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Author: Gabriel Fernández Fernández

README.md

@@ -4,6 +4,14 @@
 
 ![Interpretable autoregressive β-VAE architecture.](fig1.png)
 
+<div>
+
+[![](https://zenodo.org/badge/667817128.svg)](https://zenodo.org/doi/10.5281/zenodo.11572993)
+
+DOI
+
+</div>
+
 SPIVAE is a machine learning method to study stochastic processes. It
 tries to learn the probability distribution of input trajectories and
 permits us to interpret its functioning and generate new trajectories
@@ -50,13 +58,3 @@ If you use this library, please give us credit.
                    {Data Analysis, Statistics and Probability (physics.data-an)},
                    Quantitative Methods (q-bio.QM)}
     }
-
-    @misc{fernandez2023spivae,
-      title = {{{SPIVAE}}},
-      author = {{Fern{\'a}ndez-Fern{\'a}ndez}, Gabriel},
-      year = {2023},
-      month = jul,
-      url = {https://github.com/GabrielFernandezFernandez/SPIVAE},
-      urldate = {2023-07-21},
-      copyright = {Apache-2.0}
-    }

SPIVAE/utils.py

@@ -28,7 +28,7 @@ def __call__(self, pred, target,):
             log_likelihood = mix_gaussian_loss(y_hat, target, reduction=self.reduction)
         else:
             log_likelihood = mix_gaussian_loss(y_hat, target[:,self.RF:], reduction=self.reduction)
-            
+
         if self.reduction=='none':
             kl = kl_divergence(mu, logvar, reduction='none') if self.c else 0
             return log_likelihood, self.beta, kl

nbs/index.ipynb

@@ -15,6 +15,13 @@
     "![Interpretable autoregressive β-VAE architecture.](fig1.png)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[![DOI](https://zenodo.org/badge/667817128.svg)](https://zenodo.org/doi/10.5281/zenodo.11572993)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -75,16 +82,6 @@
     "               {Data Analysis, Statistics and Probability (physics.data-an)},\n",
     "               Quantitative Methods (q-bio.QM)}\n",
     "}\n",
-    "\n",
-    "@misc{fernandez2023spivae,\n",
-    "  title = {{{SPIVAE}}},\n",
-    "  author = {{Fern{\\'a}ndez-Fern{\\'a}ndez}, Gabriel},\n",
-    "  year = {2023},\n",
-    "  month = jul,\n",
-    "  url = {https://github.com/GabrielFernandezFernandez/SPIVAE},\n",
-    "  urldate = {2023-07-21},\n",
-    "  copyright = {Apache-2.0}\n",
-    "}\n",
     "```"
    ]
   }

nbs/source/02_utils.ipynb

@@ -85,7 +85,7 @@
     "            log_likelihood = mix_gaussian_loss(y_hat, target, reduction=self.reduction)\n",
     "        else:\n",
     "            log_likelihood = mix_gaussian_loss(y_hat, target[:,self.RF:], reduction=self.reduction)\n",
-    "            \n",
+    "\n",
     "        if self.reduction=='none':\n",
     "            kl = kl_divergence(mu, logvar, reduction='none') if self.c else 0\n",
     "            return log_likelihood, self.beta, kl\n",

nbs/tutorials/2_generation_FBM.ipynb

@@ -494,6 +494,20 @@
     "We can extract both parameters, $\\alpha$ and $D$, by fitting the scaling of the TA-MSD."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The time average mean squared displacement (TA-MSD) can be defined in terms of a trajectory that is\n",
+    "sampled at $T$ discrete times $t_i = i\\Delta t$ as,\n",
+    "$$ \\mathrm{TA−MSD}(\\Delta t) =\n",
+    "\\frac{1}{T − \\Delta t}\n",
+    "\\sum\\limits^{T −\\Delta t}_{i=1}\n",
+    "[x(t_i) − x(t_i + \\Delta t)]^2,\n",
+    "$$\n",
+    "where $\\Delta t$ is the time lag."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,