diff --git a/notebook/llvm_cbuilder_intro.pdf b/notebook/llvm_cbuilder_intro.pdf
index b647a15..a7b17d4 100644
Binary files a/notebook/llvm_cbuilder_intro.pdf and b/notebook/llvm_cbuilder_intro.pdf differ
diff --git a/notebook/parallel_vectorize.ipynb b/notebook/parallel_vectorize.ipynb
index b0bdaff..518594a 100644
--- a/notebook/parallel_vectorize.ipynb
+++ b/notebook/parallel_vectorize.ipynb
@@ -78,7 +78,7 @@
     }, 
     {
      "cell_type": "code", 
-     "collapsed": false, 
+     "collapsed": true, 
      "input": [
       "from llvm.ee import *", 
       "engine = EngineBuilder.new(m).create()         # Generate JIT engine", 
@@ -153,6 +153,97 @@
       }
      ], 
      "prompt_number": 4
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "* * *", 
+      "", 
+      "Internals", 
+      "---------", 
+      "", 
+      "There are four functions behind each multithreaded _ufunc_.", 
+      "", 
+      "1. the workload function (user defined);", 
+      "2. the thread worker function (`UFuncCoreGeneric`);", 
+      "3. the thread manager function (`ParallelUFuncPlatform`);", 
+      "4. the ufunc entry point function (`SpecializedParallelUFunc`).", 
+      "", 
+      "**UFuncCoreGeneric** specializes to a llvm function type.", 
+      "**It currently understands simple builtin scalar types (integers, float, double) only as arguments and return-type for the workload function.**", 
+      "It sends work items to the workload function and performs work-stealing when it has finished its own workqueue.", 
+      "Work-stealing uses atomic compare-exchange (or CAS) instruction to acquire ownership of a workqueue.", 
+      "Work-stealing is implemented in the `UFuncCore._do_work_stealing`.", 
+      "It can be disabled on platform that does not support atomic operations.", 
+      "", 
+      "**ParallelUFuncPlatform** specializes to the maximum number of threads. ", 
+      "It divides all works equally among all threads.", 
+      "Each thread executes the function generated by `UFuncCoreGeneric` once.", 
+      "", 
+      "**SpecializedParallelUFunc** is the specialized _ufunc_ entry point for a specific combination of ", 
+      "workload, UFuncCoreGeneric and ParallelUFuncPlatform.", 
+      "", 
+      "Here's an example that uses `SpecializedParallelUFunc` directly for the `SumOfThree` workload."
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "import parallel_vectorize as pv", 
+      "# specialize", 
+      "def_spuf = pv.SpecializedParallelUFunc(pv.ParallelUFuncPlatform(num_thread=2),", 
+      "                                       pv.UFuncCoreGeneric(llvm_sum3.type.pointee),", 
+      "                                       CFuncRef(llvm_sum3))", 
+      "# define", 
+      "spuf = def_spuf(m)", 
+      "print(spuf.name)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "specialized_parallel_ufunc_2_ufunc_worker.i32.i32.i32.i32_sum.of.three"
+       ]
+      }
+     ], 
+     "prompt_number": 5
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "`CFuncRef` also accepts arbitrary function pointer as long as the function type is provided."
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "# specialize", 
+      "fnty = llvm_sum3.type.pointee", 
+      "sum3ptr = engine.get_pointer_to_function(llvm_sum3)", 
+      "print(\"as function pointer: %x\" % sum3ptr)", 
+      "def_spuf = pv.SpecializedParallelUFunc(pv.ParallelUFuncPlatform(num_thread=2),", 
+      "                                       pv.UFuncCoreGeneric(fnty),", 
+      "                                       CFuncRef('sum3.as.ptr', fnty, sum3ptr)) # name, type, ptr", 
+      "# define", 
+      "spuf = def_spuf(m)", 
+      "print(spuf.name)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "as function pointer: 7f0bfc090740", 
+        "specialized_parallel_ufunc_2_ufunc_worker.i32.i32.i32.i32_sum3.as.ptr"
+       ]
+      }
+     ], 
+     "prompt_number": 6
     }
    ]
   }
diff --git a/notebook/parallel_vectorize.pdf b/notebook/parallel_vectorize.pdf
new file mode 100644
index 0000000..394f364
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