text:
\section{INTRODUCTION}
The phenomenon of Colossal Magnetoresistance (CMR)
in hole-doped rare-earth manganites has, in recent times, been the subject
of intense research efforts ~\cite{RVH,CHAN,URUSHI,MAHI1}.
These oxides belong to the ABO$_3$ class of perovskite oxides and
contain a mixed
valency of Mn, which occupies the B site. The A site is occupied by
rare-earth
ions like Nd, La etc. or by divalent ions like Pb, Ca etc. These oxides,
therefore,
have the general formula Re$_{1-x}$Ae$_x$MnO$_3$, where Re is
La, Nd etc. and
Ae is Ca, Pb etc.
There are a number of basic issues which need to be resolved to
understand
the unusual transport properties of these materials.
One of the interesting properties is the sharp peak in resistivity
($\rho$) close to
its ferromagnetic transition temperature ($T_c$). The peak in $\rho$ is
generally believed
to arise from an insulator-metal like transition on cooling below
$T_c$.
Since the system shows a transition from an insulator like state above
$T_c$ to a metallic state
below $T_c$, it is likely that there is a change in the density of states
(DOS) at the Fermi level
($E_f$), near $T_c$. The change in the DOS at $E_f$ ($n(E_f)$) is
thus ushered in by changing the temperature.
This issue is of fundamental importance as $n(E_f)$
will decide the nature of charge transport in the material.
Questions like the existence of a gap in the DOS at $E_f$, localization of
states near
$E_f$ etc. are still unresolved. We
formulate the following definite questions which we would like to seek
answers
to: (1) Is there a finite DOS at $E_f$ below $T_c$ i.e. in the metallic
state,
and if so, whether it has a temperature dependence? (2) Does a gap open
up in
the DOS near $E_f$ above $T_c$, i.e. in the paramagnetic insulating
state and if
so whether it is temperature dependent?

In this paper we report our extensive
investigations of the DOS of these materials as a function of
temperature, using variable temperature scanning tunneling spectroscopy.
We have carried out our studies on epitaxial
thin films and single crystals of
various compositions. Mainly we have studied two systems, namely,
La$_{0.8}$Ca$_{0.2}$MnO$_3$ epitaxial thin films and single
crystals of the
system La$_{1-x}$Pb$_x$MnO$_3$.

\section{EXPERIMENTAL DETAILS}
Single crystals of La$_{1-x}$Pb$_x$MnO$_3$ were grown by the
flux method
using PbO and PbF$_2$ as solvents ~\cite{MORRISH}. The flux ratio
has been optimized to lower
the growth temperature, to combat the high volatility of the flux. In
addition, the heating,
soaking and cooling temperatures have been optimized. The
precursors, homogenized in a
ball mill, are transferred to a Platinum-Iridium crucible and closed
tightly with a
Platinum lid. The growth process is carried out in a cylindrical
resistive furnace,
controlled by a programmable temperature controller. The charge is
soaked at 1050$^{ o}$C
for 24 hours and slow-cooled in steps of several ramp rates ranging
from 0.2 to 1.5$^{ o}$C/hour
to 850$^{ o}$C, and thereafter furnace-cooled to room temperature.
Crystals of typical
dimensions 1.5 $\times$ 1.5 $\times$ 1.5 mm$^3$ are obtained by this
method. The composition
of the as-grown crystals are found by EDX analysis. The lead content
is varied by changing
the charge-to-flux ratio. Single crystals of the compound
(La$_{1-y}$Nd$_y$)$_{1-x}$Pb$_x$MnO$_3$ are grown by a
similar method (this compound will be, hereinafter, referred to as
(NdLa)$_{1-x}$Pb$_x$MnO$_3$, which signifies that the Nd and La
concentrations are $\sim$ (1-x)/2, for the particular compound studied
here). La$_2$O$_3$, Nd$_2$O$_3$ and MnCO$_3$ are
dissolved in the ratio 1:1:4 in the flux mixture of PbO-PbF$_2$
and crystal growth initiated as in the case of La$_{1-
x}$Pb$_x$MnO$_3$. Here, crystals of typical
dimension, 2.5 $\times$ 2.5 $\times$ 1.5 mm$^3$ were obtained.

Epitaxial films of La$_{0.8}$Ca$_{0.2}$MnO$_3$ (referred as LCMO), were
prepared by pulsed laser ablation on LaAlO$_3$ substrates, using the
procedure described in ref. ~\cite{RAJ}.

The resistivity of the samples were measured by four-probe van der
Pauw method (for
the single crystals) or four probe linear method (for the thin film).
The magnetoresistance was measured using a superconducting
solenoid.

Scanning Tunneling Microscopy/Spectroscopy (STM/S) was done in a
home-made
variable temperature STM. The schematic diagram of the STM/S setup is
shown in
figure 1. The STM was operated from 100 K up to 375 K.
During the experiment
the STM chamber is kept in a cryopumped environment and all other
pumps are
disconnected from the system.

Since we have operated
our STM from temperatures up to 375 K and down to 100 K, we have
chosen samples
having a wide range of $T_c$ to get data for a good range both above
and below $T_c$.
The single crystals' surfaces were scraped mechanically to expose a
fresh
surface before loading it in the STM. The thin films was cleaned with
methanol
before loading it in the STM chamber. Mechanically cut Pt-Rh(13\%) tips
were used for all the tunneling experiments.
The samples were baked at about 370 K, in a
vacuum of 5 $\times$ 10$^{-6}$ torr, for 24 hours prior to the STM/S
measurements.
The STM chamber was then cooled to liquid nitrogen temperatures
and the chamber
was isolated from the external pumps. The samples were further
baked, at around 340 K, in a
cryopumped environment for 5-6 hours to avoid condensation of
residual gases
on the sample surface. The samples were then imaged at various
magnifications
and at different temperatures. The images obtained also served as a
test of the
cleanliness of the sample surface. The images were taken in the
constant current
mode, with the tip bias kept at 1.5 V
and the tunneling current, during imaging was stabilized at values
ranging
from 1 to 2 nA (exact values are specified for the particular images).
Reproducible images were obtained over long durations indicating that
the
surfaces were stable and only after obtaining reproducible images,
tunneling
spectroscopy was carried out.
This ensured the cleanliness of the
sample surface before the $I-V$ spectra were recorded.
We found that if gases like Nitrogen are made
to condense on the surface, most of the features in the $I-V$ curves are
washed out and the surface cannot be imaged.
During data acquisition
no external pumps were used and only the cryopump placed inside the
chamber
was used to retain the vacuum.

For recording the $I-V$ spectra , the tip bias was kept at 1.5 V and
the tunneling current ($I_t$) was stabilized at a particular value. The
feedback was then put to hold mode and the tip bias was swept
between $\pm$
1 V at a frequency of 6 Hz and a set of $I-V$ curves thus obtained, were
recorded digitally using a 16 bit AD card. The gain of the current
amplifier
is 10$^8$ V/A and the least count of the AD card is 300 $\mu$V, so
the minimum measurable
current with this setup is about 3 pA. The data were recorded at a rate
of 7.2 KHz. A  set of 5 $I-V$ curves were averaged. The $dI/dV-V$ and
$dlnI/dlnV-V$ curves were obtained by numerical differentiation of such
average $I-V$ curves. This procedure was repeated for different values
of
stabilization currents and at different points on the sample surface, at
each temperature.

To determine the exact value of the gaps observed,
variable distance tunneling
measurements were carried out for one sample
((NdLa)$_{0.73}$Pb$_{0.27}$MnO$_3$).
This was done only for positive tip bias (filled states of the sample).
The procedure followed was the same as above except, the tip bias was
swept from 0.01 to 2 V instead of $\pm$1 V and the feedback was kept in
the
sample mode. With an active feedback loop the tip went closer to the
sample
for lower biases, in order to keep the $I_t$ constant. This gave us a
large dynamic range for the measurement
of $I_t$ and we were able to measure the correct
voltage value for which the $I_t$ goes to zero and hence the correct
energy value for the band edges. For details of this method
see ref. ~\cite{FEENSTRA}.

\section{RESULTS}
In figure 2 we show the resistivity data of the samples
studied.
The materials, as expected, show a peak in $\rho$ at a temperature
close to $T_c$.
We designate this temperature, where the peak in $\rho$ occurs, as
$T_{IM}$.
The resistivities of the single crystals are much less than that of the
thin film. However, due to the small size of the crystals, the
absolute values of $\rho$ have uncertainties.
The details of the
samples are given in table I. Some of the quantities were not measured due
to experimental limitations, but the essential quantities for our
subsequent analyses and conclusions have been measured.
The resistivities are shown in zero field or in an applied field (3 or 6
Tesla). For the LCMO film the maximum magnetoresistance (MR) is in excess
of 80 \% for an applied field of 6 T. For (NdLa)$_{0.73}$Pb$_{0.27}$MnO$_3$
the maximum MR (at 3 T) is nearly 70 \%. Here we have defined the MR as
$(\rho(0)-\rho(H))/\rho(0)$.
It can be seen from the data on the
(NdLa)$_{0.73}$Pb$_{0.27}$MnO$_3$ system that the $T_c$ and
$T_{IM}$ can be varied
over a large temperature range by substituting Nd in place of La. This
is
expected, because the $T_c$, in these materials, decreases as the
average A-site cation radius
($<r_A>$) decreases. Here A-site refers to the A-site of the ABO$_3$
structure.
Substitution of smaller Nd in place of La thus leads to
the reduction of $T_c$ ~\cite{BELL,MAHI}.

Figure 3 shows an atomic resolution image obtained for the sample
La$_{0.6}$Pb$_{0.4}$MnO$_3$. The distance between the brighter
spots is
4.02 $\pm$ 0.2 \AA~  as derived from our calibration done on graphite.
These materials have a pseudo-cubic structure and the unit cell is
nearly cubic or
rhombohedral with $\alpha \approx$ 60.52$^o$ (for a perfect cube,
$\alpha$ = 60$^o$), as
obtained from x-ray structure determination.
The Mn-O-Mn distance in these materials is around 3.87 \AA. The
distance
observed by us is thus close to this distance and the difference can
arise due to
the uncertainty in calibration. One may thus argue that the surface
exposed has Mn-O-Mn chains.
However, we have not been able to ascertain, unambiguously, the
chemical identity of the imaged atoms. To determine the chemical identity
of the atoms, furthers studies involving bias dependent imaging of the
surface have to be performed.
We also observe a distortion from the perfect square array, as can be seen
from the 4.02 \AA $\times$ 4.02 \AA~  parallelogram drawn in figure 3.

Figure 4 shows a 853 \AA~ $\times$ 906 \AA~
image of the LCMO thin film. This image shows atomically smooth
terraces, which end in atomic level steps as
marked by the
arrows. These are typical growth patterns often observed in
thin film samples of these oxides ~\cite{GEETHA,WEI}.

Figure 5 shows the $dI/dV-V$ $(G-V)$ curves for two of the samples,
La$_{0.7}$Pb$_{0.3}$MnO$_3$ single crystal and LCMO thin film.
In our subsequent discussions we have referred to these curves. We
have shown the data for three distinct regions, $T < T_c$, $T
\approx
T_c$ and $T > T_c$. To avoid overcrowding of data, we have
shown only a cross-section
of the data taken.

The $G-V$ curves, for all the samples, show qualitative
variations with temperature,
when the temperature is changed across the $T_c$.
This is obvious directly from the $G-V$ curves.
Before a detailed discussion of the results, we point out some
preliminary
observations which can be made from the $G-V$ curves shown above,
which are common to all the samples studied. For $T < T_c$, the $G-V$
curves resemble those for a good metal, like platinum.
There is a finite value of the zero-bias conductance
($G_0$), and the $G-V$ curves are parabolic. The parabolic nature of
the $G-V$ curves is essentially a property of the tunneling barrier
~\cite{WOLF}.
This is expected as the metallic state is stabilized below $T_c$.
For comparison
we show, in figure 6, the $G-V$ curve for a 500 \AA~ film of platinum at
307 K. The inset shows the $G-V$ curve for the same film at 134 K.
The calculated curves shown in the figure are discussed later in section
IV B. The film was grown on a fire-polished glass surface using
electron-beam evaporation, in a base pressure of 10$^{-8}$ torr.

As the temperature is
increased to $T \approx T_c$, $G_0$ goes to zero and a gap like
feature opens up near zero bias i.e. the Fermi level.
As the temperature is increased further to $T > T_c$, $G_0$
becomes
non-zero again and the gap like feature vanishes. But these $G-V$ curves
are
qualitatively different from the metal-like $G-V$ curves for $T <
T_c$.
We will see below that this particular feature of the tunneling data for
$T > T_c$ implies the existence of a soft gap near $E_f$, with
additional contributions
to $G_0$ arising due to finite temperature.

\section{DISCUSSION}
The tunneling spectroscopy data as presented in the previous section
need to
be analyzed quantitatively before further conclusions can be drawn
from them.
There are different recipes for obtaining the density of states from
tunneling data ~\cite{AMLAN,STROSCIO,UKRAINTSEV}.
However, the problem becomes involved if the
DOS itself is temperature
dependent. This is in addition to the temperature dependence which
arises
through the Fermi function $f(E,T)$.
In the following, we have tried to take into
account all these effects to derive certain quantitative conclusions
about the DOS.
We have arranged the following discussion
in four subsections, to analyze our data, so that quantitative information
about the DOS ($n(E)$) can be obtained to the extent possible. In the
first
section we analyze the data for energy $\mid E-E_f\mid \ge$ 0.2 eV
which is the
region away from $E_f$ so that the overall temperature dependence of
$n(E)$ can
be obtained. In the second section we analyze the $n(E)$ near the $E_f$
for the ferromagnetic
region ($T < T_c$). In the third section we analyze the data for
temperatures
near the transition temperature $T_c$ ($T \approx T_c$).
In the fourth section we have investigated the region
close to $E_f$, for the paramagnetic regime ($T > T_c$).

\subsection{DOS for $\mid$ E-E$_f\mid \geq$ 0.2 eV}
In this section we discuss the features in the DOS for
$\mid E-E_f\mid \ge$ 0.2 eV. Figure 7
shows the $dlnI/dnV - V$ curves for different temperatures, for some of
the
samples  studied. $dlnI/dlnV$ is the normalized conductivity
$(dI/dV)/(I/V)$.
This quantity
is generally used as a measure of the DOS, independent of the barrier
parameters ~\cite{STROSCIO}.
The division of the differential conductance $(dI/dV)$ by
$I/V$ reduces the effect of the barrier parameters.
Within certain limits $dlnI/dlnV$ does
give a measure of the DOS
~\cite{AMLAN}.
This quantity $(dlnI/dlnV)$ is
not well-defined near zero-bias, when there is a gap like feature in the
DOS (low $G_0$) near the Fermi level ~\cite{IV}.
Due to this limitation we have calculated
$dlnI/dlnV$ outside the region of very low $G_0$
($\mid V\mid \ge$ 0.2 V), from the observed data.
The tunneling spectra for the low bias
region will be discussed in the following sections. From figure 7 we
conclude
that the DOS for $\mid E-E_f\mid \ge$ 0.2 eV changes dramatically
with temperature, when
the temperature is changed across $T_c$. The
behavior shown in figure 7(a) is a typical example.
For $T < T_c$, the DOS has a stronger
dependence on energy, on both the filled ($V < 0$) and unfilled ($V
> 0$) side than that for
$T > T_c$. Also the temperature dependence of $(dlnI/dlnV)$ saturates for
$T/T_c <$ 0.75, as shown in the inset of figure 7(b) where we have
shown
an example for La$_{0.6}$Pb$_{0.4}$MnO$_3$, which has a $T_c >$ 400 K
(we
could not measure $T_c$ due to experimental limitations, however, the
$T_{IM}$ = 401 K).

The temperature variation of $(dlnI/dlnV)$ at a given
voltage $V = 0.9$ volts ($(dlnI/dlnV)_{0.9 V}$)
is shown in figure 8 to find out the extent of variation in $(dlnI/dlnV)$.
We have chosen $V = 0.9$
volts, as it is away from $V = 0$ and thus represents states away from
$E_f$.
It can be seen from figure 8 that $(dlnI/dlnV)_{0.9 V}$ is higher
for $T < T_c$ than that for $T > T_c$ ( a preliminary
observation has been reported
in ref. ~\cite{AMLAN} and similar observations have been reported in
ref. ~\cite{WEI}).
This implies that the DOS is higher in value for $T < T_c$,
in this energy range, and it has a
distinct temperature variation as T changes through $T_c$. Eventually,
for $T \ll T_c$,
a temperature independent value is obtained. This
was seen before in the inset of figure 7(b).
The behavior seen in figure 8 has two noteworthy features. First, there
is a distinct peak in $(dlnI/dlnV)_{0.9 V}$ at $T \approx T_c$. This is

seen in all the samples. Second, the peak is sharper for the single crystal
than for the thin film.

For $T \approx T_c$, a gap like feature is present
in the DOS near $E_f$ and this results in a very sharp increase in the
DOS
beyond a particular voltage. This is seen in figure 8 as a rapid
increase of
$(dlnI/dlnV)_{0.9 V}$, close to $T_c$. The increase in
DOS at higher energies (away from $E_f$), in the temperature range
close to $T_c$ where there is
a gap at $E_f$, may imply a transfer of relative
spectral weights to higher
energies when the gap opens up.

\subsection{Tunneling data for T < T$_c$}
For $T < T_c$, there is a finite tunneling conductance at zero bias,
$G_0$. This is expected since, for $T < T_c$, the metallic state is
stabilized and so we conclude that there is a finite DOS at $E_f$
($n(E_f)$).
However $G_0$ also depends on the barrier parameters of the tunnel
junction formed
between the tip and sample, in
addition to $n(E_f$) and the temperature. For tunneling spectroscopy
done at
variable temperature it is difficult to ensure the constancy of these
parameters. The usual normalization procedures which remove the effect
of the barrier parameters, do not describe the region
near zero bias (i.e. near $E_f$) satisfactorily.
To remove this dependence on the barrier parameters
and also get an estimate of the relative change of $n(E_f$) with
temperature,
we normalize $G_0$ by the tunneling conductance at 0.9 V ($G_{0.9}$).
But $G_{0.9}$ itself might have a temperature dependence due to the
change in DOS with
temperature at that energy. We expect that the variation of
$G_0/G_{0.9}$,
due to the variation of $G_{0.9}$, can be accounted for if the observed
temperature
dependence of $G_{0.9}$ itself, is taken care of by some normalization
factor which is independent of the barrier parameters and depends only
on the DOS at that energy.
Therefore, we plot the quantity:
\begin{eqnarray}
g_{0N}(T)= \frac{G_0(T)}{G_{0.9}(T)}\left(\frac{dlnI}{dlnV}\right)_{0.9
V,T}
\end{eqnarray}
where $(dlnI/dlnV)_{0.9 V,T}$ is the value of $dlnI/dlnV$ at a sample bias
of 0.9 volts and at a temperature $T$. This quantity is known
experimentally and it is independent of the barrier parameters and
depends only on the DOS at that particular energy at a temperature $T$.
This normalized ratio $g_{0N}(T)$ in equation 1 is thus expected to mostly
reflect the variation
arising from the temperature variation of $n(E_f)$. The plots of
$g_{0N}$ for three
different samples are shown in figure 9.
For all the samples $g_{0N}(T)$ shows a rise below $T_c$ (or $T_{IM}$)
as the material
enters the metallic state and it reaches a temperature independent value
at lower temperatures. For the epitaxial film the growth of $g_{0N}$
(and hence of $n(E_f)$) is gradual whereas for the single crystals this
rise
is rather sharp. {\em These observations would imply that n(E$_f$) grows
rapidly below $T_c$
and reaches a temperature independent value, as in a metal.
This is a very important conclusion of our experiment.}

The observed parabolic shape of the $G-V$ curves and the fact that
$g_{0N}(T)$ has a negligible
dependence on temperature below $T_c$ indicate that the DOS near
$E_f$ is flat in the scale of $k_BT$
and temperature independent below $T_c$, just like a metal. To
strengthen this
conclusion, quantitatively, we
carried out a simple calculation using the expression for tunneling
current given
below and a constant DOS for both
tip and sample.
Equation 2 gives the expression for the tunneling current
for a trapezoidal barrier ~\cite{WOLF,AMLAN}:
\begin{eqnarray}
        I(s,V,W,T) &=& c\int_{-\infty}^{\infty}
N_s\left(E+\frac{eV}{2}\right)N_t\left(E-\frac{eV}{2}\right)\nonumber\\
&&\left[f\left(E-\frac{eV}{2},T
\right)-f\left(E+\frac{eV}{2},T\right)\right]\nonumber\\
&&\tilde{t}(s,E,W)dE
\end{eqnarray}
where the barrier penetration factor $\tilde{t}$ is given by
\begin{eqnarray}
\tilde{t}(s,E,W) & = & exp\left(-2ks\sqrt{2(W-E)}\right)
\end{eqnarray}
where $E$ is the energy of the electron,
$c$ is a constant dependent on the tip-sample
effective junction area,
$s$ is the tip-sample distance, $W$
is the average work function of the tip and sample surface, $V$ is the
bias between tip and sample, $T$ is the temperature, $N_t(E)$ and
$N_s(E)$ are the tip and sample DOS respectively, $k=\sqrt{m}/\hbar$
($m$ is the electron mass) and $f(E,T)$ is
the Fermi function at temperature $T$. In the above expression all the
energies are measured w.r.t. $E_f$ which is the zero of the energy
scale.

Figure 10(a) shows a comparison between an experimental $G-V$
curve, taken on the LCMO thin film at 160 K ($T < T_c$), and a
calculated
$G-V$ curve using constant tip and sample DOS, a tip-sample distance of
6.5 \AA~ and a work
function of 1.2 eV. The good agreement between the observed data and the
calculated curves, supports our conclusion
that below $T_c$, the DOS near and at $E_f$ is finite and metal-like.
For comparison, the experimental and calculated
$G-V$ curves (using again a constant tip and sample DOS and equation 2)
for a 500 \AA~ platinum film are shown in figure 6.

 The change in conductivity ($\sigma$) below $T_c$ will arise from a
change in the mobility ($\mu$) and/or a change in the
carrier concentration ($N$) [$\sigma = Ne\mu$].
The increase in $\mu$ below $T_c$ is expected due to the suppression
of the spin disorder scattering as the local magnetization builds up.
However,
if $n(E_f)$ rises rapidly below $T_c$, and builds up from a zero value
at $T_c$, it is expected that the effective carrier
concentration $N$ also rises as the sample is cooled below $T_c$.
{\em The large variation in $\rho$ near
$T_c$, may be a consequence
largely of a variable $n(E_f)$, giving rise to a large variation in $N$,
with a lesser contribution coming from the temperature
dependent mobility $\mu(T)$.}

\subsection{Tunneling data for T $\approx$ T$_c$}
For $T \approx T_c$, the value of $G_0$, goes to zero and a gap
opens up in $n(E)$ near
$E_f$, as is evident from the $G-V$ curves shown in figure 5 and the
plot of $g_{0N}$ vs. $T$
shown in figure 9. The gap ($2\Delta$) is shown for one $G-V$ curve in
figure 5. On heating from below $T_c$ this gap opens at
$\sim$15-20 K below $T_{IM}$ (or $T_c$) and sharply
rises to the maximum value. We denote the temperature where the gap
opens as $T_{gap}$.
It then decreases in magnitude as the temperature
is increased further above $T_c$ and finally disappears as the
temperature is increased well beyond $T_c$
and the observed $G_0$ becomes non-zero.
These observations would indicate that close to $T_c$ a gap
develops in the DOS near $E_f$. This gap collapses as the sample is
cooled below
$T_c$. The nature of the DOS near $E_f$ for $T \gg T_c$ will be
discussed later.

These features are observable both in the epitaxial
film and single crystals. However, the transitions are sharper for the
single
crystals. There is also a very interesting similarity between
$T_{gap}$ and the temperature where the MR of the material shows a peak.
It will be interesting to see if such large MR actually arises
due to such drastic changes in DOS on the application of a magnetic field,
when the sample temperature is near $T_c$.
In figure 11 the maximum values of the gaps ($2\Delta_{max}$) observed in
different materials have been plotted against the
$T_c$ (or $T_{IM}$)
of the materials. It is clear that the observed $2\Delta_{max}$ has a
strong correlation
with the $T_c$. The $T_c$'s of these materials are related to the
bandwidths.
{\em A material with larger bandwidth has a larger $T_c$. The
decrease in $2\Delta_{max}$ as $T_c$ increases would imply that
$2\Delta_{max}$ decreases as the bandwidth increases. This is an
important conclusion.} This also shows
that any mechanism that can change the bandwidth, will change the
value of $2\Delta_{max}$
and hence the transport properties close to $T_c$. Eventually, for
$T_c \rightarrow$ 400 K
(as in materials like La$_{0.7}$Sr$_{0.3}$MnO$_3$) the gap is
expected to
reduce to extremely small values. Interestingly, the largest $T_c$
observed in these
materials is around 400 - 450 K. These values of the gaps, measured
by tunneling, are
comparable to the transport
activation gap in these materials, as estimated from the $\rho$ vs. $T$
data,
which are $\sim$ 0.1 eV (see Table I).

To verify that the gap is real i.e. the current actually goes to zero
within
the gap region, we carried out variable separation tunneling
spectroscopy, as
described in detail in ref. ~\cite{FEENSTRA}. In this
technique, the tip is brought closer to the sample as the bias between
the tip and sample
and consequently $I_t$ approaches zero
(the particular method used is described in brief in section II).
This gives a high dynamic range in the measurement
of the tunneling current. This method enables us to effectively measure
tunneling currents
over a few orders of magnitude, so that we can properly define the
band-edges. Although we
have not converted the variable distance measurements to constant
distance measurements, our
purpose, of verifying the band-edges, is still served from just the as-
acquired data. This experiment was done only for positive tip bias i.e. for
the filled states of the sample. Therefore we were able to observe the
band-edge only for the filled states of the sample. Figure 12
shows the variable distance conductance ($G_s$) data, and it shows the
gap feature, denoted by $\Delta_{var}$, just like
the constant distance tunneling data. The experiment was done at 270 K and
the values of $\Delta_{var}$ and $\Delta$ (at $T \approx$ 270 K),
agree to within 0.01 eV.
This combination of the two techniques gives a quantitative
foundation to the observed gap.

\subsection{Tunneling data for T $>$ T$_c$}
Above $T_c$, the gap near $E_f$ closes again and $G_{0}$
assumes a finite value.
This implies, essentially, appearance of finite DOS at $E_f$. However
the transport in
the material is still activated. This is possible only if the new states
arising
close to $E_f$ are localized. We have to interpret
our tunneling data carefully since, at such high temperatures, the
temperature itself
plays an important role in determining the shape of the $G-V$ curves.
However,
we have carried out numerical calculations again using equation 2, to
find out if
the observed disappearance of the gap at high temperatures is due to
the thermal
smearing of the tunneling spectra, and {\em have found that the
disappearance of the gap
cannot be explained due to the thermal smearing alone}. In order to
explain
our tunneling data for $T > T_c$ we have to make the following
proposition. We
propose that the gap which developed near $E_f$ for $T \approx
T_c$, collapses to a
soft, Coulomb gap for $T > T_c$. The
presence of a soft, Coulomb
gap suggests that the states around $E_f$ are localized. One then has
an interplay
of Coulomb interaction and disorder. However, further
investigation is required before issues like the existence of a Coulomb
gap can be
established beyond doubt. At this moment we can only state that using the
above model, we can fit
our data quantitatively. However, we cannot guarantee that this is
the only way to explain the data. In the following, we describe the model
calculations which were carried out to determine the nature of the DOS
for $T > T_c$.

In figure 10(b), we show the comparison of the experimental $G-V$ curve
taken at 328 K (i.e. for $T \gg T_c$) for the LCMO thin film sample,
with the calculated $G-V$ curves (using equation 2) at
that temperature. The dotted line shows the calculated curve using a
constant DOS for the tip and sample.
The tunneling distance and the work function were
taken as 2.5 \AA~ and 1.2 eV respectively.
This can be taken as the background voltage dependence of $G$ for the
tunnel junction, due to just the barrier parameters, $s$ and $W$.
But unlike for $T < T_c$, the measured $G-V$ curve dips
below the calculated constant DOS curve for $\mid V\mid <$ 0.4 volts,
therefore suggesting that there is a dip in the DOS near the Fermi level
for $\mid E-E_f\mid <$ 0.4 eV.
Also, there is a significant asymmetry in the measured $G-V$ curve.
We have calculated the $G-V$ curve using the
model DOS, shown in the inset of figure 10(b), for the sample and a
constant DOS for the tip in equation 2 and
the same barrier parameters used for the constant DOS calculation,
for the bias region $\mid V \mid <$ 0.4. The model DOS is taken as a
quadratic function of $\mid E-E_f\mid$.
The value of the model DOS is
non-zero at $E_f$ (which was required for a
good match with our experimental data),
unlike a Coulomb gap. This could be due to the fact that the DOS, in the
presence of a Coulomb gap,
has an explicit temperature dependence which results in a change in the
width of the Coulomb gap as well as
a non-zero value for the DOS at $E_f$, at such high
temperatures ~\cite{SARVESTANI}.
The calculated $G-V$ curve using this model DOS is shown as the solid line
in figure 10(b). It is interesting to note that the
tunneling distance estimated
from the $G-V$ curves for $T < T_c$ (about 6.5 \AA) is
much larger than that estimated
from the $G-V$ curves for $T > T_c$ (about 2.5 \AA).
This could again be a
consequence of the fact that the
states near $E_f$ are localized for $T > T_c$. The
asymmetry in the experimental
$G-V$ curves for $T > T_c$, is reproduced, to a certain extent, by our
calculation using the model DOS. Therefore from the analysis given above,
we conclude that for $T > T_c$ a Coulomb (soft) gap is formed at $E_f$.

To summarize, our experiment suggests that the hard gap existing
close to $T_c$, closes at
a temperature somewhat higher than $T_c$ and gives way to a soft
gap with localized states
near $E_f$. This is an important observation. However, more
experiments are needed to confirm
the above picture.

\section{SUMMARY AND CONCLUSION}

From the tunneling studies carried out and the discussion in the above
sections, it is clear that
the density of states of hole doped manganites show large changes near
$E_f$, when
the temperature is changed across $T_c$. This plays an important role
in determining the transport properties, like resistance and
magnetoresistance, of
these materials. When the temperature is changed across $T_c$, there
is a transfer
of spectral weight in the DOS. Below $T_c$ the metallic state is
stabilized and there
is a finite DOS near $E_f$, which is flat in the scale of $k_BT$.

When the temperature is increased from below $T_c$, a gap appears
in the DOS near $E_f$,
just below $T_c$. The value of this gap is comparable to the transport
gap, estimated
from the resistivity data above $T_c$. The maximum value of this gap
is higher for the
samples with lower $T_c$. It may happen that, if near $T_c$ the
applied magnetic field modifies this feature of
the DOS near $E_f$, then this will be
reflected as a large change in $\rho$ and can thus be the
origin of CMR in these materials.
Our experiment suggests that, on heating much above $T_c$, the hard
gap gives way to a soft gap
near $E_f$, indicating that the states near $E_f$ are localized.
Opening up of a hard gap can arise from Jahn-Teller effect whereas, a
soft gap arises from
Coulomb interactions for localized states. Our data suggest that there is
a presence of both
these factors above $T_c$, modifying the nature of DOS.

\vspace{1cm}

\centerline{\bf Acknowledgment}

\vspace{0.5cm}

This work is supported by CSIR, Govt. of India.
The authors would like to thank Prof. C.N.R. Rao and Prof. T.V.
Ramakrishnan for helpful discussions.

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text:
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text:
AJOR Vol.6 No.2 , March 2016
A Hybrid ANN-GWO Algorithm for Prediction of Heart Disease
Author(s) Hamza Turabieh*
Information Technology Department, CIT Collage, Taif University, Taif, KSA.
The paper investigates the powerful of hybridizing two computational intelligence methods viz., Gray Wolf Optimization (GWO) and Artificial Neural Networks (ANN) for prediction of heart disease. Gray wolf optimization is a global search method while gradient-based back propagation method is a local search one. The proposed algorithm implies the ability of ANN to find a relationship between the input and the output variables while the stochastic search ability of GWO is used for finding the initial optimal weights and biases of the ANN to reduce the probability of ANN getting stuck at local minima and slowly converging to global optimum. For evaluation purpose, the performance of hybrid model (ANN-GWO) was compared with standard back-propagation neural network (BPNN) using Root Mean Square Error (RMSE). The results demonstrate that the proposed model increases the convergence speed and the accuracy of prediction.
Artificial Neural Network, Gray Wolf Optimizer, Back-Propagation, Heart Disease
Received 23 November 2015; accepted 5 March 2016; published 8 March 2016
Recently, heart problems are the major cause of deaths; human life depends on the performance of heart, which is pumping the blood to the whole parts through the body. Any heart problem will influence the other parts such as brain, kidney, lung, … etc. Many reasons will increase the risk of heart problems (diseases) such as: high or low blood pressure, smoking, high level cholesterol, obesity and lack of physical exercise. The World Health Organization (WHO) has estimated that 17.5 million deaths occur worldwide in 2012. About 7.4 million were dead based on heart disease; 6.7 million were due to stroke. As a result, heart disease is the number one cause of deaths. WHO estimated that by 2030, almost 23.6 million people will die due to heart disease [1] .
Discovering of heart disease by doctors based on symptoms, physical examinations and sings of patient body, which is hard task in the medical field. This is a multi-layered problem, which may lead to wrong presumptions and unpredictable effects. As a result, healthcare industry today develops huge amounts of complex data about patients, hospitals resources, disease diagnosis, electronic patient records, and medical devices… etc. The huge amount of data (records) is considered as key resources to be processed and analyzed for knowledge extraction that enable doctors to take the correct presumptions, which enhance the probability of survive.
In the medical field, researchers preferred to use back-propagation neural network (BPNN) to model unstructured problems due to its ability to map complex non-linear relationships between input and output variables. The back-propagation algorithm is a local search algorithm that uses gradient descent to iteratively modify the weights and biases. Minimizing the fitness function measured based on the root mean square error between the actual and ANN predicted output. Easy trapped in local minimum and slow convergence is the drawback of back-propagation algorithm. Back-propagation algorithm used to generate different set of weights and biases every re-run during training phase. As a result, each run will produce different prediction results and convergence speed.
To overcome the drawback of back-propagation algorithm, gray wolf optimizer (GWO) has been used to find the optimal starting weights and biases for back-propagation algorithm. GWO is one of the latest bio-inspired optimization algorithms, which mimic the hunting activity of gray wolves in the wildlife. GWO search for optimal solutions in different directions in order to minimize the chance of trapped in local minimum and increase the convergence speed.
The rest of the paper is organized as follows: Section 2 presents the background and literature on heart disease and Section 3 describes the methodology, in which neural networks molding of heart disease and its optimization of gray wolf optimizer through training process. Section 4 presents a discussion of the experimental results and Section 5 concludes the presented work in this paper.
A huge number of research works have been published in the prediction area for medical field. Dilip et al. [2] applied back-propagation neural network to predict neonatal disease diagnosis. The authors applied standard back-propagation on different data-sets of neonatal disease. The accuracy of the proposed model is 75% with higher stability. Yuehjen et al. [3] proposed a several hybrid models to predict heart disease such as logistic regression (LR), multivariate adaptive regression splines (MARS), artificial neural network (ANN) and rough set (RS). The performance of the proposed models is better than artificial neural network. Humar and Novruz [4] proposed a hybrid neural network that includes artificial neural network (ANN) and fuzzy neural network (FNN) to predict diabetes and heart diseases. The proposed model is able to support good accuracy values 84.24% and 86.8% for Pima Indians diabetes data-set and Cleveland heart disease data-set, respectively.
Milan and Sunila [5] investigated several data mining algorithms to solve cardiovascular disease such as: Artificial Neural Network (ANN), Support vector Machine (SVM), Decision Tree and RIPPER classifier. The accuracy of the ANN, SVM, Decision Tree and RIPPER are 80.06%, 84.12%, 79.05% and 81.08% respectively. SVM is able to predict the cardiovascular disease with higher accuracy. Mazurowski et al. [6] investigated the performance of class imbalance in training data using neural network for medical diagnosis. Two algorithms have been used standard back-propagation (BP) and particle swarm optimization ( PSO ). The results show that BP outperforms the PSO for small and large data-sets.
Resul et al. [7] introduced a methodology which uses SAS base software 9.1.3 for predicting of the heart disease. The proposed system is developed based on neural networks. The obtained accuracy is 89.01% which is considered good enough but not optimal. Archana and Sandeep [8] introduced a novel hybrid prediction algorithm with missing value imputation (HPM-MI). The authors proposed a hybrid model based on K-means clustering with Multilayer Perceptron. The performance of the proposed algorithm is investigated on three benchmark medical data sets namely Pima Indians Diabetes, Wisconsin Breast Cancer, and Hepatitis from the UCI Repository of Machine Learning. The results are very strong and the proposed model works fine when numbers of missing value are large in the data-set. Bajaj et al. [9] applied three data mining classification algorithm for heart disease such as decision tree, split validation and apply model. The proposed system is able to reduce medical mistakes and provide high accuracy prediction. Beheshti et al. [10] proposed a new meta-heuristics approach named Centripetal Accelerated Particle Swarm Optimization (CAPSO). The proposed approach is used to enhance the performance of ANN learning and accuracy. The performance has been evaluated over nine standard medical data-sets and the results are promising. Interested readers can find more related work on [11] - [13] .
This section gives a detailed account of the basic ANN and GWO, followed by a discussion on the ANN-GWO.
3.1. Artificial Neural Network
Artificial Neural Network (ANN) is adopted from the biological complex system, the human brain, which consists of a huge number of highly connected elements called neurons. ANN tries to find the relationships between input-output data pairs. In general, the collected data were randomized and split into three groups; Training (70% of the data-set), Validation and Testing (30% of the data-set) data-sets. The training data-sets used to learn the ANN based on finding the relationship between input and out pairs by adjusting the weights and biases using back-propagation algorithm. However; through learning process, there is a probability of the neural network to over-fit or over-learn the input-output data-set. This problem will generate a weak mapping between input-output especially for unseen data-set. Once over-fitting occurs, the validation data-set is used through learning process to guide and stop training if the validation error begins to rise. The prediction evaluation of the developed ANN model is done after finishing training phase though testing data-set [14] [15] . Artificial neural network have been successfully applied to solve hard and complex problems in the field of industry and research. A huge number of publications have proved the strength of ANN in the medical field [16] [17] .
The basic model of ANN consists of three layers, where each layer has different number of neurons. The three layers are input, hidden and output layers. All these layers are connected to each other in such a way so that each neuron in one layer is connected to all neurons in the following layer. The basic diagram for a network with a single neuron is illustrated in Figure 1.
The neurons of the input layer take the input data-set from the real environment. The input vector ( ) is transmitted using the connection that multiplies its strength by a weight (w) to produce the product ( ). Each neuron has a biases ( ). The output of the neuron is generated by and , which is a summation function and activation function. An activation function consists of two algebraic formulas linear and non-linear ones. These two functions enable the neural network to find the relationships between input and output. The outputs either send to other interconnected neurons or directly to the environment. The difference between the output and neural network output is considered as error.
3.2. Gray Wolf Optimizer
Gray Wolf Optimizer (GWO) is a new bio-inspired evolutionary algorithm proposed by Seyedali et al. [18] . GWO simulates the hunting process of gray wolves in the wildlife. Wolves used to live in a pack and there are two gray wolves (male and female) managing the other wolves in the pack. A very strong social dominate hierarchy is founded inside every pack. The size of each pack usually from 5 to 12 on average. According to [18] the social hierarchy of the pack is organized as following:
Figure 1. Mathematical principal of a neuron.
1) The alphas wolves (α): The leading wolves in the pack and responsible for making decisions. The alphas orders are dictated to the pack.
2) The betas wolves (β): The second level wolves after alphas in the pack. The main job of betas wolves to help and support alphas decisions.
3) The deltas wolves (δ): The third level in the pack is delta wolves. They used to follow alpha and beta wolves. The delta wolves have 5 categories as following:
a) Scouts: wolves are used to control and monitor the boundaries of the territory and alert the pack in case of danger.
b) Sentinels: protect and guarantee the safety of the pack.
c) Elders: strong wolves used to be alpha or beta wolves in the future.
d) Hunters: wolves used to help alpha and beta though hunting prey and providing food the pack.
e) Caretakers: wolves are responsible for caring the ill, wounded and weak wolves.
4) The omegas wolves (ω): are the lowest levels in the pack and they have to follow alpha, beta and delta wolves. They are the last wolves that are allowed to eat.
GWO algorithm consider alpha (α) wolves are the fittest solution inside the pack, while the second and third best solutions are named Beta (β) and delta (δ) respectively. The result of solutions inside the pack (population) are considered omega (ω). The process of hunting a prey is guided by α, β and ω.
The first step of hunting a prey is circling it by α, β and ω. The mathematical model of circling process as shown in equations 1, 2, 3 and 4.
where is the gray wolf position. t is the number of iteration. is prey position and is evaluated from Equation (2).
the A and C are coefficient vectors are evaluated based on Equations (3) and (4) respectively.
where a is a linearly decreased from 2 to 0 through the number of iterations, which is used to control the tradeoff between exploration and exploitation. Equation (5) used to update the value of variable a, where NumIter is the total number of iterations. Two random vectors between [0,1] namely and to simulate hunting a prey (find the optimal solution). The solutions alpha, beta and delta are considered to have a good knowledge about the potential location of prey. These three solutions helps others wolves (omega) to update their positions according to the position of alpha, beta and delta. Equation 6 presents the formula of updating wolves' positions.
The values of x1, X2 and x3 is evaluated as in Equations (7) (8) and (9) respectively.
The x1, X2 and x3 are the best 3 solutions in the population at iteration t. The values of A1, A2 andA3 are evaluated in Equation (3). The values of , and are evaluated as shown in Equations (10) (11) and (12) respectively.
The values of C1, C2 andC3 is evaluated in Equation (4). The pseudo code for GWO is shown in Figure 2.
3.2. Gray Wolf Optimizer of Neural Networks (ANN-GWO)
To find an accurate ANN model and reduce the drawback of back-propagation algorithm, GWO is hybridized with ANN. The proposed idea consists of two major steps. In the first one, ANN is trained using GWO. GWO is used to find the optimal initial weight and biases. The second step involves training the neural network using back-propagation algorithm. The weights and biases evolved from GWO. This idea will enhance the performance of back-propagation to search for global optima model. The weights and biases are evaluated as a vector of variables for the proposed model. The fitness of each vector is evaluated based on the Root Mean Square Error (RMSE), which finds the error between the actual input and predicted output. Equation (13) presents the RMSE, where Ti is the target output and Pi is predicted value from ANN. A lower value of RMSE indicates a better model. Figure 3 illustrates the pseudo code of the hybrid ANN-GWO algorithm.
4. Experimental Results
In the experiments, the proposed ANN-GWO is implemented using MATLAB and simulation are performed on an Intel Pentium 4, 2.33 GHz computer. We execute 11 independent runs on the data-set.
4.1. Problem Description
In this work, the data-set is adopted from UCI Machine Learning Repository, Cleveland database [19] which is a medical data-set related to heart disease. Cleveland database used to classify person into four classes (Normal (0), First Stroke (1), Second Stroke (2) and End of life (3)) regarding to the heart disease. The data-set has 166
Figure 2. Gray wolf optimizer algorithm.
Figure 3. The hybrid ANN-GWO algorithm.
records with 13 attributes (inputs) for each record and 4 classes (outputs). Table 1 and Table 2 illustrate the benchmark data-set and classes respectively.
4.2. Tuning Parameters for ANN and GWO
To find an accurate ANN model, a good parameters setting should be used for training and testing the ANN model. GWO is used to search for the initial optimal weights and biases. The parameters setting used for the proposed ANN-GWO after some preliminary experiments are shown in Table 3 and Table 4. GWO is able to find an optimal initial weights and biases in 51 generations, and the time used to reach optimal value of RMSE 2.812 mm was evaluated in 29.532 s. Figure 4 presents the convergence process in smooth curve with a fast decrease at the start and gradually slow down.
Table 1. Bechmark data-sets attributes.
Table 2. Benchmark datasets classes.
Table 3. Parameters setting for GWO.
Table 4. Parameters setting for ANN.
Figure 4. Evolving optimal weights and biases using gray wolf optimizer.
4.3. Results
The performance of GWO in finding the initial optimal weights and biases is founded by minimizing the RMSE (Equation (13)). The experiments for finding the initial weights and biases were implemented eleven times to ensure that RMSR reach the optimal value. In the heart disease problem, the RMSE converges to a value 2.812 mm using GWO, which is very close to 0.
In order to evaluate the performance of ANN-GWO, a comparison is done between standard ANN and ANN- GWO. Table 5 presents the results obtained for both models. The neural network architecture used for modeling ANN-GWO and standard ANN (13-8-5-2-1) is trained using back-propagation algorithm. The proposed model (ANN-GWO) is able to achieve a high quality performance goal 0.0029 in 40 epochs taking 2.435 s as shown in Figure 5. Whilst, the standard neural network based on back-propagation algorithm took 3000 epochs and 73.43 s to reach the 0.0019 goal as shown in Figure 6.
4.4. Discussions
The performance of ANN-GWO in tracking the original and predicted output for training and testing data-set is illustrated in Figure 7 and Figure 8 respectively. Analyzing the results shows that the performance of standard ANN is easy to trap in local minima and slow convergence. Whilst, ANN-GWO is faster convergence and reach optimal values better than the standard ANN. Figure 7 and Figure 8 show the values of the original and predicted results of the ANN-GWO and standard ANN respectively. It is clear that the performance of ANN-GWO is much better than standard ANN.
Figure 9 and Figure 10 show the box plots that illustrate the distribution results of the ANN-GWO and standard ANN respectively. It is clear that the ANN-GWO reduces gab between the best, average, and worst prediction
Table 5. Results of RMSE (mm).
Figure 5. Training of ANN-GWO model.
Figure 6. Training of standard ANN model.
Figure 7. Original and predicted output for training data-set.
Figure 8. Original and predicted output for testing data-set.
Figure 9. Box plot of RMSE for ANN-GWO.
Figure 10. Box plot of RMSE for standard ANN.
qualities, which shows that the proposed method is robust and mush better than the standard ANN. We believe that this since gray wolf optimizer helps the back-propagation to overcome the drawback of standard ANN.
This work has proposed a new hybrid algorithm between artificial neural network and gray wolf optimizer to enhance the performance of back-propagation algorithm and overcome the drawback of stuck at local minima. Based on the results of this work, GWO helps ANN to find optimal initial weights and biases, which speed up the convergence speed and reduce the RMSE error. The proposed hybrid model uses GWO as a global search algorithm, while back-propagation as a local search one. This kind of hybridization makes a balance between exploration and exploitation. Moreover, ANN-GWO model in comparison with standard back-propagation ANN, took almost more than the half time to find the optimal model. However, we believe that a future study is needed to investigate the optimal design of the neural network architecture such as number of hidden layers, number of neurons, transfer functions and learning functions.
Turabieh, H. (2016) A Hybrid ANN-GWO Algorithm for Prediction of Heart Disease. American Journal of Operations Research, 6, 136-146. doi: 10.4236/ajor.2016.62016.
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http://www.who.int/cardiovascular_diseases/en/
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[3] Shao, Y.E., Hou, C.-D. and Chiu, C.-C. (2014) Hybrid Intelligent Modeling Schemes for Heart Disease Classification. Applied Soft Computing, 14, 47-52.
http://dx.doi.org/10.1016/j.asoc.2013.09.020
[4] Kahramanli, H. and Allahverdi, N.(2008) Design of a Hybrid System for the Diabetes and Heart Diseases. Expert Systems with Applications, 35, 82-89.
http://dx.doi.org/10.1016/j.eswa.2007.06.004
[5] Kumari, M. and Godara, S. (2011) Comparative Study of Data Mining Classification Methods in Cardiovascular Disease Prediction 1. International Journal of Computer Science and Technology, 2, 304-308.
[6] Mazurowski, M.A., Habas, P.A., Zurada, J.M., Lo, J.Y., Baker, J.A. and Tourassi, G.D. (2008) Training Neural Network Classifiers for Medical Decision Making: The Effects of Imbalanced Datasets on Classification Performance. Neural Networks, 21, 427-436.
http://dx.doi.org/10.1016/j.neunet.2007.12.031
[7] Das, R., Turkoglu, I. and Sengur, A. (2009) Effective Diagnosis of Heart Disease through Neural Networks Ensembles. Expert Systems with Applications, 36, 7675-7680.
[8] Purwar, A. and Singh, S.K. (2015) Hybrid Prediction Model with Missing Value Imputation for Medical Data. Expert Systems with Applications, 42, 5621-5631.
[9] Bajaj, P., Choudhary, K. and Chauhan, R. (2015) Prediction of Occurrence of Heart Disease and Its Dependability on RCT Using Data Mining Techniques. Advances in Intelligent Systems and Computing, Springer India, 340, 851-858.
[10] Beheshti, Z., Shamsuddin, S.M., Beheshti, E. and Yuhaniz, S.S. (2014) Enhancement of Artificial Neural Network Learning Using Centripetal Accelerated Particle Swarm Optimization for Medical Diseases Diagnosis. Soft Computing, 18, 2253-2270.
[11] Seera, M. and Lim, C.P. (2014) A Hybrid Intelligent System for Medical Data Classification. Expert Systems with Applications, 41, 2239-2249.
[12] Wozniak, M., Graña, M. and Corchado, E. (2014) A Survey of Multiple Classifier Systems as Hybrid Systems. Information Fusion, 16, 3-17.
http://dx.doi.org/10.1016/j.inffus.2013.04.006
[13] Nishara Banu, M.A. and Gomathy, B. (2014) Disease Forecasting System Using Data Mining Methods. International Conference on Intelligent Computing Applications (ICICA), Coimbatore, 6-7 March 2014, 130-133.
[14] Hagan, M.T., Demuth, H.B. and Beale, M. (1996) Neural Network Design. PWS Publishing Co., Boston.
[15] Zhao, Y., Gao, J. and Yang, X.Z. (2005) A Survey of Neural Network Ensembles. International Conference on Neural Networks and Brain, 1, 438-442.
[16] James, A.R. (2014) A Fuzzy Nearest Neighbor Neural Network Statistical Model for Predicting Demand for Natural Gas and Energy Cost Savings in Public Buildings. Expert Systems with Applications, 41, 1813-1829.
[17] Wang, W.-C., Chau, K.-W., Qiu, L. and Chen, Y.-B. (2015) Improving Forecasting Accuracy of Medium and Long-Term Runoff Using Artificial Neural Network Based on EEMD Decomposition. Environmental Research, 139, 46-54.
http://dx.doi.org/10.1016/j.envres.2015.02.002
[18] Mirjalili, S., Mirjalili, S.M. and Lewis, A. (2014) Grey Wolf Optimizer. Advances in Engineering Software, 69, 46-61.
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[19] UCI, Machine Learning Repository, Cleveland Database.
https://archive.ics.uci.edu/ml/datasets/Heart+Disease
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We know it's so easy to get carried away especially with the beautiful selection of jewellery today, but do stick to your budget and trust us, you will be proud. There are a lot of beautiful jewellery pieces that you can buy in very reasonable prices today, especially capsule jewellery like gold earrings, rings and necklaces, all of which can be interchanged and worn. Imagine you have a beautiful pair of gold earrings and a matching necklace. The pendant can actually be re-worn as a ring and voila! You now have two sets of jewellery.
Yes, you're about to pick up that gorgeous pair of earrings or that pretty dainty ring and you're very excited, but remember one thing: you need to protect your jewellery and ensure you are buying genuine materials. Only visit a reputed jeweller who is transparent with the information. Ask about the purity of the metal or stone, its warranty and how to maintain the lustre. Asking the right questions will ensure that you are not cheated by anyone and you will learn new things to help buy jewellery further on.
Buying your own jewellery is a beautiful journey that every woman must have the experience of. Head over to Krishna Jewellers, Pearls & Gems at any of our various stores to sample our envious collection of jewellery all for you.


Douglas Shire Council governs the area from north of Cairns to north of Cape Tribulation.
DIVE Queensland is a membership-based organisation that promotes Queensland's diving industry.
Conservation Volunteers assists Australians to care for the natural environment by volunteering on conservation projects.
The Cassowary Coast Regional Council overseas the districts around the towns of Innisfail, Cardwell and Tully.
CANEGROWERS advocates, represents and provides services for sugar cane farmers.
The Cairns and Far North Environment Centre is an environmental organisation focussed on nature conservation and environmental protection.
Blue Hand Steam is a local Cairns business working to establish steam weeding technology to manage weeds.