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Cybersecurity and Applied Mathematics [Mīkstie vāki]

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(PhD (Applied Mathematics)), (PhD (Mathematics), Co-Editor in Chief, ACM Digital Threats)
  • Formāts: Paperback / softback, 240 pages, height x width: 235x191 mm, weight: 430 g
  • Izdošanas datums: 07-Jun-2016
  • Izdevniecība: Syngress Media,U.S.
  • ISBN-10: 0128044527
  • ISBN-13: 9780128044520
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  • Cena: 69,01 €
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Cybersecurity and Applied MathematicsPalielināt
  • Formāts: Paperback / softback, 240 pages, height x width: 235x191 mm, weight: 430 g
  • Izdošanas datums: 07-Jun-2016
  • Izdevniecība: Syngress Media,U.S.
  • ISBN-10: 0128044527
  • ISBN-13: 9780128044520
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780128044520.html
Keywords:

Cybersecurity and Applied Mathematics explores the mathematical concepts necessary for effective cyber security research and practice, taking an applied approach for practitioners, as well for students about to enter the field. This book covers methods of statistical exploratory data analysis and visualization as a type of model for driving decisions, as well as key topics such as graph theory, topological complexes, and persistent homology. Defending the Internet is a complex effort, but applying the right techniques from mathematics can make this task more manageable. Cybersecurity and Applied Mathematics is essential reading for creating useful and replicable methods for analyzing data.

  • Describes mathematical tools for solving cybersecurity problems, enabling analysts to pick the most optimal tool for the task at hand
  • Numerous cybersecurity examples and exercises throughout using real world data
  • Written by mathematicians and statisticians with hands-on practitioner experience

Papildus informācija

Explores the mathematical concepts of effective cybersecurity research and practice, taking an applied approach for practitioners and students entering the field
Biography xi
Chapter 1 Introduction 1(2)
Chapter 2 Metrics, Similarity, and Sets 3(20)
2.1 Introduction to Set Theory
3(2)
2.2 Operations on Sets
5(4)
2.2.1 Complement
5(1)
2.2.2 Intersection
5(1)
2.2.3 Union
6(1)
2.2.4 Difference
7(1)
2.2.5 Symmetric Difference
8(1)
2.2.6 Cross Product
8(1)
2.3 Set Theory Laws
9(1)
2.4 Functions
9(1)
2.5 Metrics
10(1)
2.6 Distance Variations
11(1)
2.6.1 Pseudometric
11(1)
2.6.2 Quasimetric
12(1)
2.6.3 Semimetric
12(1)
2.7 Similarities
12(1)
2.8 Metrics and Similarities of Numbers
13(3)
2.8.1 Lp Metrics
13(3)
2.8.2 Gaussian Kernel
16(1)
2.9 Metrics and Similarities of Strings
16(1)
2.9.1 Levenshtein Distance
16(1)
2.9.2 Hamming Distance
17(1)
2.10 Metrics and Similarities of Sets of Sets
17(3)
2.10.1 Jaccard Index
17(1)
2.10.2 Tanimoto Distance
18(1)
2.10.3 Overlap Coefficient
18(1)
2.10.4 Hausdorff Metric
19(1)
2.10.5 Kendall's Tau
19(1)
2.11 Mahalanobis Distance
20(1)
2.12 Internet Metrics
21(2)
2.12.1 Great Circle Distance
21(1)
2.12.2 Hop Distance
21(1)
2.12.3 Keyword Distance
22(1)
Chapter 3 Probability Models 23(20)
3.1 Basic Probability Review
23(7)
3.1.1 Language and Axioms of Probability
25(1)
3.1.2 Combinatorics Aka Parlor Tricks
26(2)
3.1.3 Joint and Conditional Probability
28(1)
3.1.4 Independence and Bayes Rule
29(1)
3.2 From Parlor Tricks to Random Variables
30(4)
3.2.1 Types of Random Variables
30(1)
3.2.2 Properties of Random Variables
31(3)
3.3 The Random Variable as a Model
34(5)
3.3.1 Bernoulli and Geometric Distributions
35(1)
3.3.2 Binomial Distribution
35(1)
3.3.3 Poisson Distribution
36(1)
3.3.4 Normal Distribution
36(2)
3.3.5 Pareto Distributions
38(1)
3.3.6 Uniform Distribution
39(1)
3.4 Multiple Random Variables
39(1)
3.5 Using Probability and Random Distributions
40(2)
3.6 Conclusion
42(1)
Chapter 4 Introduction to Data Analysis 43(24)
4.1 The Language of Data Analysis
43(3)
4.1.1 Producing Data
44(1)
4.1.2 Exploratory Data Analysis
45(1)
4.1.3 Inference
45(1)
4.2 Units, Variables, and Repeated Measures
46(4)
4.2.1 Measurement Error and Random Variation
48(2)
4.3 Distributions of Data
50(2)
4.4 Visualizing Distributions
52(4)
4.4.1 Bar Plot
52(1)
4.4.2 Histogram
53(1)
4.4.3 Box Plots
53(2)
4.4.4 Density Plot
55(1)
4.5 Data Outliers
56(1)
4.6 Log Transformation
57(1)
4.7 Parametric Families
58(1)
4.8 Bivariate Analysis
59(3)
4.8.1 Visualizing Bipartite Variables
59(2)
4.8.2 Correlation
61(1)
4.9 Time Series
62(1)
4.10 Classification
63(1)
4.11 Generating Hypotheses
64(1)
4.12 Conclusion
64(3)
Chapter 5 Graph Theory 67(28)
5.1 An Introduction to Graph Theory
67(1)
5.2 Varieties of Graphs
68(2)
5.2.1 Undirected Graph
68(1)
5.2.2 Directed Graph
68(1)
5.2.3 Multigraph
69(1)
5.2.4 Bipartite Graph
69(1)
5.2.5 Subgraph
69(1)
5.2.6 Graph Complement
70(1)
5.3 Properties of Graphs
70(3)
5.3.1 Graph Sizes
70(1)
5.3.2 Vertices and Their Edges
71(1)
5.3.3 Degree
71(1)
5.3.4 Directed Graphs and Degrees
72(1)
5.3.5 Scale Free Graphs
72(1)
5.4 Paths, Cycles and Trees
73(3)
5.4.1 Paths and Cycles
73(1)
5.4.2 Shortest Paths
74(1)
5.4.3 Connected and Disconnected Graphs
74(1)
5.4.4 Trees
75(1)
5.4.5 Cycles and Their Properties
75(1)
5.4.6 Spanning Trees
76(1)
5.5 Varieties of Graphs Revisited
76(2)
5.5.1 Graph Density, Sparse and Dense Graphs
76(1)
5.5.2 Complete and Regular Graphs
77(1)
5.5.3 Weighted Graph
77(1)
5.5.4 And Yet More Graphs!
78(1)
5.6 Representing Graphs
78(2)
5.6.1 Adjacency Matrix
78(2)
5.6.2 Incidence Matrix
80(1)
5.7 Triangles, the Smallest Cycle
80(3)
5.7.1 Introduction and Counting
80(1)
5.7.2 Triangle Free Graphs
81(1)
5.7.3 The Local Clustering Coefficient
81(2)
5.8 Distances on Graphs
83(1)
5.8.1 Eccentricity
83(1)
5.8.2 Cycle Length Properties
84(1)
5.9 More Properties of Graphs
84(3)
5.9.1 Cut
85(1)
5.9.2 Bridge
85(1)
5.9.3 Partitions
86(1)
5.9.4 Vertex Separators
86(1)
5.9.5 Cliques
87(1)
5.10 Centrality
87(2)
5.10.1 Betweenness
87(1)
5.10.2 Degree Centrality
88(1)
5.10.3 Closeness and Farness
88(1)
5.10.4 Cross-Clique Centrality
89(1)
5.11 Covering
89(1)
5.11.1 Vertex Covering
89(1)
5.11.2 Edge Cover
90(1)
5.12 Creating New Graphs from Old
90(3)
5.12.1 Union Graphs
91(1)
5.12.2 Intersection Graphs
91(1)
5.12.3 Uniting Graphs
92(1)
5.12.4 The Intersection Graph
92(1)
5.12.5 Modifying Existing Graphs
93(1)
5.13 Conclusion
93(2)
Chapter 6 Game Theory 95(18)
6.1 The Prisoner's Dilemma
96(1)
6.2 The Mathematical Definition of a Game
97(3)
6.2.1 Strategies, Payoffs and Normal Form
97(1)
6.2.2 Normal Form
98(1)
6.2.3 Extensive Form
99(1)
6.3 Snowdrift Game
100(1)
6.4 Stag Hunt Game
101(1)
6.5 Iterative Prisoner's Dilemma
102(1)
6.6 Game Solutions
103(3)
6.6.1 Cooperative and Non-Cooperative Games
104(1)
6.6.2 Zero Sum Game
104(1)
6.6.3 Dominant Strategy
105(1)
6.6.4 Nash Equilibrium
105(1)
6.6.5 Mixed Strategy Nash Equilibrium
106(1)
6.7 Partially Informed Games
106(2)
6.8 Leader-Follower Game
108(2)
6.8.1 Stackelberg Game
108(1)
6.8.2 Colonel Blotto
109(1)
6.9 Signaling Games
110(3)
Chapter 7 Visualizing Cybersecurity Data 113(22)
7.1 Why Visualize?
113(1)
7.2 What We Visualize
114(5)
7.2.1 Considering the Efficacy of a Visualization
114(1)
7.2.2 Data Collection and Visualization
115(1)
7.2.3 Visualizing Malware Features
116(1)
7.2.4 Existence Plots
117(1)
7.2.5 Combining Plots
118(1)
7.3 Visualizing IP Addresses
119(5)
7.3.1 Hilbert Curve
120(3)
7.3.2 Heat Map
123(1)
7.4 Plotting Higher Dimensional Data
124(3)
7.4.1 Principal Component Analysis
124(2)
7.4.2 Sammon Mapping
126(1)
7.5 Graph Plotting
127(3)
7.6 Visualizing Malware
130(1)
7.7 Visualizing Strings
131(2)
7.7.1 Word Cloud
131(1)
7.7.2 Sammon Mapping for Strings
132(1)
7.8 Visualization with a Purpose
133(2)
Chapter 8 String Analysis for Cyber Strings 135(22)
W. Casey
8.1 String Analysis and Cyber Data
135(5)
8.1.1 Cyber Data
135(1)
8.1.2 Modes of Analyzing Cyber Data
136(1)
8.1.3 Alphabets and Finite Strings
137(1)
8.1.4 Formal Languages
138(2)
8.2 Discrete String Matching
140(10)
8.2.1 Hashing
140(2)
8.2.2 Applications of Hashing
142(7)
8.2.3 Other Methods
149(1)
8.3 Affine Alignment String Similarity
150(6)
8.3.1 Optimality and Dynamic Programming
150(1)
8.3.2 Global Affine Alignment
151(3)
8.3.3 Example Alignments
154(2)
8.4 Summary
156(1)
Chapter 9 Persistent Homology 157(16)
9.1 Triangulations
158(4)
9.2 α Shapes
162(2)
9.3 Holes
164(1)
9.4 Homology
165(1)
9.5 Persistent Homology
166(1)
9.6 Visualizing Persistent Homology
167(4)
9.6.1 Comparing Point Clouds
170(1)
9.7 Conclusions
171(2)
Appendix 173(6)
Bibliography 179(4)
Index 183
Leigh Metcalf researchs network security, game theory, formal languages, and dynamical systems. She is Editor in Chief of the Journal on Digital Threats and has a PhD in Mathematics. Will Casey works in threat analysis, code analysis, natural language processing, genomics, bioinformatics, and applied mathematics. He has a MS and MA in Mathematics and a PhD in Applied Mathematics.