some typos fixed

notebook/dfa_simulations.ipynb

@@ -31,15 +31,15 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Detrended Fluctuation Analysis is a method which allows to measure self-affinity properties of time series. It is claimed to be very roboust method for Hurst exponent calculation even for nonstationary signals. It consists of three main steps:\n",
+    "Detrended Fluctuation Analysis is a method which allows to measure self-affinity properties of time series. It is claimed to be very roboust method for Hurst exponent estimation even for nonstationary signals. It consists of three main steps:\n",
     "\n",
     "1) Cumulative sum calculation;\n",
     "\n",
     "2) Detrending time series in windows $\\Delta n$ equally distributed on logarithmic scale;\n",
     "\n",
     "3) Mean squared residuals $F$ calculation on a set of windows $\\Delta n_i$;\n",
     "\n",
-    "Finally to determine DFA exponent one need to fit a line to so-called fluctuation function $F(\\Delta n)$. A slope of the line is estimated Hurst exponent. \n",
+    "Finally, to determine DFA exponent one need to fit a line to so-called fluctuation function $F(\\Delta n)$. A slope of the line is our Hurst exponent estimator.\n",
     "\n",
     "In the following simulations we test robustness of the method to short and high amplitude artifacs and signal slicing. We use self-implemented version of DFA algorithm, which may be slower but for testing reasons is more transparent and thus easier to understand."
    ]
@@ -232,7 +232,7 @@
    "source": [
     "### Simulation 1: artifacts\n",
     "\n",
-    "Now we are ready to perform the first simulation. In biomedical signals (EEG in particular) many high amplitude artifacts appear. Those can be caused by body movements, eyes blinking or by recording device. Typically in most of the studies researchers inspect signals visually and remove parts of the signals is neccessary. Although some more sophisticated methods exist, this is still the most common choice giving best efficiency. However, because DFA is considered to be valid also for non-stationary time series we could take an adventage of that property. Beforehand let's test it if it is true.\n",
+    "Now we are ready to perform the first simulation. In biomedical signals (EEG in particular) many high amplitude artifacts appear. Those can be caused by body movements, eyes blinking or just by recording device. Typically, in most of the studies researchers inspect signals visually and remove parts of them when neccessary. Although some more sophisticated methods exist, this is still the most common choice giving the best efficiency. However, because DFA is considered to be valid also for non-stationary time series we could take an adventage of that property. Beforehand let's test it if it is true.\n",
     "\n",
     "First of all, we need some model of signal artifacs."
    ]
@@ -347,7 +347,7 @@
     }
    ],
    "source": [
-    "Nrep = 1000                    # how many resamplings\n",
+    "Nrep = 1000                   # how many resamplings\n",
     "x_down, x_top = 400, 3500     # range of artifacts beginnings\n",
     "sig_amp, mu_amp = 3.5, 10     # amplitude parameters (to random Gauss generator)\n",
     "sig_ncut, mu_ncut = 100, 500  #length of the artifact\n",