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الأبحاث

Crazy Truth-Teller–Liar Puzzles

Authors : Laith Alzboon & Benedek Nagy

Abstract :In this manuscript, we define and discuss a new type of logical puzzles. These puzzles are based on the simplest truth-teller and liar puzzles. Graphs are used to represent graphically the puzzles. (The solution of) these logical puzzles contain three types of people. Strong Truth-tellers who can say only true statements, Strong Liars who can make only false statements and Weak Crazy people who must make at least one self-contradicting statement if he/she says anything. Self-contradicting statements are related to the Liar paradox, such that, there is no Truth-teller or a Liar could say “I am a Liar”. In any good puzzle there is a unique solution, while the puzzle is clear if only the people of the puzzle and their statements are given to solve the puzzle

Keywords : SS-puzzles,SSW-puzzles,Weak Crazy people,Self-contradictory, statements,Graphrepresentation of puzzles,Solvability of puzzles

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Counting the number of shortest chamfer paths in the square grid

Authors : Laith Alzboon, Bashar Khassawneh, Benedek Nagy

Abstract :In this paper, the number of shortest paths between any point pairs of the square grid, based on weighted distances, is computed. We use two types of steps on the gridlines and diagonal steps. Consequently, we use an 8-adjacency square grid, that is, one where a first weight is associated with the horizontal and vertical movements, while a second weight (not necessarily different from the first) is assigned to the diagonal steps. The chamfer distance of two points depends on the numbers and weights of the steps in a ‘shortest path’. In special cases, the cityblock and the chessboard distances, the two most basic and widely used digital distances (they are also referred as L1 and L∞ distances, respectively) of the two-dimensional digital space occur. Although our combinatorial result is theoretical, it is closely connected to applications, such as communication networks, path counting in digital images, traces and trajectories in 2D digital grids

Keywords : traces; trajectories; weighted distances; shortest paths; digital distances; combinatorics

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Truth-Teller--Liar Puzzles with Self-Reference

Authors : Laith Alzboon & Benedek Nagy

Abstract :In this paper, we use commonsense reasoning and graph representation to study logical puzzles with three types of people. Strong Truth-Tellers say only true atomic statements, Strong Liars say only false atomic statements, and Strong Crazy people say only self-contradicting statements. Self-contradicting statements are connected to the Liar paradox, i.e., no Truth-Teller or a Liar could say “I am a Liar”. A puzzle is clear if it only contains its given statements to solve it, and a puzzle is good if it has exactly one solution. It is known that there is no clear and good Strong Truth-Teller–Strong Liar (also called SS) puzzle

Keywords : SS-puzzles; SSS-puzzles; Crazy people; self-contradictory statements; puzzle-graphs

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On the number of weighted shortest paths in the square grid

Authors : Laith Alzboon, Bashar Khassawneh, Benedek Nagy

Abstract :In this paper the number of shortest paths between two points of the square grid using weighted distances is discussed. We use 8-adjacency square grid, that is, the weighted distance depends on the numbers and the weights of the horizontal, vertical and diagonal steps. Two types of neighborhood, and consequently two weights are used. As special cases, the Manhattan distance and chessboard distance, the two well-known and widely used digital distances of the two dimensional digital space occur. Despite our combinatorial result is theoretical, it is closely connected to applications, e.g., in communication networks

Keywords :weighted distance , chamfer distance , shortest path , neighborhood in square grid , Manhattan distance , chessboard distance , combinatorics , networks , metrics , digital geometry , image processing , communication networks

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A Comparison of Various Extensions of Strong Truthteller and Strong Liar Puzzles (Mutes and Crazies

Authors : Laith Alzboon & Benedek Nagy

Abstract :Truthteller liar puzzles are popular in science and also in recreational mathematics. In this paper, we compare five different types of puzzles. In each of our puzzles, the persons of the puzzle may state some statements about their types. In strong truthteller–strong liar puzzles (SS puzzles), each statement of a truthteller must be true and each statement of a liar must be false, and there is no third type of person in these puzzles. It is known that there is no good SS puzzle, where a puzzle is good if it has exactly one solution. In fact, because of symmetry, by flipping the type of person in a solution, another (dual) solution is obtained. Therefore, to break this symmetry, there are various ways to introduce a third type of person, e.g., Mutes and crazies. In SSS puzzles, crazy people may appear, each of whom can tell only a self-contradicting statement.

Keywords :good puzzles; self-contradicting statement; self-reference; mute persons; crazy persons; puzzle solvability; breaking symmetry in puzzles; breaking symmetry in logic

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Neural Network Prediction Model to Explore Complex Nonlinear Behavior in Dynamic Biological Network

Authors : Mohammad A. Alsharaiah, Laith H. Baniata, Omar Al Adwan, Orieb Abu Alghanam, Ahmad Adel Abu-Shareha, Laith Alzboon, Nedal Mustafa, Mohammad Baniata

Abstract :Organism network systems provide a biological data with high complex level. Besides, these data reflect the complex activities in organisms that identifies nonlinear behavior as well. Hence, mathematical modelling methods such as Ordinary Differential Equations model (ODE's) are becoming significant tools to predict, and expose implied knowledge and data. Unfortunately, the aforementioned approaches face some of cons such as the scarcity and the vagueness in the biological knowledge to expect the protein concentrations measurements. So, the main object of this research presents a computational model such as a neural Feed Forward Network model using Back Propagation algorithm to engage with imprecise and missing biological knowledge to provide more insight about biological systems in organisms

Keywords :artificial neural Feed Forward Network, Back Propagation; organism, Cyclin E;, Progression process, synthesis, prediction model, Ordinary differential equations model(ODE's)

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