diff --git a/GPy/mappings/__init__.py b/GPy/mappings/__init__.py
index b0d90ba2..97573aba 100644
--- a/GPy/mappings/__init__.py
+++ b/GPy/mappings/__init__.py
@@ -1,7 +1,7 @@
 # Copyright (c) 2013, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
-#from kernel import Kernel
+from kernel import Kernel
 from linear import Linear
 from mlp import MLP
 #from rbf import RBF
diff --git a/GPy/mappings/kernel.py b/GPy/mappings/kernel.py
index a794e561..07ac3cf6 100644
--- a/GPy/mappings/kernel.py
+++ b/GPy/mappings/kernel.py
@@ -3,7 +3,7 @@
 
 import numpy as np
 from ..core.mapping import Mapping
-from ..kern.kern import kern
+import GPy
 
 class Kernel(Mapping):
     """
@@ -25,7 +25,7 @@ class Kernel(Mapping):
     def __init__(self, X, output_dim=1, kernel=None):
         Mapping.__init__(self, input_dim=X.shape[1], output_dim=output_dim)
         if kernel is None:
-            kernel = kern.rbf(self.input_dim)
+            kernel = GPy.kern.rbf(self.input_dim)
         self.kern = kernel
         self.X = X
         self.num_data = X.shape[0]
diff --git a/GPy/mappings/mlp.py b/GPy/mappings/mlp.py
index ce0e04b0..61b2f80e 100644
--- a/GPy/mappings/mlp.py
+++ b/GPy/mappings/mlp.py
@@ -89,6 +89,7 @@ class MLP(Mapping):
 
     def df_dtheta(self, dL_df, X):
         self._df_computations(dL_df, X)
+        g = np.array([])
         for gW, gbias in zip(self._dL_dW, self._dL_dbias):
             g = np.hstack((g, gW.flatten(), gbias))
         return g
@@ -117,7 +118,6 @@ class MLP(Mapping):
         self._dL_dW[0] = (dL_da[:, :, None]*X[:, None, :]).sum(0).T
         self._dL_dbias[0] = (dL_da.sum(0))
         self._dL_dX = (dL_da[:, None, :]*W[None, :, :]).sum(2)
-        g = np.array([])
 
         
     def df_dX(self, dL_df, X):
diff --git a/GPy/testing/gplvm_tests.py b/GPy/testing/gplvm_tests.py
index ebb5c4e5..6223d833 100644
--- a/GPy/testing/gplvm_tests.py
+++ b/GPy/testing/gplvm_tests.py
@@ -7,33 +7,33 @@ import GPy
 
 class GPLVMTests(unittest.TestCase):
     def test_bias_kern(self):
-        N, num_inducing, input_dim, D = 10, 3, 2, 4
-        X = np.random.rand(N, input_dim)
+        num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4
+        X = np.random.rand(num_data, input_dim)
         k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
         K = k.K(X)
-        Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
+        Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T
         k = GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
         m = GPy.models.GPLVM(Y, input_dim, kernel = k)
         m.randomize()
         self.assertTrue(m.checkgrad())
 
     def test_linear_kern(self):
-        N, num_inducing, input_dim, D = 10, 3, 2, 4
-        X = np.random.rand(N, input_dim)
+        num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4
+        X = np.random.rand(num_data, input_dim)
         k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
         K = k.K(X)
-        Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
+        Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T
         k = GPy.kern.linear(input_dim) + GPy.kern.white(input_dim, 0.00001)
         m = GPy.models.GPLVM(Y, input_dim, kernel = k)
         m.randomize()
         self.assertTrue(m.checkgrad())
 
     def test_rbf_kern(self):
-        N, num_inducing, input_dim, D = 10, 3, 2, 4
-        X = np.random.rand(N, input_dim)
+        num_data, num_inducing, input_dim, output_dim = 10, 3, 2, 4
+        X = np.random.rand(num_data, input_dim)
         k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
         K = k.K(X)
-        Y = np.random.multivariate_normal(np.zeros(N),K,input_dim).T
+        Y = np.random.multivariate_normal(np.zeros(num_data),K,output_dim).T
         k = GPy.kern.rbf(input_dim) + GPy.kern.white(input_dim, 0.00001)
         m = GPy.models.GPLVM(Y, input_dim, kernel = k)
         m.randomize()