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https://github.com/Zenithsiz/ist-ddrs-lab2
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48 lines
1.8 KiB
Typst
48 lines
1.8 KiB
Typst
#import "/util.typ" as util: indent_par
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#indent_par[The 2-DTMC process is capable of performing both what the Bernoulli process can, as well as another interesting behavior]
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#figure(
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image("/diagrams/1.svg", width: 50%),
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caption: [2-DTMC process]
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)
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==== a. Interesting behavior
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#indent_par[When the α and β parameters are on opposite sides of the spectrum, the 2-DTMC process exhibits an interesting behavior:]
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#figure(
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image("/images/1b (α=0.9, β=0.1).svg", width: 50%),
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caption: [2-DTMC and Bernoulli processes (α=0.9, β=0.1)]
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)
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#indent_par[Unlike the Bernoulli process, the 2-DTMC "remembers" it's previous state, ensuring that both states are very stable, not wanting to transition to the other side.]
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#pagebreak()
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==== b. Bernoulli-like behavior
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#indent_par[When the α and β parameters are equal, the 2-DTMC process performs almost exactly as the Bernoulli process:]
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#grid(
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columns: (1fr, 1fr, 1fr),
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figure(
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image("/images/1a (α=0.1, β=0.1).svg", width: 80%),
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caption: [2-DTMC and Bernoulli processes (α=0.1, β=0.1)]
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),
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figure(
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image("/images/1a (α=0.5, β=0.5).svg", width: 80%),
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caption: [2-DTMC and Bernoulli processes (α=0.5, β=0.5)]
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),
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figure(
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image("/images/1a (α=0.9, β=0.9).svg", width: 80%),
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caption: [2-DTMC and Bernoulli processes (α=0.9, β=0.9)]
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)
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)
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#indent_par[When α and β are close to 0.0 or 1.0, one of the states will become very stable while the other state will become very unstable, quickly wanting to transition to the other state.]
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#indent_par[When α and β are close to 0.5, both states are very unstable.]
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#indent_par[The existence of one or more unstable states imply that the system can no longer as easily "remember" it's previous state and thus the probability of finding the system in a given state can now be approximated by a bernoulli process]
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