diff --git a/eo/app/Makefile.am b/eo/app/Makefile.am
new file mode 100644
index 00000000..64ca3c70
--- /dev/null
+++ b/eo/app/Makefile.am
@@ -0,0 +1,17 @@
+###############################################################################
+##
+## Makefile.am for app
+##
+###############################################################################
+
+SUBDIRS = gprop
+
+###############################################################################
+
+all:
+	for i in $(SUBDIRS); do pushd $$i && $(MAKE) all; popd; done
+
+clean:
+	for i in $(SUBDIRS); do pushd $$i && $(MAKE) clean; popd; done
+
+###############################################################################
diff --git a/eo/app/gprop/Makefile.am b/eo/app/gprop/Makefile.am
new file mode 100644
index 00000000..bc4a7b85
--- /dev/null
+++ b/eo/app/gprop/Makefile.am
@@ -0,0 +1,25 @@
+###############################################################################
+#
+# Makefile.am for app/gprop
+#
+###############################################################################
+
+DEPS = $(top_builddir)/src/libeo.a $(top_builddir)/src/utils/libeoutils.a
+
+###############################################################################
+
+INCLUDES = -I$(top_builddir)/src
+LDADDS = $(top_builddir)/src/libeo.a $(top_builddir)/src/utils/libeoutils.a
+
+###############################################################################
+
+bin_PROGRAMS = gprop
+
+###############################################################################
+
+gprop_SOURCES = gprop.cc
+gprop_DEPENDENCIES = $(DEPS)
+gprop_LDFLAGS = -lm
+gprop_LDADD = $(LDADDS)
+
+###############################################################################
diff --git a/eo/app/gprop/gprop.cc b/eo/app/gprop/gprop.cc
new file mode 100644
index 00000000..7890b18a
--- /dev/null
+++ b/eo/app/gprop/gprop.cc
@@ -0,0 +1,146 @@
+//-----------------------------------------------------------------------------
+// gprop
+//-----------------------------------------------------------------------------
+
+#include <stdlib.h>         // EXIT_SUCCESS EXIT_FAILURE
+#include <stdexcept>        // exception 
+#include <iostream>         // cerr cout
+#include <fstream>          // ifstream
+#include <string>           // string
+#include <utils/eoParser.h> // eoParser
+#include <eoPop.h>          // eoPop
+#include <eoGenContinue.h>  // eoGenContinue
+#include <eoProportional.h> // eoProportional
+#include <eoSGA.h>          // eoSGA
+#include "gprop.h"          // Chrom eoChromInit eoChromMutation eoChromXover eoChromEvaluator
+
+//-----------------------------------------------------------------------------
+// global variables
+//-----------------------------------------------------------------------------
+
+
+
+//-----------------------------------------------------------------------------
+// parameters
+//-----------------------------------------------------------------------------
+
+eoValueParam<unsigned> pop_size(10, "pop_size", "default population size", 'p');
+eoValueParam<unsigned> generations(10, "generations", "default generation number", 'g');
+eoValueParam<double> mut_rate(0.1, "mut_rate", "default mutation rate", 'm');
+eoValueParam<double> xover_rate(0.1, "xover_rate", "default crossover rate", 'x');
+eoValueParam<string> file("", "file", "common part of patterns filenames *.trn *.val and *.tst", 'f');
+
+//-----------------------------------------------------------------------------
+// auxiliar functions
+//-----------------------------------------------------------------------------
+
+void arg(int argc, char** argv);
+void load_file(mlp::set& s, const string& s);
+void ga();
+
+//-----------------------------------------------------------------------------
+// main
+//-----------------------------------------------------------------------------
+
+int main(int argc, char** argv)
+{
+  try
+    {
+      arg(argc, argv);
+      ga();
+    }
+  catch (exception& e)
+    {
+      cerr << argv[0] << ": " << e.what() << endl;
+      exit(EXIT_FAILURE);
+    }
+
+  return 0;
+}
+
+//-----------------------------------------------------------------------------
+// implementation
+//-----------------------------------------------------------------------------
+
+void arg(int argc, char** argv)
+{
+  eoParser parser(argc, argv);
+  
+  parser.processParam(pop_size,    "genetic operators");
+  parser.processParam(generations, "genetic operators");
+  parser.processParam(mut_rate,    "genetic operators");
+  parser.processParam(xover_rate,  "genetic operators");
+  parser.processParam(file,        "files");
+
+  if (parser.userNeedsHelp())
+    {
+      parser.printHelp(cout);
+      exit(EXIT_SUCCESS);
+    }
+
+  load_file(trn_set, "trn");
+  load_file(val_set, "val");
+  load_file(tst_set, "tst");
+    
+  phenotype::trn_max = trn_set.size();
+  phenotype::val_max = val_set.size();
+  phenotype::tst_max = tst_set.size();
+}
+
+//-----------------------------------------------------------------------------
+
+void load_file(mlp::set& set, const string& ext)
+{
+  string filename = file.value(); filename += "." + ext;
+
+  ifstream ifs(filename.c_str());
+  if (!ifs)
+    {
+      cerr << "can't open file \"" << filename << "\"" << endl;
+      exit(EXIT_FAILURE);
+    } 
+  
+  ifs >> set;
+
+  cout << "set.size() = " << set.size() << endl;
+  
+  if (set.size() == 0)
+    {
+      cerr << filename << " data file is empty!";
+      exit(EXIT_FAILURE);
+    }
+}
+
+//-----------------------------------------------------------------------------
+
+void ga()
+{
+  eoGenContinue<Chrom> continuator(generations.value());
+ 
+  eoProportional<Chrom> select;
+  eoChromMutation mutation(generations);
+  eoChromXover xover;
+  eoEvalFuncPtr<Chrom> evaluator(eoChromEvaluator);
+
+  eoSGA<Chrom> sga(select,
+		   xover, xover_rate.value(), 
+		   mutation, mut_rate.value(), 
+		   evaluator, 
+		   continuator);
+
+  eoInitChrom init;
+  eoPop<Chrom> pop(pop_size.value(), init);
+  apply<Chrom>(evaluator, pop);
+
+  cout << pop << endl;
+  
+  sga(pop);
+
+  cout << pop << endl;
+}
+
+//-----------------------------------------------------------------------------
+
+// Local Variables: 
+// mode:C++
+// End:
diff --git a/eo/app/gprop/gprop.h b/eo/app/gprop/gprop.h
new file mode 100644
index 00000000..392a51bb
--- /dev/null
+++ b/eo/app/gprop/gprop.h
@@ -0,0 +1,183 @@
+//-----------------------------------------------------------------------------
+// gprop.h
+//-----------------------------------------------------------------------------
+
+#ifndef gprop_h
+#define gprop_h
+
+//-----------------------------------------------------------------------------
+
+#include <iostream>               // istream ostream
+#include <string>                 // string
+#include <EO.h>                   // EO
+#include <eoOp.h>                 // eoMonOp eoQuadraticOp
+#include <eoEvalFuncPtr.h>        // eoEvalFunc
+#include <eoInit.h>               // eoInit
+#include <utils/rnd_generators.h> // normal_generator
+#include "mlp.h"                  // mlp::net mlp::set
+#include "qp.h"                   // qp::set
+#include "mse.h"                  // mse::error
+
+//-----------------------------------------------------------------------------
+// phenotype
+//-----------------------------------------------------------------------------
+
+struct phenotype
+{
+  unsigned trn_ok, val_ok, tst_ok;
+  double mse_error;
+
+  static unsigned trn_max, val_max, tst_max;
+
+  phenotype(const double& _mse_error = 0): mse_error(_mse_error) {}
+
+  operator double(void) const { return mse_error; }
+
+  friend bool operator<(const phenotype& a, const phenotype& b)
+  {
+    return a.mse_error < b.mse_error;
+  }
+
+  friend ostream& operator<<(ostream& os, const phenotype& p)
+  {
+    return os << p.trn_ok << "/" << p.trn_max << " "
+	      << p.val_ok << "/" << p.val_max << " "
+	      << p.tst_ok << "/" << p.tst_max << " "
+	      << p.mse_error;
+  }
+  
+  friend istream& operator>>(istream& is, phenotype& p)
+  {
+    return is;
+  }
+};
+
+unsigned phenotype::trn_max = 0, phenotype::val_max = 0, phenotype::tst_max = 0;
+
+//-----------------------------------------------------------------------------
+// genotype
+//-----------------------------------------------------------------------------
+
+typedef mlp::net genotype;
+
+//-----------------------------------------------------------------------------
+// Chrom
+//-----------------------------------------------------------------------------
+
+class Chrom: public EO<phenotype>, public genotype
+{
+public:
+  Chrom(): genotype(25, 2) {}
+
+  string className() const { return "Chrom"; }
+
+  void printOn (ostream& os) const 
+  { 
+    // os << static_cast<genotype>(*this) << " " << fitness(); 
+    os << fitness();
+  }
+  
+  void readFrom (istream& is) 
+  {
+    invalidate();
+  }
+};
+
+//-----------------------------------------------------------------------------
+// eoChromInit
+//-----------------------------------------------------------------------------
+
+class eoInitChrom: public eoInit<Chrom>
+{
+public:
+  void operator()(Chrom& chrom)
+  {
+    chrom.reset();
+    chrom.invalidate();
+  }
+};
+
+//-----------------------------------------------------------------------------
+// global variables
+//-----------------------------------------------------------------------------
+
+mlp::set trn_set, val_set, tst_set;
+
+//-----------------------------------------------------------------------------
+// eoChromMutation
+//-----------------------------------------------------------------------------
+
+class eoChromMutation: public eoMonOp<Chrom>
+{
+public:
+  eoChromMutation(eoValueParam<unsigned>& _generation):
+    generation(_generation) {}
+  
+  void operator()(Chrom& chrom)
+  {
+    mse::net tmp(chrom);
+    tmp.train(trn_set, 10, 0, 0.001);
+  }
+  
+private:
+  eoValueParam<unsigned>& generation;
+};
+
+//-----------------------------------------------------------------------------
+// eoChromXover
+//-----------------------------------------------------------------------------
+
+class eoChromXover: public eoQuadraticOp<Chrom>
+{
+public:
+  void operator()(Chrom& chrom1, Chrom& chrom2)
+  {
+  }
+};
+
+//-----------------------------------------------------------------------------
+// eoChromEvaluator
+//-----------------------------------------------------------------------------
+
+unsigned correct(const mlp::net& net, const qp::set& set)
+{
+  unsigned sum = 0;
+  
+  for (qp::set::const_iterator s = set.begin(); s != set.end(); ++s)
+    {
+      unsigned partial = 0;
+      
+      for (unsigned i = 0; i < s->output.size(); ++i)
+        if (s->output[i] < 0.5 && net(s->input)[i] < 0.5 ||
+            s->output[i] > 0.5 && net(s->input)[i] > 0.5)
+          ++partial;
+      
+      if (partial == s->output.size())
+        ++sum;
+    }
+
+  return sum;
+}
+
+
+
+phenotype eoChromEvaluator(const Chrom& chrom)
+{
+  //  extern mlp::set trn_set, val_set, tst_set;
+
+  phenotype p;
+  p.trn_ok = correct(chrom, trn_set);
+  p.val_ok = correct(chrom, val_set);
+  p.tst_ok = correct(chrom, tst_set);
+  p.mse_error = mse::error(chrom, val_set);
+
+  return p;
+};
+
+//-----------------------------------------------------------------------------
+
+#endif // gprop_h
+
+// Local Variables: 
+// mode:C++ 
+// End:
diff --git a/eo/app/gprop/l2.h b/eo/app/gprop/l2.h
new file mode 100644
index 00000000..011c6610
--- /dev/null
+++ b/eo/app/gprop/l2.h
@@ -0,0 +1,140 @@
+//-----------------------------------------------------------------------------
+// l2.h
+//-----------------------------------------------------------------------------
+
+#ifndef l2_h
+#define l2_h
+
+//-----------------------------------------------------------------------------
+
+#include <math.h>  // log
+#include <qp.h>    // neuron layer net set
+
+//-----------------------------------------------------------------------------
+
+namespace l2
+{
+  //---------------------------------------------------------------------------
+  // useful typedefs
+  //---------------------------------------------------------------------------
+
+  using qp::real;
+  using qp::vector;
+  using qp::max_real;
+  using qp::min_real;
+  using qp::set;
+  using qp::neuron;
+  using qp::layer;
+
+  //---------------------------------------------------------------------------
+  // error
+  //---------------------------------------------------------------------------
+  
+  real error(const mlp::net& net, const set& ts)
+  {
+    real error_ = 0.0;
+
+    for (set::const_iterator s = ts.begin(); s != ts.end(); ++s)
+      {
+	vector out = net(s->input);
+	
+	for (unsigned i = 0; i < out.size(); ++i)
+	  {
+	    real target = s->output[i];
+	    real value = out[i];
+	    error_ -= target * log(value + min_real) + 
+	      (1.0 - target) * log(1.0 - value + min_real);
+	  }
+      }
+
+    return error_;
+  }
+
+  //-------------------------------------------------------------------------
+  // l2
+  //-------------------------------------------------------------------------
+  
+  class net: public qp::net
+  {
+  public:
+    net(mlp::net& n): qp::net(n) {}
+    
+    real error(const set& ts)
+    {
+      real error_ = 0;
+      
+      for (set::const_iterator s = ts.begin(); s != ts.end(); ++s)
+	{
+	  forward(s->input);
+	  error_ -= backward(s->input, s->output);
+	}
+      
+      return error_;
+    }
+    
+  private:
+    real backward(const vector& input, const vector& output)
+    {
+      reverse_iterator current_layer = rbegin();
+      reverse_iterator backward_layer = current_layer + 1;
+      real error_ = 0;
+
+      // output layer
+      for (unsigned j = 0; j < current_layer->size(); ++j)
+	{
+	  neuron& n = (*current_layer)[j];
+	  real out = output[j];
+	  n.ndelta += n.delta = (out - n.out) / 
+	    (n.out * (1.0 - n.out) + min_real) * n.out * (1.0 - n.out);
+
+	  if (size() == 1)                                        // monolayer
+	    n.dxo += n.delta * input;
+	  else                                                    // multilayer
+	    for (unsigned k = 0; k < n.dxo.size(); ++k)
+	      n.dxo[k] += n.delta * (*backward_layer)[k].out;
+	  
+	  error_ += out * log(n.out + min_real) + 
+	    (1.0 - out) * log(1.0 - n.out + min_real);
+	}
+      
+      // hidden layers
+      while (++current_layer != rend())
+	{
+	  reverse_iterator forward_layer  = current_layer - 1;
+          reverse_iterator backward_layer = current_layer + 1;
+	  
+	  for (unsigned j = 0; j < current_layer->size(); ++j)
+	    {
+	      neuron& n = (*current_layer)[j];
+	      real sum = 0; 
+	      for (unsigned k = 0; k < forward_layer->size(); ++k)
+		{
+		  neuron& nf = (*forward_layer)[k];
+		  sum += nf.delta * (nf.n->weight[j] + nf.dweight1[j]);
+		}
+	      n.delta = n.out * (1.0 - n.out) * sum;
+	      n.ndelta += n.delta;
+	      
+	      if (backward_layer == rend())               // first hidden layer
+		n.dxo += n.delta * input;
+	      else                                     // rest of hidden layers
+		for (unsigned k = 0; k < n.dxo.size(); ++k)
+		  n.dxo[k] += n.delta * (*backward_layer)[k].out;
+	    }
+	}
+    
+      return error_;
+    }
+  };
+  
+  //---------------------------------------------------------------------------
+  
+} // namespace l2
+
+//-----------------------------------------------------------------------------
+
+#endif // l2_h
+
+// Local Variables: 
+// mode:C++ 
+// End:
diff --git a/eo/app/gprop/mlp.h b/eo/app/gprop/mlp.h
new file mode 100644
index 00000000..68e81a58
--- /dev/null
+++ b/eo/app/gprop/mlp.h
@@ -0,0 +1,290 @@
+//-----------------------------------------------------------------------------
+// mlp.h
+//-----------------------------------------------------------------------------
+
+#ifndef mlp_h
+#define mlp_h
+
+//-----------------------------------------------------------------------------
+
+#include <values.h>               // MAXFLOAT MINFLOAT
+#include <math.h>                 // exp
+#include <stdexcept>              // invalid_argument
+#include <iostream>               // istream ostream
+#include <algorithm>              // generate
+#include <vector>                 // vector
+#include <utils/eoRNG.h>          // eoRng
+#include <utils/rnd_generators.h> // normal_geneurator
+#include <vecop.h>                // *
+
+//-----------------------------------------------------------------------------
+
+namespace mlp
+{
+  //---------------------------------------------------------------------------
+  // useful typedefs
+  //---------------------------------------------------------------------------
+  
+  typedef double            real;
+  typedef std::vector<real> vector;
+  
+  const real max_real = MAXFLOAT;
+  const real min_real = MINFLOAT;
+
+
+  //---------------------------------------------------------------------------
+  // sigmoid
+  //---------------------------------------------------------------------------
+  
+  real sigmoid(const real& x)
+  {
+    return 1.0 / (1.0 + exp(-x));
+  }
+  
+  
+  //---------------------------------------------------------------------------
+  // neuron
+  //---------------------------------------------------------------------------
+  
+  struct neuron
+  {
+    real   bias;
+    vector weight;
+    
+    neuron(const unsigned& num_inputs = 0): weight(num_inputs) {}
+    
+    void reset()
+    {
+      normal_generator<real> rnd(1.0);
+      bias = rnd();
+      generate(weight.begin(), weight.end(), rnd);
+    }
+    
+    real operator()(const vector& input) const
+    {
+      return sigmoid(bias + weight * input);
+    }
+
+    unsigned length() { return weight.size() + 1; }
+    
+    void normalize()
+    {
+      real n = sqrt(bias * bias + weight * weight);
+      bias /= n;
+      weight /= n;
+    }
+
+    void desaturate()
+    {
+      bias = -5.0 + 10.0 / (1.0 + exp(bias / -5.0));
+      
+      for (vector::iterator w = weight.begin(); w != weight.end(); ++w)
+	*w = -5.0 + 10.0 / (1.0 + exp(*w / -5.0));
+    }
+  };
+
+  ostream& operator<<(ostream& os, const neuron& n)
+  {
+    return os << n.bias << " " << n.weight;
+  }
+  
+  
+  //---------------------------------------------------------------------------
+  // layer
+  //---------------------------------------------------------------------------
+  
+  class layer: public std::vector<neuron>
+  {
+  public:
+    layer(const unsigned& num_inputs = 0, const unsigned& num_neurons = 0): 
+      std::vector<neuron>(num_neurons, neuron(num_inputs)) {}
+
+    void reset()
+    {
+      normal_generator<real> rnd(1.0);
+      for(iterator n = begin(); n != end(); ++n)
+	n->reset();
+    }
+    
+    vector operator()(const vector& input) const
+    {
+      vector output(size());
+      
+      for(unsigned i = 0; i < output.size(); ++i)
+	output[i] = (*this)[i](input);
+
+      return output;
+    }
+
+    unsigned length() { return front().length() * size(); }
+
+    void normalize()
+    {
+      for(iterator n = begin(); n != end(); ++n)
+	n->normalize();
+    }
+
+    void desaturate()
+    {
+      for(iterator n = begin(); n != end(); ++n)
+	n->desaturate();
+    }
+  };
+
+
+  //---------------------------------------------------------------------------
+  // net
+  //---------------------------------------------------------------------------
+
+  class net: public std::vector<layer>
+  {
+  public:
+    net(const unsigned& num_inputs = 0,
+	const unsigned& num_outputs = 0, 
+	const std::vector<unsigned>& hidden = std::vector<unsigned>())
+    {
+      switch(hidden.size())
+	{
+	case 0:
+	  push_back(layer(num_inputs, num_outputs));
+	  break;
+	default:
+	  push_back(layer(num_inputs, hidden.front()));
+	  for (unsigned i = 0; i < hidden.size() - 1; ++i)
+	    push_back(layer(hidden[i], hidden[i + 1]));
+	  push_back(layer(hidden.back(), num_outputs));
+	  break;
+	}
+    }
+
+    void reset()
+    {
+      normal_generator<real> rnd(1.0);
+      for(iterator l = begin(); l != end(); ++l)
+	l->reset();
+    }
+
+    vector operator()(const vector& input) const
+    {
+      vector tmp = input;
+      
+      for(const_iterator l = begin(); l != end(); ++l)
+	tmp = (*l)(tmp);
+      
+      return tmp;
+    }   
+
+    unsigned winner(const vector& input) const
+    {
+      vector tmp = (*this)(input);
+      return (max_element(tmp.begin(), tmp.end()) - tmp.begin());
+    }
+
+    unsigned length() 
+    {
+      unsigned sum = 0;
+
+      for(iterator l = begin(); l != end(); ++l)
+	sum += l->length();
+      
+      return sum; 
+    } 
+
+    void normalize()
+    {
+      for(iterator l = begin(); l != end(); ++l)
+	l->normalize();
+    }
+
+    void desaturate()
+    {
+      for(iterator l = begin(); l != end(); ++l)
+	l->desaturate();
+    }
+  };
+
+
+  //---------------------------------------------------------------------------
+  // sample
+  //---------------------------------------------------------------------------
+  
+  struct sample
+  {
+    vector input, output;
+    
+    sample(unsigned input_size = 0, unsigned output_size = 0):
+      input(input_size), output(output_size) {}
+  };
+  
+  istream& operator>>(istream& is, sample& s)
+  {
+    return is >> s.input >> s.output;
+  }
+  
+  ostream& operator<<(ostream& os, const sample& s)
+  {
+    return os << s.input << " " << s.output;
+  }
+
+  
+  //---------------------------------------------------------------------------
+  // set
+  //---------------------------------------------------------------------------
+
+  class set: public std::vector<sample>
+  {
+  public:
+    set(unsigned input_size  = 0, unsigned output_size = 0, 
+	unsigned num_samples = 0): 
+      std::vector<sample>(num_samples, sample(input_size, output_size)) {}
+
+    set(istream& is)
+    {
+      is >> (*this);
+    }
+  };
+
+  ostream& operator<<(ostream& os, const set& s)
+  {
+    os << "<" << endl;
+    for (unsigned i = 0; i < s.size(); ++i)
+      os << s[i] << endl;
+    return os << ">";
+  }
+
+  //---------------------------------------------------------------------------
+  // euclidean_distance
+  //---------------------------------------------------------------------------
+
+  real euclidean_distance(const net& n1, const net& n2)
+  {
+    real sum = 0;
+
+    for(net::const_reverse_iterator l1 = n1.rbegin(), l2 = n2.rbegin(); 
+	l1 != n1.rend() && l2 != n2.rend(); ++l1, ++l2)
+      for(layer::const_iterator n1 = l1->begin(), n2 = l2->begin(); 
+	  n1 != l1->end() && n2 != l2->end(); ++n1, ++n2)
+	{
+	  real b = n1->bias - n2->bias;
+	  vector w = n1->weight - n2->weight;
+	  sum += b * b + w * w;
+	}
+    /*
+      #include <fstream>
+      std::ofstream file("dist.stat", ios::app);
+      file << sqrt(sum) << endl;
+    */
+    return sqrt(sum);
+  }
+
+  //---------------------------------------------------------------------------
+
+} // namespace mlp
+
+//-----------------------------------------------------------------------------
+
+#endif // mlp_h
+
+// Local Variables: 
+// mode:C++ 
+// End:
diff --git a/eo/app/gprop/mse.h b/eo/app/gprop/mse.h
new file mode 100644
index 00000000..841a88e3
--- /dev/null
+++ b/eo/app/gprop/mse.h
@@ -0,0 +1,140 @@
+//-----------------------------------------------------------------------------
+// mse.h
+//-----------------------------------------------------------------------------
+
+#ifndef mse_h
+#define mse_h
+
+//-----------------------------------------------------------------------------
+
+#include <qp.h>  // neuron layer net set
+
+//-----------------------------------------------------------------------------
+
+namespace mse
+{
+  //---------------------------------------------------------------------------
+  // useful typedefs
+  //---------------------------------------------------------------------------
+
+  using qp::real;
+  using qp::vector;
+  using qp::max_real;
+  using qp::min_real;
+  using qp::set;
+  using qp::neuron;
+  using qp::layer;
+
+  //---------------------------------------------------------------------------
+  // error
+  //---------------------------------------------------------------------------
+  
+  real error(const mlp::net& net, const set& ts)
+  {
+    real error_ = 0.0;
+
+    for (set::const_iterator s = ts.begin(); s != ts.end(); ++s)
+      {
+	vector out = net(s->input);
+	
+	for (unsigned i = 0; i < out.size(); ++i)
+	  {
+	    real diff = s->output[i] - out[i];
+	    error_ += diff * diff;
+	  }
+      }
+
+    return error_ / ts.size();
+  }
+  //-------------------------------------------------------------------------
+  // mse
+  //-------------------------------------------------------------------------
+  
+  class net: public qp::net
+  {
+  public:
+    net(mlp::net& n): qp::net(n) {}
+    
+    real error(const set& ts)
+    {
+      real error_ = 0;
+      
+      for (set::const_iterator s = ts.begin(); s != ts.end(); ++s)
+	{
+	  forward(s->input);
+	  error_ += backward(s->input, s->output);
+	}
+      error_ /= ts.size();
+	
+      return error_;
+    }
+      
+  private:
+    real backward(const vector& input, const vector& output)
+    {
+      reverse_iterator current_layer = rbegin();
+      reverse_iterator backward_layer = current_layer + 1;
+      real error_ = 0;
+
+      // output layer
+      for (unsigned j = 0; j < current_layer->size(); ++j)
+	{
+	  neuron& n = (*current_layer)[j];
+
+	  real diff = output[j] - n.out;
+	  n.ndelta += n.delta = diff * n.out * (1.0 - n.out);
+
+	  if (size() == 1)                                        // monolayer
+	    n.dxo += n.delta * input;
+	  else                                                    // multilayer
+	    for (unsigned k = 0; k < n.dxo.size(); ++k)
+	      n.dxo[k] += n.delta * (*backward_layer)[k].out;
+	  
+	  error_ += diff * diff;
+	}
+      
+      // hidden layers
+      while (++current_layer != rend())
+	{
+	  reverse_iterator forward_layer  = current_layer - 1;
+	  reverse_iterator backward_layer = current_layer + 1;
+	  
+	  for (unsigned j = 0; j < current_layer->size(); ++j)
+	    {
+	      
+	      neuron& n = (*current_layer)[j];
+	      real sum = 0;
+	      
+	      for (unsigned k = 0; k < forward_layer->size(); ++k)
+		{
+		  neuron& nf = (*forward_layer)[k];
+		  sum += nf.delta * (nf.n->weight[j] + nf.dweight1[j]);
+		}
+
+	      n.delta = n.out * (1.0 - n.out) * sum;
+	      n.ndelta += n.delta;
+	      
+	      
+	      if (backward_layer == rend())              // first hidden layer
+		n.dxo += n.delta * input;
+	      else                                     // rest of hidden layers
+		for (unsigned k = 0; k < n.dxo.size(); ++k)
+		  n.dxo[k] += n.delta * (*backward_layer)[k].out;
+	    }
+	}
+    
+      return error_;
+    }
+  };
+
+  //---------------------------------------------------------------------------
+  
+} // namespace mse
+
+//-----------------------------------------------------------------------------
+
+#endif // mse_h
+
+// Local Variables: 
+// mode:C++ 
+// End:
diff --git a/eo/app/gprop/qp.h b/eo/app/gprop/qp.h
new file mode 100644
index 00000000..e9142562
--- /dev/null
+++ b/eo/app/gprop/qp.h
@@ -0,0 +1,251 @@
+//-----------------------------------------------------------------------------
+// qp.h
+//-----------------------------------------------------------------------------
+
+#ifndef qp_h
+#define qp_h
+
+//-----------------------------------------------------------------------------
+
+#include <iostream>               // istream ostream
+#include <algorithm>              // fill
+#include <vector>                 // vector
+#include <utils/rnd_generators.h> // uniform_generator
+#include <mlp.h>                  // neuron layer net
+
+//-----------------------------------------------------------------------------
+
+namespace qp
+{
+  //---------------------------------------------------------------------------
+  // useful typedefs
+  //---------------------------------------------------------------------------
+
+  using mlp::real;
+  using mlp::vector;
+
+  using mlp::max_real;
+  using mlp::min_real;
+
+  using mlp::set;
+
+  //---------------------------------------------------------------------------
+  // useful constants
+  //---------------------------------------------------------------------------
+
+  const real eta_default    = 0.5;
+  const real eta_floor      = 0.0001;
+  const real alpha_default  = 0.9;
+  const real lambda_default = 0.5;
+  const real lambda0        = 0.1;
+  const real backtrack_step = 0.5;
+  const real me_floor       = 0.0001;
+  const real mw_floor       = 0.0001;
+  
+
+  //---------------------------------------------------------------------------
+  // neuron
+  //---------------------------------------------------------------------------
+  
+  struct neuron
+  {
+    mlp::neuron* n;
+    real out, delta, ndelta, dbias1, dbias2;
+    vector dweight1, dweight2, dxo;
+    
+    neuron(mlp::neuron& _n): 
+      n(&_n), out(0), delta(0), ndelta(0), dbias1(0), dbias2(0), 
+      dweight1(n->weight.size(), 0), 
+      dweight2(n->weight.size(), 0), 
+      dxo(n->weight.size(), 0) {}
+    
+    void reset()
+    {
+      // underlaying neuron
+      n->reset();
+      
+      // addons
+      out = delta = ndelta = dbias1 = dbias2 = 0;
+      fill(dweight1.begin(), dweight1.end(), 0);
+      fill(dweight2.begin(), dweight2.end(), 0);
+      fill(dxo.begin(), dxo.end(), 0);
+    }
+    
+    real operator()(const vector& input)
+    {
+      return out = mlp::sigmoid(n->bias + dbias1 + 
+				(n->weight + dweight1) * input);
+    }
+  };
+  
+  ostream& operator<<(ostream& os, const neuron& n)
+  {
+    return os << *n.n << " " << n.out << " " << n.delta << " " 
+	      << n.ndelta << " " << n.dbias1 << " " << n.dbias2 << " " 
+	      << n.dweight1 << " " << n.dweight2 << " " << n.dxo;
+  }
+  
+  
+  //---------------------------------------------------------------------------
+  // layer
+  //---------------------------------------------------------------------------
+  
+  class layer: public std::vector<neuron>
+  {
+  public:
+    layer(mlp::layer& l)//: std::vector<neuron>(l.begin(), l.end()) {}
+    {
+      for (mlp::layer::iterator n = l.begin(); n != l.end(); ++n)
+	push_back(neuron(*n));
+    }
+
+    void reset()
+    {
+      for(iterator n = begin(); n != end(); ++n)
+        n->reset();
+    }
+
+    vector operator()(const vector& input)
+    {
+      vector output(size());
+      
+      for(unsigned i = 0; i < output.size(); ++i)
+        output[i] = (*this)[i](input);
+      
+      return output;
+    }
+  };
+
+
+  //---------------------------------------------------------------------------
+  // net
+  //---------------------------------------------------------------------------
+  
+  class net: public std::vector<layer>
+  {
+  public:  
+    net(mlp::net& n) //: std::vector<layer>(n.begin(), n.end()) { reset(); }
+    {
+      for (mlp::net::iterator l = n.begin(); l != n.end(); ++l)
+	push_back(*l);
+    }
+
+    virtual ~net() {}
+
+    void reset()
+    {
+      for(iterator l = begin(); l != end(); ++l)
+        l->reset();
+    }
+    
+    real train(const set& ts, 
+	       unsigned   epochs, 
+	       real       target_error, 
+	       real       tolerance,
+	       real       eta      = eta_default, 
+	       real       momentum = alpha_default, 
+	       real       lambda   = lambda_default)
+    {
+      real error_ = max_real;
+      
+      while (epochs-- && error_ > target_error)
+	{
+	  real last_error = error_;
+	  
+	  init_delta();
+
+	  error_ = error(ts);
+	  
+	  if (error_ < last_error + tolerance)
+	    {
+	      coeff_adapt(eta, momentum, lambda);
+	      weight_update(ts.size(), true, eta, momentum);
+	    }
+	  else
+	    {
+	      eta *= backtrack_step;
+	      eta = max(eta, eta_floor);
+	      momentum = eta * lambda;
+	      weight_update(ts.size(), false, eta, momentum);
+	      error_ = last_error;
+	    }
+	}
+      
+      return error_;
+    }
+    
+    virtual real error(const set& ts) = 0;
+
+    // protected:
+    void forward(vector input)
+    {
+      for (iterator l = begin(); l != end(); ++l)
+	{
+	  vector tmp = (*l)(input);
+	  input.swap(tmp);
+	}
+    }
+     
+    // private:
+    void init_delta()
+    {
+      for (iterator l = begin(); l != end(); ++l)
+	for (layer::iterator n = l->begin(); n != l->end(); ++n)
+	  fill(n->dxo.begin(), n->dxo.end(), n->ndelta = 0.0);
+    }
+    
+    void coeff_adapt(real& eta, real& momentum, real& lambda)
+    {
+      real me = 0, mw = 0, ew = 0;
+      
+      for (iterator l = begin(); l != end(); ++l)
+	for (layer::iterator n = l->begin(); n != l->end(); ++n)
+	  {
+	    me += n->dxo * n->dxo;
+	    mw += n->dweight1 * n->dweight1;
+	    ew += n->dxo * n->dweight1;
+	  }
+      
+      me = max(static_cast<real>(sqrt(me)), me_floor);
+      mw = max(static_cast<real>(sqrt(mw)), mw_floor);
+      eta *= (1.0 + 0.5 * ew / ( me * mw));
+      eta = max(eta, eta_floor);
+      lambda = lambda0 * me / mw;
+      momentum = eta * lambda;
+#ifdef DEBUG
+      cout << me << "  \t" << mw << "  \t" << ew << "  \t" 
+	   << eta << "  \t" << momentum << "  \t" << lambda << endl;
+#endif // DEBUG
+    }
+    
+    void weight_update(unsigned size, bool fire, real eta, real momentum)
+    {
+      for (iterator l = begin(); l != end(); ++l)
+	for (layer::iterator n = l->begin(); n != l->end(); ++n)
+	  {
+	    n->ndelta /= size;
+	    n->dxo /= size;
+	    if (fire)
+	      {
+		n->n->weight += n->dweight1;
+		n->dweight2 = n->dweight1;
+		n->n->bias += n->dbias1;
+		n->dbias2 = n->dbias1;
+	      }
+	    n->dweight1 = eta * n->dxo + momentum * n->dweight2;
+	    n->dbias1 = eta * n->ndelta + momentum * n->dbias2;
+	  }
+    }
+  };
+
+  //---------------------------------------------------------------------------
+  
+} // namespace qp
+
+//-----------------------------------------------------------------------------
+
+#endif // qp_h
+
+// Local Variables: 
+// mode:C++ 
+// End:
diff --git a/eo/app/gprop/vecop.h b/eo/app/gprop/vecop.h
new file mode 100644
index 00000000..6e45a5d5
--- /dev/null
+++ b/eo/app/gprop/vecop.h
@@ -0,0 +1,213 @@
+//-----------------------------------------------------------------------------
+// vecop.h
+//-----------------------------------------------------------------------------
+
+#ifndef VECOP_H
+#define VECOP_H
+
+//-----------------------------------------------------------------------------
+
+#include <iostream>    // ostream istream
+#include <vector>      // vector
+#include <functional>  // plus minus multiplies divides
+#include <numeric>     // inner_product
+
+//-----------------------------------------------------------------------------
+// vector + vector
+//-----------------------------------------------------------------------------
+
+template<class T> vector<T> operator+(const vector<T>& v1, const vector<T>& v2)
+{
+  vector<T> tmp = v1;
+  transform(tmp.begin(), tmp.end(), v2.begin(), tmp.begin(), plus<T>());
+  return tmp;
+}
+
+template<class T> vector<T> operator-(const vector<T>& v1, const vector<T>& v2)
+{
+  vector<T> tmp = v1;
+  transform(tmp.begin(), tmp.end(), v2.begin(), tmp.begin(), minus<T>());
+  return tmp;
+}
+
+template<class T> T operator*(const vector<T>& v1, const vector<T>& v2)
+{
+  return inner_product(v1.begin(), v1.end(), v2.begin(), static_cast<T>(0));
+}
+
+template<class T> T operator/(const vector<T>& v1, const vector<T>& v2)
+{
+  return inner_product(v1.begin(), v1.end(), v2.begin(), static_cast<T>(0),
+		       plus<T>(), divides<T>());
+}
+
+//-----------------------------------------------------------------------------
+// vector += vector
+//-----------------------------------------------------------------------------
+
+template<class T> vector<T>& operator+=(vector<T>& v1, const vector<T>& v2)
+{
+  transform(v1.begin(), v1.end(), v2.begin(), v1.begin(), plus<T>());
+  return v1;
+}
+
+template<class T> vector<T>& operator-=(vector<T>& v1, const vector<T>& v2)
+{
+  transform(v1.begin(), v1.end(), v2.begin(), v1.begin(), minus<T>());
+  return v1;
+}
+
+//-----------------------------------------------------------------------------
+// vector + number
+//-----------------------------------------------------------------------------
+
+template<class A, class B> vector<A> operator+(const vector<A>& a, const B& b)
+{
+  vector<A> tmp = a;
+  transform(tmp.begin(), tmp.end(), tmp.begin(), bind2nd(plus<A>(), b));
+  return tmp;
+}
+
+template<class A, class B> vector<A> operator-(const vector<A>& a, const B& b)
+{
+  vector<A> tmp = a;
+  transform(tmp.begin(), tmp.end(), tmp.begin(), bind2nd(minus<A>(), b));
+  return tmp;
+}
+
+template<class A, class B> vector<A> operator*(const vector<A>& a, const B& b)
+{
+  vector<A> tmp = a;
+  transform(tmp.begin(), tmp.end(), tmp.begin(), bind2nd(multiplies<A>(), b));
+  return tmp;
+}
+
+template<class A, class B> vector<A> operator/(const vector<A>& a, const B& b)
+{
+  vector<A> tmp = a;
+  transform(tmp.begin(), tmp.end(), tmp.begin(), bind2nd(divides<A>(), b));
+  return tmp;
+}
+
+//-----------------------------------------------------------------------------
+// number + vector
+//-----------------------------------------------------------------------------
+
+template<class A, class B> vector<A> operator+(const B& b, const vector<A>& a)
+{
+  vector<A> tmp = a;
+  transform(tmp.begin(), tmp.end(), tmp.begin(), bind2nd(plus<A>(), b));
+  return tmp;
+}
+
+template<class A, class B> vector<A> operator-(const B& b, const vector<A>& a)
+{
+  vector<A> tmp(a.size(), b);
+  transform(tmp.begin(), tmp.end(), a.begin(), tmp.begin(), minus<A>());
+  return tmp;
+}
+
+template<class A, class B> vector<A> operator*(const B& b, const vector<A>& a)
+{
+  vector<A> tmp = a;
+  transform(tmp.begin(), tmp.end(), tmp.begin(), bind2nd(multiplies<A>(), b));
+  return tmp;
+}
+
+template<class A, class B> vector<A> operator/(const B& b, const vector<A>& a)
+{
+  vector<A> tmp(a.size(), b);
+  transform(tmp.begin(), tmp.end(), a.begin(), tmp.begin(), divides<A>());
+  return tmp;
+}
+
+//-----------------------------------------------------------------------------
+// vector += number
+//-----------------------------------------------------------------------------
+
+template<class A, class B> vector<A>& operator+=(vector<A>& a, const B& b)
+{
+  transform(a.begin(), a.end(), a.begin(), bind2nd(plus<A>(), b));
+  return a;
+}
+
+template<class A, class B> vector<A>& operator-=(vector<A>& a, const B& b)
+{
+  transform(a.begin(), a.end(), a.begin(), bind2nd(minus<A>(), b));
+  return a;
+}
+
+template<class A, class B> vector<A>& operator*=(vector<A>& a, const B& b)
+{
+  transform(a.begin(), a.end(), a.begin(), bind2nd(multiplies<A>(), b));
+  return a;
+}
+
+template<class A, class B> vector<A>& operator/=(vector<A>& a, const B& b)
+{
+  transform(a.begin(), a.end(), a.begin(), bind2nd(divides<A>(), b));
+  return a;
+}
+
+//-----------------------------------------------------------------------------
+// I/O
+//-----------------------------------------------------------------------------
+
+template<class T> ostream& operator<<(ostream& os, const vector<T>& v)
+{
+  os << '<';
+  if (v.size())
+    {
+      copy(v.begin(), v.end() - 1, ostream_iterator<T>(os, " "));
+      os << v.back();
+    } 
+  return os << '>';
+}
+
+template<class T> istream& operator>>(istream& is, vector<T>& v)
+{
+  v.clear();
+  
+  char c;
+  is >> c;
+  if (!is || c != '<')
+    is.setstate(ios::failbit);
+  else
+    {
+      T t;
+      do {
+	is >> c;
+	if (is && c!= '>')
+	  {
+	    is.putback(c);
+	    is >> t;
+	    if (is)
+	      v.push_back(t);
+	  }
+      } while (is && c != '>');
+    }
+  
+  return is;
+}
+
+//-----------------------------------------------------------------------------
+// euclidean_distance
+//-----------------------------------------------------------------------------
+
+template<class T> T euclidean_distance(const vector<T>& v1, 
+				       const vector<T>& v2)
+{
+  T sum = 0, tmp;
+  
+  for (unsigned i = 0; i < v1.size(); ++i)
+    {
+      tmp = v1[i] - v2[i];
+      sum += tmp * tmp;
+    }
+
+  return sqrt(sum);
+}
+
+//-----------------------------------------------------------------------------
+
+#endif VECOP_H