We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
sklearn.covariance.LedoitWolf or ConnectivityMeasure in plot_adhd_spheres
`ConnectivityMeasure` can be used here, and its default covariance estimator is `LedoitWolf`from `sklearn.covariance`.
I also prefer using partial correlations rather than precision, because no need for negating the connections.


--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `examples/03_connectivity/plot_adhd_spheres.py`
Content:
```
1 """
2 Extracting brain signal from spheres
3 ====================================
4 
5 This example extract brain signals from spheres described by the coordinates
6 of their center in MNI space and a given radius in millimeters. In particular,
7 this example extracts signals from Default Mode Network regions and compute a
8 connectome from them.
9 
10 """
11 
12 ##########################################################################
13 # Retrieve the dataset
14 from nilearn import datasets
15 adhd_dataset = datasets.fetch_adhd(n_subjects=1)
16 
17 # print basic information on the dataset
18 print('First subject functional nifti image (4D) is at: %s' %
19       adhd_dataset.func[0])  # 4D data
20 
21 
22 ##########################################################################
23 # Coordinates of Default Mode Network
24 dmn_coords = [(0, -52, 18), (-46, -68, 32), (46, -68, 32), (1, 50, -5)]
25 labels = [
26     'Posterior Cingulate Cortex',
27     'Left Temporoparietal junction',
28     'Right Temporoparietal junction',
29     'Medial prefrontal cortex'
30 ]
31 
32 
33 ##########################################################################
34 # Extracts signal from sphere around DMN seeds
35 from nilearn import input_data
36 
37 masker = input_data.NiftiSpheresMasker(
38     dmn_coords, radius=8,
39     detrend=True, standardize=True,
40     low_pass=0.1, high_pass=0.01, t_r=2.5,
41     memory='nilearn_cache', memory_level=1, verbose=2)
42 
43 func_filename = adhd_dataset.func[0]
44 confound_filename = adhd_dataset.confounds[0]
45 
46 time_series = masker.fit_transform(func_filename,
47                                    confounds=[confound_filename])
48 
49 ##########################################################################
50 # Display time series
51 import matplotlib.pyplot as plt
52 for time_serie, label in zip(time_series.T, labels):
53     plt.plot(time_serie, label=label)
54 
55 plt.title('Default Mode Network Time Series')
56 plt.xlabel('Scan number')
57 plt.ylabel('Normalized signal')
58 plt.legend()
59 plt.tight_layout()
60 
61 
62 ##########################################################################
63 # Compute precision matrices
64 from sklearn.covariance import LedoitWolf
65 cve = LedoitWolf()
66 cve.fit(time_series)
67 
68 
69 ##########################################################################
70 # Display connectome
71 from nilearn import plotting
72 
73 plotting.plot_connectome(cve.precision_, dmn_coords,
74                          title="Default Mode Network Connectivity")
75 
76 # Display connectome with hemispheric projections.
77 # Notice (0, -52, 18) is included in both hemispheres since x == 0.
78 title = "Connectivity projected on hemispheres"
79 plotting.plot_connectome(cve.precision_, dmn_coords, title=title,
80                          display_mode='lyrz')
81 
82 plotting.show()
83
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/examples/03_connectivity/plot_adhd_spheres.py b/examples/03_connectivity/plot_adhd_spheres.py
--- a/examples/03_connectivity/plot_adhd_spheres.py
+++ b/examples/03_connectivity/plot_adhd_spheres.py
@@ -60,23 +60,25 @@
 
 
 ##########################################################################
-# Compute precision matrices
-from sklearn.covariance import LedoitWolf
-cve = LedoitWolf()
-cve.fit(time_series)
-
+# Compute partial correlation matrix using object
+# :class:`nilearn.connectome.ConnectivityMeasure`: Its default covariance
+# estimator is Ledoit-Wolf, allowing to obtain accurate partial correlations.
+from nilearn.connectome import ConnectivityMeasure
+connectivity_measure = ConnectivityMeasure(kind='partial correlation')
+partial_correlation_matrix = connectivity_measure.fit_transform(
+    [time_series])[0]
 
 ##########################################################################
 # Display connectome
 from nilearn import plotting
 
-plotting.plot_connectome(cve.precision_, dmn_coords,
+plotting.plot_connectome(partial_correlation_matrix, dmn_coords,
                          title="Default Mode Network Connectivity")
 
 # Display connectome with hemispheric projections.
 # Notice (0, -52, 18) is included in both hemispheres since x == 0.
 title = "Connectivity projected on hemispheres"
-plotting.plot_connectome(cve.precision_, dmn_coords, title=title,
+plotting.plot_connectome(partial_correlation_matrix, dmn_coords, title=title,
                          display_mode='lyrz')
 
 plotting.show()

{"golden_diff": "diff --git a/examples/03_connectivity/plot_adhd_spheres.py b/examples/03_connectivity/plot_adhd_spheres.py\n--- a/examples/03_connectivity/plot_adhd_spheres.py\n+++ b/examples/03_connectivity/plot_adhd_spheres.py\n@@ -60,23 +60,25 @@\n \n \n ##########################################################################\n-# Compute precision matrices\n-from sklearn.covariance import LedoitWolf\n-cve = LedoitWolf()\n-cve.fit(time_series)\n-\n+# Compute partial correlation matrix using object\n+# :class:`nilearn.connectome.ConnectivityMeasure`: Its default covariance\n+# estimator is Ledoit-Wolf, allowing to obtain accurate partial correlations.\n+from nilearn.connectome import ConnectivityMeasure\n+connectivity_measure = ConnectivityMeasure(kind='partial correlation')\n+partial_correlation_matrix = connectivity_measure.fit_transform(\n+    [time_series])[0]\n \n ##########################################################################\n # Display connectome\n from nilearn import plotting\n \n-plotting.plot_connectome(cve.precision_, dmn_coords,\n+plotting.plot_connectome(partial_correlation_matrix, dmn_coords,\n                          title=\"Default Mode Network Connectivity\")\n \n # Display connectome with hemispheric projections.\n # Notice (0, -52, 18) is included in both hemispheres since x == 0.\n title = \"Connectivity projected on hemispheres\"\n-plotting.plot_connectome(cve.precision_, dmn_coords, title=title,\n+plotting.plot_connectome(partial_correlation_matrix, dmn_coords, title=title,\n                          display_mode='lyrz')\n \n plotting.show()\n", "issue": "sklearn.covariance.LedoitWolf or ConnectivityMeasure in plot_adhd_spheres\n`ConnectivityMeasure` can be used here, and its default covariance estimator is `LedoitWolf`from `sklearn.covariance`.\nI also prefer using partial correlations rather than precision, because no need for negating the connections.\n\n", "before_files": [{"content": "\"\"\"\nExtracting brain signal from spheres\n====================================\n\nThis example extract brain signals from spheres described by the coordinates\nof their center in MNI space and a given radius in millimeters. In particular,\nthis example extracts signals from Default Mode Network regions and compute a\nconnectome from them.\n\n\"\"\"\n\n##########################################################################\n# Retrieve the dataset\nfrom nilearn import datasets\nadhd_dataset = datasets.fetch_adhd(n_subjects=1)\n\n# print basic information on the dataset\nprint('First subject functional nifti image (4D) is at: %s' %\n      adhd_dataset.func[0])  # 4D data\n\n\n##########################################################################\n# Coordinates of Default Mode Network\ndmn_coords = [(0, -52, 18), (-46, -68, 32), (46, -68, 32), (1, 50, -5)]\nlabels = [\n    'Posterior Cingulate Cortex',\n    'Left Temporoparietal junction',\n    'Right Temporoparietal junction',\n    'Medial prefrontal cortex'\n]\n\n\n##########################################################################\n# Extracts signal from sphere around DMN seeds\nfrom nilearn import input_data\n\nmasker = input_data.NiftiSpheresMasker(\n    dmn_coords, radius=8,\n    detrend=True, standardize=True,\n    low_pass=0.1, high_pass=0.01, t_r=2.5,\n    memory='nilearn_cache', memory_level=1, verbose=2)\n\nfunc_filename = adhd_dataset.func[0]\nconfound_filename = adhd_dataset.confounds[0]\n\ntime_series = masker.fit_transform(func_filename,\n                                   confounds=[confound_filename])\n\n##########################################################################\n# Display time series\nimport matplotlib.pyplot as plt\nfor time_serie, label in zip(time_series.T, labels):\n    plt.plot(time_serie, label=label)\n\nplt.title('Default Mode Network Time Series')\nplt.xlabel('Scan number')\nplt.ylabel('Normalized signal')\nplt.legend()\nplt.tight_layout()\n\n\n##########################################################################\n# Compute precision matrices\nfrom sklearn.covariance import LedoitWolf\ncve = LedoitWolf()\ncve.fit(time_series)\n\n\n##########################################################################\n# Display connectome\nfrom nilearn import plotting\n\nplotting.plot_connectome(cve.precision_, dmn_coords,\n                         title=\"Default Mode Network Connectivity\")\n\n# Display connectome with hemispheric projections.\n# Notice (0, -52, 18) is included in both hemispheres since x == 0.\ntitle = \"Connectivity projected on hemispheres\"\nplotting.plot_connectome(cve.precision_, dmn_coords, title=title,\n                         display_mode='lyrz')\n\nplotting.show()\n", "path": "examples/03_connectivity/plot_adhd_spheres.py"}], "after_files": [{"content": "\"\"\"\nExtracting brain signal from spheres\n====================================\n\nThis example extract brain signals from spheres described by the coordinates\nof their center in MNI space and a given radius in millimeters. In particular,\nthis example extracts signals from Default Mode Network regions and compute a\nconnectome from them.\n\n\"\"\"\n\n##########################################################################\n# Retrieve the dataset\nfrom nilearn import datasets\nadhd_dataset = datasets.fetch_adhd(n_subjects=1)\n\n# print basic information on the dataset\nprint('First subject functional nifti image (4D) is at: %s' %\n      adhd_dataset.func[0])  # 4D data\n\n\n##########################################################################\n# Coordinates of Default Mode Network\ndmn_coords = [(0, -52, 18), (-46, -68, 32), (46, -68, 32), (1, 50, -5)]\nlabels = [\n    'Posterior Cingulate Cortex',\n    'Left Temporoparietal junction',\n    'Right Temporoparietal junction',\n    'Medial prefrontal cortex'\n]\n\n\n##########################################################################\n# Extracts signal from sphere around DMN seeds\nfrom nilearn import input_data\n\nmasker = input_data.NiftiSpheresMasker(\n    dmn_coords, radius=8,\n    detrend=True, standardize=True,\n    low_pass=0.1, high_pass=0.01, t_r=2.5,\n    memory='nilearn_cache', memory_level=1, verbose=2)\n\nfunc_filename = adhd_dataset.func[0]\nconfound_filename = adhd_dataset.confounds[0]\n\ntime_series = masker.fit_transform(func_filename,\n                                   confounds=[confound_filename])\n\n##########################################################################\n# Display time series\nimport matplotlib.pyplot as plt\nfor time_serie, label in zip(time_series.T, labels):\n    plt.plot(time_serie, label=label)\n\nplt.title('Default Mode Network Time Series')\nplt.xlabel('Scan number')\nplt.ylabel('Normalized signal')\nplt.legend()\nplt.tight_layout()\n\n\n##########################################################################\n# Compute partial correlation matrix using object\n# :class:`nilearn.connectome.ConnectivityMeasure`: Its default covariance\n# estimator is Ledoit-Wolf, allowing to obtain accurate partial correlations.\nfrom nilearn.connectome import ConnectivityMeasure\nconnectivity_measure = ConnectivityMeasure(kind='partial correlation')\npartial_correlation_matrix = connectivity_measure.fit_transform(\n    [time_series])[0]\n\n##########################################################################\n# Display connectome\nfrom nilearn import plotting\n\nplotting.plot_connectome(partial_correlation_matrix, dmn_coords,\n                         title=\"Default Mode Network Connectivity\")\n\n# Display connectome with hemispheric projections.\n# Notice (0, -52, 18) is included in both hemispheres since x == 0.\ntitle = \"Connectivity projected on hemispheres\"\nplotting.plot_connectome(partial_correlation_matrix, dmn_coords, title=title,\n                         display_mode='lyrz')\n\nplotting.show()\n", "path": "examples/03_connectivity/plot_adhd_spheres.py"}]}