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Diffstat (limited to 'examples/tutorial.ipynb')
| -rw-r--r-- | examples/tutorial.ipynb | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/examples/tutorial.ipynb b/examples/tutorial.ipynb index 6d9bae1..529bb6e 100644 --- a/examples/tutorial.ipynb +++ b/examples/tutorial.ipynb @@ -11,7 +11,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this example, we will generate a fake measured flavour composition using a multivariate Gaussian distribution and sample from it using the [emcee](https://emcee.readthedocs.io/) MCMC algorithm." + "In this example, we will generate a fake measured flavor composition using a multivariate Gaussian distribution and sample from it using the [emcee](https://emcee.readthedocs.io/) MCMC algorithm." ] }, { @@ -50,7 +50,7 @@ "\n", "$$\\pi\\:\\text{decay}\\rightarrow\\left(f_e:f_\\mu:f_\\tau\\right)_\\text{S}=\\left(1:2:0\\right)_\\text{S}$$\n", "\n", - "where $f_\\alpha$ is the flavor composition of a neutrino with flavor $\\alpha\\in\\{e,\\mu,\\tau\\}$ and the subscript S represents that this is the flavour composition at the source. In the code below we normalize this to 1 for later calculations." + "where $f_\\alpha$ is the flavor composition of a neutrino with flavor $\\alpha\\in\\{e,\\mu,\\tau\\}$ and the subscript S represents that this is the flavor composition at the source. In the code below we normalize this to 1 for later calculations." ] }, { @@ -84,7 +84,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "For the three massive neutrinos, the flavour eigenstates of the neutrino $|\\nu_\\alpha>$, $\\alpha\\in\\{e,\\mu,\\tau\\}$, are related to the mass eigenstates $|\\nu_i>$, $i\\in\\{1,2,3\\}$ via a unitary mixing matrix $U_{\\alpha i}$ known as the PMNS matrix:\n", + "For the three massive neutrinos, the flavor eigenstates of the neutrino $|\\nu_\\alpha>$, $\\alpha\\in\\{e,\\mu,\\tau\\}$, are related to the mass eigenstates $|\\nu_i>$, $i\\in\\{1,2,3\\}$ via a unitary mixing matrix $U_{\\alpha i}$ known as the PMNS matrix:\n", " \n", "$$ |\\nu_\\alpha>=\\sum^3_{i=1}U^*_{\\alpha i}|\\nu_i> $$\n", "\n", @@ -117,7 +117,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This mixing matrix says that neutrinos can oscillation from one flavor state $\\alpha\\in\\{e,\\mu,\\tau\\}$ to another $\\beta\\in\\{e,\\mu,\\tau\\}$ as a function of the propagation distance. The oscillation probability gives the probability that a neutrino produced in a flavour state $\\alpha$ is then detected in a flavour state $\\beta$ after a propagation distance $L$:\n", + "This mixing matrix says that neutrinos can oscillation from one flavor state $\\alpha\\in\\{e,\\mu,\\tau\\}$ to another $\\beta\\in\\{e,\\mu,\\tau\\}$ as a function of the propagation distance. The oscillation probability gives the probability that a neutrino produced in a flavor state $\\alpha$ is then detected in a flavor state $\\beta$ after a propagation distance $L$:\n", "\n", "$$\n", "\\begin{align}\n", @@ -295,9 +295,9 @@ " Parameters\n", " ----------\n", " fr : List[float], length 3\n", - " The flavour composition to evaluate at.\n", + " The flavor composition to evaluate at.\n", " fr_bf : List[float], length 3\n", - " The bestfit / injected flavour composition.\n", + " The bestfit / injected flavor composition.\n", " smearing : float\n", " The amount of smearing.\n", " offset : float, optional\n", @@ -350,7 +350,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Now we have everything we need to do scan over our likelihood, from which we will be able to visualize the effect of this smearing. However, scanning directly in the space of the flavour composition would not be the correct way to do the scan. This particular parameterization has degeneracies, since the total flavor composition must add up to 1, $\\sum_{\\alpha}f_\\alpha=1$, which introduces an unwanted prior dependence." + "Now we have everything we need to do scan over our likelihood, from which we will be able to visualize the effect of this smearing. However, scanning directly in the space of the flavor composition would not be the correct way to do the scan. This particular parameterization has degeneracies, since the total flavor composition must add up to 1, $\\sum_{\\alpha}f_\\alpha=1$, which introduces an unwanted prior dependence." ] }, { |