diff --git a/bayeso/acquisition.py b/bayeso/acquisition.py
index ea153c9..a31f325 100644
--- a/bayeso/acquisition.py
+++ b/bayeso/acquisition.py
@@ -1,10 +1,11 @@
 #
-# author: Jungtaek Kim (jtkim@postech.ac.kr)
-# last updated: November 29, 2022
+# author: Jungtaek Kim (jungtaek.kim.mail@gmail.com)
+# last updated: May 26, 2024
 #
 """It defines acquisition functions, each of which
 is employed to determine where next to evaluate."""
 
+import typing
 import numpy as np
 import scipy.stats
 
@@ -44,9 +45,9 @@ def pi(
     assert isinstance(pred_std, np.ndarray)
     assert isinstance(Y_train, np.ndarray)
     assert isinstance(jitter, float)
-    assert len(pred_mean.shape) == 1
-    assert len(pred_std.shape) == 1
-    assert len(Y_train.shape) == 2
+    assert pred_mean.ndim == 1
+    assert pred_std.ndim == 1
+    assert Y_train.ndim == 2
     assert pred_mean.shape[0] == pred_std.shape[0]
 
     with np.errstate(divide="ignore"):
@@ -84,9 +85,9 @@ def ei(
     assert isinstance(pred_std, np.ndarray)
     assert isinstance(Y_train, np.ndarray)
     assert isinstance(jitter, float)
-    assert len(pred_mean.shape) == 1
-    assert len(pred_std.shape) == 1
-    assert len(Y_train.shape) == 2
+    assert pred_mean.ndim == 1
+    assert pred_std.ndim == 1
+    assert Y_train.ndim == 2
     assert pred_mean.shape[0] == pred_std.shape[0]
 
     with np.errstate(divide="ignore"):
@@ -100,7 +101,7 @@ def ei(
 def ucb(
     pred_mean: np.ndarray,
     pred_std: np.ndarray,
-    Y_train: constants.TYPING_UNION_ARRAY_NONE = None,
+    Y_train: typing.Union[type(None), np.ndarray] = None,
     kappa: float = 2.0,
     increase_kappa: bool = True,
 ) -> np.ndarray:
@@ -135,10 +136,10 @@ def ucb(
     assert isinstance(Y_train, (np.ndarray, type(None)))
     assert isinstance(kappa, float)
     assert isinstance(increase_kappa, bool)
-    assert len(pred_mean.shape) == 1
-    assert len(pred_std.shape) == 1
+    assert pred_mean.ndim == 1
+    assert pred_std.ndim == 1
     if Y_train is not None:
-        assert len(Y_train.shape) == 2
+        assert Y_train.ndim == 2
     assert pred_mean.shape[0] == pred_std.shape[0]
 
     if increase_kappa and Y_train is not None:
@@ -182,9 +183,9 @@ def aei(
     assert isinstance(Y_train, np.ndarray)
     assert isinstance(noise, float)
     assert isinstance(jitter, float)
-    assert len(pred_mean.shape) == 1
-    assert len(pred_std.shape) == 1
-    assert len(Y_train.shape) == 2
+    assert pred_mean.ndim == 1
+    assert pred_std.ndim == 1
+    assert Y_train.ndim == 2
     assert pred_mean.shape[0] == pred_std.shape[0]
 
     with np.errstate(divide="ignore"):
@@ -212,7 +213,7 @@ def pure_exploit(pred_mean: np.ndarray) -> np.ndarray:
     """
 
     assert isinstance(pred_mean, np.ndarray)
-    assert len(pred_mean.shape) == 1
+    assert pred_mean.ndim == 1
 
     return -pred_mean
 
@@ -233,6 +234,6 @@ def pure_explore(pred_std: np.ndarray) -> np.ndarray:
     """
 
     assert isinstance(pred_std, np.ndarray)
-    assert len(pred_std.shape) == 1
+    assert pred_std.ndim == 1
 
     return pred_std