scholarly journals The Arbitrarily Varying Relay Channel

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 516 ◽  
Author(s):  
Uzi Pereg ◽  
Yossef Steinberg
Keyword(s):  
State Constraints ◽  
Upper Bounds ◽  
Relay Channel ◽  
Frequency Division ◽  
Lower And Upper Bounds ◽  
Random Code ◽  
Code Capacity ◽  
Special Cases ◽  
Input And State Constraints

We study the arbitrarily varying relay channel, which models communication with relaying in the presence of an active adversary. We establish the cutset bound and partial decode-forward bound on the random code capacity. We further determine the random code capacity for special cases. Then, we consider conditions under which the deterministic code capacity is determined as well. In addition, we consider the arbitrarily varying Gaussian relay channel with sender frequency division under input and state constraints. We determine the random code capacity, and establish lower and upper bounds on the deterministic code capacity. Furthermore, we show that as opposed to previous relay models, the primitive relay channel has a different behavior compared to the non-primitive relay channel in the arbitrarily varying scenario.

Properties of the Solution Set for Generalized Equilibrium Problems with Lower and Upper Bounds in FC-Metric Spaces

2013 ◽  
Vol 671-674 ◽  
pp. 1557-1560
Author(s):  
Kai Ting Wen
Keyword(s):  
Metric Spaces ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Upper Bounds ◽  
Solution Set ◽  
Lower And Upper Bounds ◽  
Paper Properties ◽  
Special Cases ◽  
Mathematical Problems ◽  
Generalized Equilibrium

The equilibrium problem includes many fundamental mathematical problems, e.g., optimization problems, saddle point problems, fixed point problems, economics problems, comple- mentarity problems, variational inequality problems, mechanics, engineering, and others as special cases. In this paper, properties of the solution set for generalized equilibrium problems with lower and upper bounds in FC-metric spaces are studied. In noncompact setting, we obtain that the solution set for generalized equilibrium problems with lower and upper bounds is nonempty and compact. Our results improve and generalize some recent results in the reference therein.

THE GRAPH-BIN PACKING PROBLEM

2011 ◽  
Vol 22 (08) ◽  
pp. 1971-1993 ◽  
Author(s):  
CSILLA BUJTÁS ◽  
GYÖRGY DÓSA ◽  
CSANÁD IMREH ◽  
JUDIT NAGY-GYÖRGY ◽  
ZSOLT TUZA
Keyword(s):  
Bin Packing ◽  
General Structure ◽  
Packing Problem ◽  
Upper Bounds ◽  
Performance Guarantee ◽  
Lower And Upper Bounds ◽  
Polynomial Time Algorithms ◽  
Special Cases ◽  
Online Setting ◽  
Host Graph

We deal with a very general problem: a given graph G is to be "packed" into a host graph H, and we are asked about some natural optimization questions concerning this packing. The problem has never been investigated before in this general form. The input of the problem is a simple graph G = (V, E) with lower and upper bounds on its edges and weights on its vertices. The vertices correspond to items which have to be packed into the vertices (bins) of a host graph, such that each host vertex can accommodate at most L weight in total, and if two items are adjacent in G, then the distance of their host vertices in H must be between the lower and upper bounds of the edge joining the two items. Special cases are bin packing with conflicts, chromatic number, and many more. We give some general structure statements, treat some special cases, and investigate the performance guarantee of polynomial-time algorithms both in the offline and online setting.

scholarly journals General Multiplicative Zagreb Indices of Graphs with a Small Number of Cycles

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 514 ◽  
Author(s):  
Monther R. Alfuraidan ◽  
Tomáš Vetrík ◽  
Selvaraj Balachandran
Keyword(s):  
Upper Bounds ◽  
Extremal Graphs ◽  
Lower And Upper Bounds ◽  
Zagreb Indices ◽  
Special Cases ◽  
Tricyclic Graphs ◽  
Bicyclic Graphs ◽  
Number Of Cycles

We present lower and upper bounds on the general multiplicative Zagreb indices for bicyclic graphs of a given order and number of pendant vertices. Then, we generalize our methods and obtain bounds for the general multiplicative Zagreb indices of tricyclic graphs, tetracyclic graphs and graphs of given order, size and number of pendant vertices. We show that all our bounds are sharp by presenting extremal graphs including graphs with symmetries. Bounds for the classical multiplicative Zagreb indices are special cases of our results.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number
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