question: Which dual frame $G$ for $F$ - if it exists - completes the given set $H$? Solutions are explored through a direct and an indirect approach, as well as via the singular value decomposition of the synthesis operator of $F$.

math.FA↗

arXiv2022

Cross Frame Potential

We introduce the notion of a cross-frame potential function, which takes one frame as input and returns its cross-frame potential value with respect to another frame. We analyze the behavior of this new function to determine what information the cross-frame potential value can reveal about the relationship between the two frames.

math.FA↗

arXiv2020

Local sparsity and recovery of fusion frames structured signals

The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in fusion frames, we introduce a compressed sensing framework in which we split the dense information into sub-channel or local pieces and then fuse the local estimations. Each piece of information is measured by potentially low quality sensors, modeled by linear matrices and recovered via compressed sensing -- when necessary. Finally, by a fusion process within the fusion frames, we are able to recover accurately the original signal. Using our new method, we show, and illustrate on simple numerical examples, that it is possible, and sometimes necessary, to split a signal via local projections and / or filtering for accurate, stable, and robust estimation. In particular, we show that by increasing the size of the fusion frame, a certain robustness to noise can also be achieved. While the computational complexity remains relatively low, we achieve stronger recovery performance compared to usual single-device compressed sensing systems.

cs.IT↗

arXiv2018

On near-optimal time samplings for initial data best approximation

Leveraging on the work of De Vore and Zuazua, we further explore their methodology and deal with two open questions presented in their paper. We show that for a class of linear evolutionary PDEs the admissible choice of relevant parameters used to construct the near-optimal sampling sequence is not influenced by the spectrum of of the operator controlling the spatial part of the PDE, but only by its order. Furthermore, we show that it is possible to extend their algorithm to a simple version of a non-autonomous heat equation in which the heat diffusivity coefficient depends explicitly on time.

math.AP↗

arXiv2016

Scalability of frames generated by dynamical operators

Let $A$ be an operator on {a separable } Hilbert space $\cH$, and let $G \subset \cH$. It is known that - under appropriate conditions on $A$ and $G$ - the set of iterations $F_G(A)= \{A^j \gbf \; | \; \gbf \in G, \; 0 \leq j \leq L(\gbf) \} $ is a frame for $\cH$. We call $F_G(A)$ a dynamical frame for $\cH$, and explore further its properties; in particular, we show that the canonical dual frame of $F_G(A)$ also has an iterative set structure. We explore the relations between the operator $A$, the set $G$ and the number of iterations $L$ which ensure that the system $F_G(A)$ is a scalable frame. We give a general statement on frame scalability, We and study in detail the case when $A$ is a normal operator, utilizing the unitary diagonalization in finite dimensions. In addition, we answer the question of when $F_G(A)$ is a scalable frame in several special cases involving block-diagonal and companion operators.

math.FA↗