text:
\section{Introduction}

Quantum entanglement, which began with the famous EPR controversy
\cite{mermin}, has become one of the most exciting and important
fields of research in recent times. Stated simply, entanglement is the
quantum correlation among different parts of a many-body system. It is a
property of a quantum state and does not have any classical counterpart.
It signifies that when a quantum system consists of two parts, one part
is correlated with the other part even when the two parts
are far apart and not `physically' connected. Besides being fundamentally
important in understanding or interpreting quantum mechanics, there are
three main motivations for considering entanglement seriously
\cite{vedral}; it can be used to study the quantum-to-classical transition,
it can be used for studying quantum phase transitions, and it has the
potential to play a significant role in modern technology. Entanglement is at
the heart of quantum computation and quantum communication which may be
viewed as the future of computation and communication science.

In this paper, we will study the entanglement of a number of many-body
systems in order to characterize and better understand the eigenstates of a
many-body Hamiltonian. A wide range of entanglement studies have already been
carried out on many-body systems \cite{amico}, but to the best of our
knowledge, the role of long-range interactions has not been investigated.
Unlike many of the other studies of many-body
systems, we will not try to find the scaling properties of entanglement with
the system size; instead, we will make a
comparative study of finite systems to understand the relative behaviors of
different interacting models. The Pariser-Parr-Pople (PPP) Hamiltonian with
standard parameters, the Hubbard Hamiltonian with different values of the
on-site interaction and the antiferromagnetic Heisenberg Hamiltonian with
both spin 1/2 and 1 sites will be used for our comparative studies. The
investigations will be done for the ground states of chains with either
varying lengths (with equal block sizes) or varying block sizes (with fixed
chain length). In the case of the interacting electron systems, we will also
study a few important excited states such as $1^1A_g^+$, $2^1A_g^+$,
$1^1B_u^-$ and $1^3B_u^+$. These correspond to the important states of
a conjugated polymer, namely, the ground state
($1^1A_g^+$), the lowest energy two-photon state ($2^1A_g^+$), the lowest
energy one-photon state ($1^1B_u^-$), and the lowest energy triplet state
($1^3B_u^+$). The labels `$A$' and `$B$' correspond to even and odd parity
states under reflection of the chain. For linear chains these
are also even or odd under inversion, and hence the subscript `$g$' goes
with `$A$' state and `$u$' with `$B$' states. The superscript `+' or `-'
refers to even or odd states under electron-hole symmetry. The `+' space
includes `covalent' many-body basis states with one electron per site,
while `ionic' space excludes these states. To better understand the effect
of long-range interactions, we will also study the entanglement spectrum of
the ground state of a chain. A comparison will be done with the results for
the short-range interacting Hubbard model (with $U/t = 4$).

Our study serves the important purpose of understanding the high accuracy of
density matrix renormalization group (DMRG) technique \cite{schollwock} when
applied to the PPP model, even though it incorporates long-range
electron-electron interactions.
The success of the DMRG method in low-dimensional systems is attributed to
the connection between the area law of the entanglement entropy, $S$
\cite{srednicki,vidal}, and the cut-off, $m$, in the number of density matrix
eigenvectors (DMEVs) that should be retained in a DMRG calculation for a
given accuracy. The entanglement entropy of a system surrounded by an
environment scales as the area between the system and the environment. The
cut-off in the number of DMEVs for a fixed accuracy scales exponentially with
the entanglement entropy ($m\sim 2^S$) \cite{schollwock}.
However, one-dimensional systems away from criticality have a constant
entanglement entropy independent of the size of the system. This explains why
the DMRG method is so successful in studying correlated
one-dimensional systems. It also underlines the difficulties with the DMRG
technique in studying higher dimensional systems as well as one-dimensional
systems close to criticality; the latter systems have a logarithmic correction
to the entropy which leads to an increase in the entanglement entropy
as one approaches the critical point. The area law arises due to the
dangling bonds which are created by cutting the system from the environment.
This would seem to imply that when we have systems with long-range
interactions, even in one dimension the DMRG method should not retain the
same accuracy for a given cut-off as the system size is increased because
the number of interactions that are cut resulting in
dangling bonds increases with increasing system size. However, DMRG
calculations on quasi-one-dimensional systems with diagonal long-range
interactions have proved to be very accurate. Our entanglement study of
one-dimensional systems is aimed at understanding this feature.

We will also investigate the entanglement properties of a 12-site icosahedral
system using the PPP Hamiltonian. This system has the largest non-Abelian
point group symmetry; this enables us to examine
the role of spatial and spin symmetries in the entanglement of a state.
In this context, we will explicitly discuss the issue of degeneracies,
noting that the entanglement obtained for different
degenerate states are not the same. Additionally, for both the chain and
icosahedral systems, a comparative
study will be made between the entanglement profiles (across the
energy spectrum) and the corresponding profile of the density of
states (DoS) leading to some interesting observations.

In the next section (Sec. 2), we will first discuss the theoretical
background of our work where we discuss the measure of bipartite entanglement
for pure states. Subsequently, we will introduce the different
Hamiltonians used and the numerical techniques employed. In Sec. 3, we
will present and discuss our results, first for chains and then for the
icosahedral system. At the end of this section, we will
compare the entanglement profiles with the corresponding DoS profiles.
We will then conclude our work with some remarks on our observations.

\section{Theoretical Background and Numerical Techniques}

In this section we will briefly describe the entanglement measure, the
Hamiltonians for strongly correlated systems and the numerical techniques
used in this work.

\subsection{The Entanglement Measure}

In the introductory section we introduced the notion of entanglement
intuitively. In a more formal language, the
bipartite entanglement for pure states is defined as follows. Two parts of
a system are said to be entangled in a particular state if the
corresponding wave function of the total system cannot be expressed
as a direct product of some states of the two parts. Similar definitions
can be given for the bipartite entanglement of mixed states and also for the
multipartite entanglement of both pure
and mixed states, but we will not be interested in these in the present work.
Quantifying entanglement is generally non-trivial and can have different
measures according to the usefulness in different contexts
\cite{amico,horodecki}. Fortunately, bipartite entanglement for pure states
has a well defined and simple measure, namely, the von Neumann entropy which
is given by
\begin{eqnarray} S = -Tr ~(\rho~{\rm log_2}~\rho), \label{entrp1}
\end{eqnarray}
where $\rho$ is the reduced density matrix of either one of the two
parts, `Tr' implies tracing over an operator (or matrix), and `log' is the
logarithm which is conventionally calculated with base 2. If $w_i$'s are
the eigenvalues of $\rho$, then $S$ can be written as
\begin{eqnarray} S = -\sum_i ~w_i~{\rm log_2}~w_i. \label{entrp2}
\end{eqnarray}
Here we note that, $w_i\geq 0$ and $\displaystyle \sum_i w_i = 1$. Now let
$\displaystyle|\psi\rangle = \sum_{ij} C_{ij} |\phi_i\rangle^l |\phi_j
\rangle^r$ be some pure state (say, an eigenstate of a given Hamiltonian),
where $|\phi_i\rangle^l$s and
$|\phi_i\rangle^r$s are the normalized basis states of the two parts
(conveniently called the left and right parts) of a system. Then the elements
of the reduced density matrix of the left part are given in terms of
$C_{ij}$ by
\begin{eqnarray} \rho_{ij} = \sum_k C_{ik}C_{jk}^*, \label{rdm}
\end{eqnarray}
with `*' implies complex conjugation. Alternatively, one can consider the
reduced density matrix of the right part whose matrix elements are given by
\begin{eqnarray} \rho'_{ij} = \sum_k C_{ki}C_{kj}^*. \label{rdm1}
\end{eqnarray}
The dimensionalities and hence the number of eigenvalues of $\rho$ and $\rho'$
can be quite different from each other. However,
it can be shown, using the Schmidt singular value decomposition,
that the {\it non-zero} eigenvalues of $\rho$ and $\rho'$
are always equal to each other; hence the von Neumann entropy given in
Eq. (\ref{entrp2}) is the same regardless of whether it is calculated
using the eigenvalues of $\rho$ or $\rho'$.

\subsection{Interacting Model Hamiltonians}

A number of model Hamiltonians for strongly correlated systems will be used
in this study. The Pariser-Parr-Pople (PPP) model Hamiltonian, which
includes interactions between distant neighbors in addition
to on-site interactions, is given by
\begin{eqnarray} {\hat H}~=~ -\sum_{<ij>,\sigma}t_{ij}
(\hat c^{\dagger}_{i\sigma} \hat c_{j\sigma} ~+~ H.c.)~+~ \sum_i
\frac{U_i}{2}\hat n_i(\hat n_i-1) ~+~\sum_{i>j}V_{ij}(\hat n_i-z_i)
(\hat n_j-z_j). \label{ppp} \end{eqnarray}
Here, the first term of the Hamiltonian is the nearest-neighbor transfer
term also called the H\"uckel term, with $\hat c_{i\sigma}^{~\dagger}$
($\hat c_{i\sigma}$) creating (annihilating) an electron with spin
$\sigma$ at the $i^{th}$ site, and the summation is over a bonded pair of
sites $<ij>$ (in our case nearest neighbors). The second term is the Hubbard
term with $U_i$ being the on-site repulsion energy for the $i^{th}$ site; here
$\hat n_i = \sum_\sigma c^{\dagger}_{i\sigma} c_{i\sigma}$ denotes
the number operator for the $i^{th}$ site. The Hamiltonian with only the
first term described the one-band tight-binding model or the
H\"uckel model while inclusion of the second term gives the Hubbard
Hamiltonian \cite{hubbard}. The third term brings in the effects of
long-range interactions, where $V_{ij}$ is the density-density
electron repulsion integral between sites $i$ and $j$, $z_i$ is the local
chemical potential given by the occupancy of the $i^{th}$ site for which
the site is neutral. This term was first introduced for conjugated $\pi$
electronic systems, by Pariser and Parr \cite{pariser} as well as by
Pople \cite{pople} independently in 1953. We employ the Ohno interpolation
scheme (applicable to conjugated systems) to parametrize $V_{ij}$ \cite{ohno},
\begin{eqnarray}
V_{ij}=14.397\left[\left(\frac{28.794}{U_i+U_j}\right)^2+r_{ij}^2\right]
^{-1/2}. \label{ohno_eq} \end{eqnarray}
Here $r_{ij}$ is the distance (in \AA\hspace*{.09cm}) between the $i^{th}$ and
$j^{th}$ sites and the energies are in eV. One uses $t = -2.4$ eV and
$U = 11.26$ eV as the standard parameters for the PPP Hamiltonian of a
conjugated system.  In the large $|U/t|$ limit,
Hamiltonian in Eq. (\ref{ppp}) reduces to an isotropic spin Hamiltonian
(the Heisenberg Hamiltonian). The Heisenberg Hamiltonian with site
spin $\vec{S}_i$ at the $i^{th}$ site can be written as,
\begin{eqnarray} H=\sum_{<ij>}J_{ij} \vec{S}_i\cdot \vec{S}_j,
\label{hspin} \end{eqnarray}
where $J_{ij}$ is the exchange coupling constant between sites $i$ and $j$.

\subsection{Numerical Techniques}

For one-dimensional electronic systems we will use the Rumer-Pauling valence
bond (VB) basis, which is spin-adapted and complete but non-orthogonal
\cite{pauling,soos}. The $C_2$ symmetry
and electron-hole symmetry are applied to break the spin adapted space
(only singlets and triplets are considered in our study) into four symmetry
adapted subspaces, namely, $A_g^+$,
$A_g^-$, $B_u^+$ and $B_u^-$ \cite{ramasesha,bondeson}. Once we
diagonalize a Hamiltonian in some
particular space, we get eigenstates which are linear combinations of
symmetrized VB basis states. These eigenstates can be expressed as linear
combination of the initial VB basis (unsymmetrized) states. We can also
expand the VB basis states into linear combination of basis states with a
constant values of $M_S$ (i.e., $S_z$) \cite{ramasesha,sahoo1}, and can thus
express the eigenstates as linear combinations of states with a particular
value of $M_S$. This constant $M_S$ basis conserves the $z$-component of the
total spin and being orthonormal, it is convenient to use in our study. For
spin chains (both spin-1/2 and spin-1), we only studied the ground state to
compare them with those from the electronic models. We also
recently developed a hybrid VB-constant $M_S$ basis technique, which can
exploit both spin and spatial symmetries of an arbitrary point group
\cite{sahoo1,sahoo2}. Here the eigenstates are automatically obtained as
linear combinations of constant $M_S$ basis. We used this hybrid method
for the entanglement study of a half-filled 12-site icosahedral system
(see Fig. \ref{ico_fig}) which has a huge Hilbert space (with dimension
1,778,966) \cite{sahoo1}. Once we get an eigenstate as a linear combination
of constant $M_S$ basis, we can use Eq. (\ref{rdm}) to compute the
reduced density matrices. These matrices can be diagonalized to obtain the
eigenvalues and subsequently the entropy using Eq. (\ref{entrp2}). In Table
(\ref{tab_ico}) we show the dimensionalities of different spin and
spatial symmetry adapted subspaces of the icosahedral system. These
dimensionalities have some significance related to the entropy profiles of
different subspaces; this will be discussed in Sec. 3.2.

Since all our results will be interpreted in terms of the VB basis, we give
a very brief description of the basis \cite{soos}. For spin systems, the
spin of a magnetic site ``$s_i$" is replaced by $2s_i$ spin-half objects.
Now to obtain a state with total spin $S$ from $N$ such
spin-1/2 objects from all the magnetic centers of the system, a total of
$2S$ such objects are left unpaired and the remaining  $N - 2S$ of the
spin-1/2 objects are singlet spin paired explicitly, subject to the following
restrictions: (i) there should be no singlet pairing of any two spin-half
objects belonging to the same magnetic center (this ensures that the $2s_i$
objects are in a
totally symmetric combination), (ii) when all the spin-half objects are
arranged as $N$ dots on a regular $N$-sided polygon and lines are drawn
between spin paired objects, there should be no intersecting lines in the
diagram, and (iii) these lines should not enclose any unpaired spin-1/2
objects which are connected by an arrow when all the sites are aligned on a
straight line and the VB diagram is drawn such that all singlet lines are
above this straight line. These rules follow from the generalization of the
Rumer-Pauling rules to objects with spin greater than 1/2 and total spin
greater than zero. The set of diagrams which obey these rules are called
``legal" VB diagrams (or basis states). All legal VB diagrams form a complete
and linearly independent set. VB diagrams which do not follow these rules are
called ``illegal" and can be expressed as linear combination of ``legal"
diagrams. Note that for an odd number of spin-1/2 objects and total spin
$S = 1/2$, we cannot have an arrow. In this case we add a $``phantom"$ site
and generate singlet diagrams; the phantom site does not appear in the
Hamiltonian.

For electronic systems, a given orbital can be in one of four states; it can
be (1) empty, (2) singly occupied with an up-spin electron, (3) singly
occupied with a down-spin electron, and (4) doubly occupied. Let $N$ be the
number of orbitals, $N_e$ be the number of electrons with $N_{\uparrow}$
up-spin electrons and $N_{\downarrow}$ down-spin electrons, so that $N_e =
N_{\uparrow} + N_{\downarrow}$. Now, for a fixed occupancy of the orbitals,
a linearly independent and complete set of states with total spin $S$ and
$M_S = S$ is obtained by the extended Rumer-Pauling rules as follows.
(i) The $N$ orbitals are arranged as dots along a straight line.
(ii) Doubly occupied sites are marked as crosses. (iii) An arrow is passed
through $2S$ of the singly occupied sites, passing on or above the straight
line on which the system is represented. The arrow denotes the spin coupling
corresponding to total spin $S$ and
total $z$-component $M_S = S$. VB diagrams corresponding to other $M_S$
states can be obtained by operating on the arrow with the $S^-$ operator the
required number of times. (iv) Remaining singly occupied
sites are singlet paired and are denoted by lines drawn between them.
(v) Diagrams with (a) two or more crossing lines, or (b) crossing line and
the arrow, or (c) a line enclosing the arrow are called ``illegal" and are
rejected. The remaining set of diagrams
correspond to a complete and linearly independent set of VB states for the
chosen orbital occupancy. The set of VB diagrams which obey the extended
Rumer-Pauling rules are called ``legal" VB diagrams. Note that for $N_e$ odd
and total spin $S = 1/2$, we cannot have an arrow. As with the
pure spin case, we handle this situation by the concept of a $``phantom"$ site.

\begin{figure}[]
\begin{center} {\includegraphics[width=9.0cm]{fig1_vbbasis.eps}}
\caption{\small Some legal VB diagrams are shown for an 8-site system. The
first three diagrams, (a), (b) and (c), are for total spin zero while the
last one, (d), is for total spin one. Diagram (c) is possible only for
electronic systems.} \label{vbbasis} \end{center} \end{figure}

Some legal diagrams are shown in Fig. \ref{vbbasis}; these will be referred
to in the next section.

Before finishing this section let us stress two important points: (i) the
procedure above will give us states with $M_S$ equal to the total spin $S$,
and (ii) any basis (a diagram) can be
written as a direct product of states of lines (representing singlets),
arrow (representing the spin of the diagram) and crosses (representing doubly
occupied sites) in any order. Since each of the
objects contain a pair of fermionic operators, those operators commute.
Note, crosses or dots do not appear for pure spin systems. If we calculate
the entropy for a VB diagrammatic basis, it would give a non-zero value
only if the boundary plane dividing the system
into two parts (left and right) intersects at least one line of the diagram.
If the boundary plane intersects only an arrow (if present), it would give
zero entropy as the arrow is the direct product
state of all the unpaired spins (or electrons) as we have chosen $M_S = S$.
To clarify this we note that in diagram (a) of Fig. \ref{vbbasis}, if the
boundary plane intersects the system in between sites 3 and 4, the calculated
entropy will not be zero; on the other hand, when the plane intersects the
system in between sites 4 and 5, the calculated entropy will be zero. Since the
eigenstates of a system can be written as linear combination of VB diagrams,
the entropy calculated for an eigenstate would be high if the leading VB
diagrams (with large coefficients) themselves have non-zero entropy.

\section{Results and Discussion}

In this section, we first present results for spin and electronic system for
the chains. We follow this with results and discussions for the icosahedral
cluster. In the last part of the section, we
compare and discuss the DoS profiles with the corresponding entanglement
profiles for different spaces of both the chain and icosahedral systems.

\subsection{Entanglement Studies of Chains}

We have performed entanglement studies on the chain system mainly to
explore the effect of long-range interactions. In these studies we will also
see the role of the chain length and block size on the entanglement
entropy. For this purpose we study Hubbard chains (with $U/t =$ 0,
2, 4, 6, 8, 12 and 40) and PPP chains. Electronic systems are always taken to
be half-filled. We also study the entanglement
of spin-1/2 and spin-1 Heisenberg antiferromagnetic spin chains in order to
compare its size dependence with the results for electronic systems.

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig2_entr_grndst.eps}}
\caption{\small (a) Ground state entanglement studied with equal block
sizes and increasing chain length. (b) Ground state entanglement studied
with different block sizes for a fixed chain length (16 sites).}
\label{entr_grndst} \end{center} \end{figure}

First we study the entanglement in the ground state of different models, with
respect to variations in both the chain length and the block size (see Fig.
\ref{entr_grndst}). We find that for the electronic
systems, for odd block sizes (having an odd number of sites), the
entropy is high, while for even block sizes the entropy is low. This can be
explained from the VB theory. In the ground state of a chain,
the contribution of the Kekule basis states (see Fig. \ref{vbbasis} a),
is large since this basis state corresponds to nearest-neighbor singlets.
Now depending on the position of the boundary plane (whether it intersects a
singlet line or not; see the discussion in Sec. 2.3), the entropy of the ground
state will be high or low. This is the reason why for equal block sizes, the
$4n+2$ ($n$ being a positive integer) chains have higher entropy than the
$4n$ chains; in the former, we cut a singlet line in the Kekule diagram while
in the latter, the system is divided between nearest-neighbor lines of the
Kekule diagram (see Fig. \ref{entr_grndst} a). In order to further verify
this odd-even effect, we also studied 16-sites fermionic chains, with
different sizes of blocks (see Fig. \ref{entr_grndst} b). Here, we find
that the entropy is large (small) whenever it has an odd
(even) number of sites in a block.

In this regard we also note that the odd-even effect is more prominent or
sharper for the PPP model compared to that for the Hubbard model. This is
because the PPP term (the third term in Eq. (\ref{ppp})) is a diagonal
interaction term between empty and doubly occupied sites. The lines or
arrow (singly occupied sites) remain unchanged by the term. This signifies
that the long-range term favours ionic states; as a result, the number of
covalent states (as in Fig. \ref{vbbasis} b) present in the
ground state is less compared to the case of the Hubbard model. Now due to
dominance of diagrams like in Fig. \ref{vbbasis} a among the other less important
covalent diagrams present in the ground state (anyway ionic diagrams contribute
less towards entropy due to lack of lines), odd-even effect becomes sharper for
the PPP model.

We further notice that, within the even or odd block sizes, the entropy
increases as shown in Fig. \ref{entr_grndst} a and it takes a dome-like
structure as shown in Fig. \ref{entr_grndst} b. This is because
the entropy of a system generally increases with the Schmidt number
(coming from the Schmidt decomposition). As this number grows as the minimum of
the Fock space dimensions of two blocks, in the first case
(Fig. \ref{entr_grndst} a) it increases linearly with the system size and
in the second case (Fig. \ref{entr_grndst} b) it is maximum when the block sizes
are the same.

Another important observation for the Hubbard system is that the entropy
decreases with increasing $U/t$. This is because an increase in $U/t$ leads
to a smaller contribution from the ionic functions to the ground state. This
effectively reduces the number of states involved (or equivalently the
Schmidt number), which results in a decreased entropy. This fact is further
supported by the result that the entropy profile for the Hubbard chain
approaches that of the spin-1/2 antiferromagnetic Heisenberg spin chain with
increase in $U/t$. We remember here that the ground state of the spin
chain is dominated by the Kekule states.

In order to study the entanglement behavior of spin systems and compare the
result with the corresponding behavior of electronic systems, we have also
studied the entropy in the ground state of the
spin-1/2 and spin-1 Heisenberg spin chains. Firstly, we note that the
entropy profile of the spin-1/2 chain closely matches that of the Hubbard
chain with $U/t$ = 40, and it exhibits a strong
odd-even effect. The entropy of the spin-1 chain, on the other hand, shows
a very weak odd-even effect. The magnitude of the entropy is higher in all
cases compared to the spin-1/2 chain due to the large Fock space dimensionality
of the spin-1 chain (note that a spin-1 can be considered as two spin-1/2's
without the singlet combinations between them). The weakness of the odd-even
effect in the spin-1 chain implies that not only the Kekule states, but also
other VB basis states (where singlets form
between distant sites) contribute significantly to the ground state.

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig3_entr_excite_hub_ppp.eps}}
\caption{\small Entropy for some important excited states (along with the
ground state) are shown here as a function of chain length (equal block size).
Values shown here are for the Hubbard model with $U/t$ = 0, 2, 4, 6, 40, and
for the PPP model.} \label{entr_excite_hub_ppp} \end{center} \end{figure}

We also study the entanglement for some important excited states of the Hubbard
model for different $U/t$ values and the PPP model (see Fig.
\ref{entr_excite_hub_ppp}). Here we find that the entropy for 2$^1A_g^+$
(lowest energy two-photon singlet state) is higher compared to the other
states considered when $U$ =0. This is due to the fact that its energy is
higher compared to others, hence it has a greater admixture of basis states
like the ones shown in Fig. \ref{vbbasis} b. Since these basis states
contain singlet
lines between distant neighbors, the state has a high entropy. However, the
entropy of this state decreases as $U$ increases. This is because as $U/t$
increases, the 2$^1A_g^+$ state becomes the spin wave excitation of a
spin-1/2 Heisenberg antiferromagnetic chain. As already
discussed, the entropy of spin chains is smaller than that of the fermionic
chains. We also find that the odd-even effect in this state is smaller
compared to the other states in the Hubbard model while the effect
is nearly absent in the $1^1B_u^-$ state of the PPP model. This observation in
the Hubbard model can be understood from the fact that the $2^1A_g^+$ state is
composed of two triplets. These triplets tend to be separated. This implies
that in the half-blocks, the favored states correspond to large spin and hence
the odd-even effect will be less pronounced. The absence of the odd-even
effect in the $1^1B_u^-$ state for the PPP model can also be understood from
the fact that in the one-photon state, purely covalent
basis states are absent, and that the PPP term favors basis states with more
ion-pairs. Since there are many such ionic basis states present in
significant amounts in this state, the odd-even effect will be suppressed
here. We further notice that the odd-even effect reverses for $2^1A_g^+$
state when one goes from $U = 0$ to even a small value (we have taken
$U = 2$ here). An understanding of this feature requires further analysis.

To better understand the dome-like structure of the entropy across the energy
spectrum, we histogram the number $n_p(\rho)$ of density matrix eigenvalues
in the range $10^{-p} > \rho > 10^{-(p+1)}$ and plot it against the negative
logarithm of eigenvalues $-{\rm log_2} \rho$.
These are shown for states from the spaces $1^1A_g^+$, $1^1B_u^-$ and $1^3B_u^+$
in Figs. \ref{agp_rdmdos}, \ref{bum_rdmdos} and \ref{3bup_rdmdos} respectively.
{}From the profiles we note that for states with very low and very high
energies, the histograms have a broader
distribution, while the states in the middle of the energy spectrum
have a narrow distribution (having large $n(\rho)$) and are centered towards
the origin of the axis. It is clear from Eq. (\ref{entrp2}), that this
distribution leads to a large entropy for the states with intermediate
energies and a small entropy for states at either end of
the energy eigenvalue spectrum.

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig4_agp_rdmdos.eps}}
\caption{\small DoS profiles of eigenvalues of reduced density matrix (RDM)
for three different states
from the $^1A_g^+$ space. The result is obtained for the half-filled 10-site
chain using the PPP Hamiltonian.} \label{agp_rdmdos} \end{center} \end{figure}

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig5_bum_rdmdos.eps}}
\caption{\small DoS profiles of eigenvalues of RDM for three different states
from the $^1B_u^-$ space.  The result is obtained for the half-filled 10-site
chain using the PPP Hamiltonian.} \label{bum_rdmdos} \end{center} \end{figure}

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig6_3bup_rdmdos.eps}}
\caption{\small DoS profiles of eigenvalues of RDM for three different states
from the $^3B_u^+$ space. The result is obtained for the half-filled 10-site
chain using the PPP Hamiltonian.} \label{3bup_rdmdos} \end{center} \end{figure}

Our results also show why the DMRG technique is so successful for the
one-dimensional PPP model even though the model has long-range interactions.
Note that the long-range interactions renders the system topologically
higher dimensional since cutting the system leads to dangling bonds
whose number increases with increasing system size; hence, according to the
area law, the cut-off in the number of DMEVs for a fixed accuracy should
increase with the system size. But we can see
from Fig. \ref{entr_grndst} that, even though the odd-even effect is sharper
for the PPP model compared to different short-range models, the change of
the entropy with the system size is essentially the same as for
the short-range models. This can be understood in the following way: the
long-range part of the PPP Hamiltonian in Eq. (\ref{ppp}) involves diagonal
interactions between sites which are empty or doubly occupied. This term
only weakly affects the weightage of states with large single occupancies
(i.e., lines and arrow, in the VB language). Since the covalent states (lines)
which actually contribute towards the entropy are not significantly affected
by this long-range term, the overall entropy of an eigenstate does not change
much. The only consequence of this term is the sharper odd-even effect which
results, as we already explained, due to the dominance of diagrams like in
Fig \ref{vbbasis} a in the ground state of the PPP model.

To further substantiate our claim that the long-range interactions do not
affect the entanglement entropy significantly, we have considered the the
ground state and a few excited states of a chain of 10 sites in the PPP
and Hubbard models and calculated the entanglement entropy within different
sectors of total electron numbers and $z$-component of total spin for one
half of the system. The idea of an entanglement
spectrum was introduced in Ref. \cite{li}, and it has proved to be very
useful for studying a number of strongly correlated quantum systems; in that
work, the entanglement spectrum was obtained by calculating $-log_2(w_i)$ for
all the eigenvalues of the reduced
density matrix in different sectors corresponding to the values of various
additive quantum numbers (i.e., eigenvalues of conserved quantities whose
values for the entire system are equal to the sum of their values for the
two parts of the system). In the same spirit, we have separated out the
contributions of the different total $S_z$ and $n$ sectors, where the former
corresponds to the $z$ component of the total spin and the latter to the
number of electrons in the part of the chain for which we compute the
entanglement entropy; within each of these sectors, we have calculated the
sum $-\sum_i w_i {\rm log_2} w_i$ (instead of $-{\rm log_2}w_i$ as was done
in Ref. \cite{li}). The result is shown in Table \ref{en_sp}. In
Fig. \ref{entg_spct_agp} we show the DoS of the
reduced density matrix for the PPP model in some sectors of $S_z$ and $n$.
Due to the electron-hole and spin-inversion symmetries many sectors have the
same DoS within the numerical accuracy.

Our results show that the entropy for different sectors are almost the same
for long-range and short-range models. This supports our previous arguments
about the reason for the success of the DMRG method for the PPP model.

\begin{table}[t]
\caption{Entanglement spectrum for different sectors of total electron
number $N_e$ and $z$-component of total spin $M_s$ for one half of the system.
We present results for both PPP
and Hubbard models (with $U/t = 4$) for comparison.}

\label{en_sp}
\centering
\begin{tabular}{|l|c|c|c|c|}
\hline
Model & State & \multicolumn{2}{|c|}{Sector} & Entropy \\
\cline{3-4}
& & M$_{s}$ & N$_{e}$ & \\
\hline
& & 0.5 & 5 & 0.557 \\
& & 0.0 & 4 & 0.408 \\
& A$_{g}$$^{+}$ & 1.0 & 4 & 6.1x$10^{-3}$\\
& & 0.5 & 3 & 4.9x$10^{-4}$\\
& & 1.5 & 5 & 4.6x$10^{-4}$\\
& & 0.0 & 2 & 1.1x$10^{-8}$\\
\cline {2-5}
& & 0.5 & 5 & 0.686 \\
& & 0.0 & 4 & 0.576 \\
PPP & B$_{u}$$^{-}$ & 1.0 & 4 & 1.9x$10^{-2}$\\
& & 0.5 & 3 & 6.1x$10^{-3}$\\
& & 1.5 & 5 & 9.2x$10^{-5}$\\
& & 0.0 & 2 & 6.1x$10^{-7}$\\
\cline {2-5}
& & 0.5 & 5 & 1.049 \\
& & -0.5 & 5 & 0.282 \\
& $^{3}$B$_{u}$$^{+}$ & 1.5 & 5 & 0.282 \\
& & 0.0 & 4 & 0.274 \\
& & 1.0 & 6 & 0.274 \\
& & 0.0 & 6 & 0.274 \\
\hline
& & 0.5 & 5 & 0.545 \\
& & 0.0 & 4 & 0.275 \\
& A$_{g}$$^{+}$ & 1.0 & 4 & 6.1x$10^{-3}$ \\
& & 1.5 & 5 & 1.5x$10^{-3}$\\
& & 0.5 & 3 & 3.5x$10^{-4}$\\
& & 0.0 & 2 & 2.4x$10^{-8}$\\
\cline {2-5}
& & 0.0 & 4 & 0.622 \\
& & 0.5 & 5 & 0.445 \\
Hubbard & B$_{u}$$^{-}$ & 1.0 & 4 & 6.7x$10^{-2}$\\
(U/t~=~4) & & 0.5 & 3 & 3.6x$10^{-2}$ \\
& & 1.5 & 5 & 1.5x$10^{-4}$ \\
& & 0.0 & 2 & 4.2x$10^{-5}$ \\
\cline {2-5}
& & 0.5 & 5 & 1.057 \\
& & 1.5 & 5 & 0.345 \\
& $^{3}$B$_{u}$$^{+}$ & -0.5 & 5 & 0.345 \\
& & 0.0 & 4 & 0.178\\
& & 1.0 & 6 & 0.178\\
& & 0.0 & 6 & 0.178\\
\hline
\end{tabular}
\end{table}

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig7_entg_spct_agp.eps}}
\caption{\small DoS profiles of eigenvalues of RDM for different sectors
corresponding to different electron numbers and $z$-components of total spin.
The state studied here is the ground state ($A_g^+$) of a 10-site chain using
the PPP Hamiltonian.} \label{entg_spct_agp} \end{center} \end{figure}

\subsection{Entanglement Studies of an Icosahedron}

To learn if symmetries play any recognizable role in entanglement, we have
studied a 12-site half-filled icosahedron with the Hamiltonian of the PPP
model \cite{sahoo1}. The first important issue here is of the degeneracies.
In general, the entanglement is not the same for degenerate states, and
a linear combination of two such states can give another degenerate state
with a different entanglement. In the following we address this problem of
non-unique entanglement of degenerate states.

\begin{table}[htbp]
\caption{\small Dimensionalities of different symmetry and spin subspaces of
a half-filled icosahedral cluster.}
\label{tab_ico}
\begin{center}
\begin{tabular}{|l||r|r|r|r|r|r|r|} \hline
S$_{tot} \rightarrow$ & & & & & & & \\
$\Gamma$ $\downarrow$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \hline
A$_{g}$ & 2040 & 3128 & 1684 & 382 & 38 & 3 & 1 \\ \hline
T$_{1g}$ & 16602 & 28821 & 14625 & 3261 & 309 & 6 & 0 \\ \hline
T$_{2g}$ & 16602 & 28821 & 14625 & 3261 & 309 & 6 & 0 \\ \hline
G$_{g}$ & 30272 & 50932 & 26236 & 5880 & 568 & 16 & 0 \\ \hline
H$_{g}$ & 47940 & 79305 & 41255 & 9220 & 900 & 40 & 0 \\ \hline
A$_{u}$ & 1852 & 3188 & 1644 & 348 & 40 & 0 & 0 \\ \hline
T$_{1u}$ & 17082 & 28686 & 14700 & 3372 & 294 & 18 & 0 \\ \hline
T$_{2u}$ & 17082 & 28686 & 14700 & 3372 & 294 & 18 & 0 \\ \hline
G$_{u}$ & 30160 & 50992 & 26176 & 5888 & 560 & 16 & 0 \\ \hline
H$_{u}$ & 46880 & 79680 & 40980 & 9060 & 900 & 20 & 0 \\ \hline \hline
Tot Dim $\rightarrow$ & 226512 & 382239 & 196625 & 44044 & 4212 & 143 & 1 \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{figure}[]
\begin{center} {\includegraphics[width=5.0cm]{fig8_ico_fig.eps}}
\caption{\small An icosahedron system of 12 sites is shown here. The upper six
sites of the system constitute one part and the rest of the sites constitute
the other part for our entanglement calculations.} \label{ico_fig} \end{center}
\end{figure}

For spin degeneracies (i.e., same total spin but different $M_S$ values) the
problem is not severe. Since the $z$-component of the total spin is an
observable, we can always choose one of its eigenstates. In our study we
have chosen states with $M_S=S$.

The non-uniqueness problem cannot be trivially solved for the case of
discrete symmetries. In this case we do not have any observable to select
one of the degenerate states for our study. It is known that
the projection operator to the full degenerate space is invariant. If
$\rho_i$ is the density matrix of the $i^{th}$ state in a degenerate manifold,
then the density matrix averaged over the $g$-fold degeneracy is given by
$\rho_{av} = (1/g) ~\sum_{i=1}^g ~\rho_i$. This $\rho_{av}$ is invariant
under a change of the basis states. To obtain the reduced density matrix,
and subsequently the entanglement entropy, we take the upper half of the
system (upper 6 sites of the Fig. \ref{ico_fig}) as one part and the rest
as the other part.

The eigenstates of the Hamiltonian correspond to integer spins lying between
0 and 6 and belong to one of the ten irreducible representations of the
icosahedral cluster. To see the role of symmetry, we calculate the entropy
in different spatial symmetry subspaces for two
chosen spin states 0 and 1. This is shown in Figs. \ref{entr_ico} a and b.
To see the effect of the spin, we calculate the entropy
in different spin subspaces for two chosen spatial symmetries $A_g$ and $G_u$.
This is shown in Figs. \ref{entr_ico} c and d.

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig9_entr_ico.eps}}
\caption{\small Entropy calculated across the energy spectrum of different
subspaces. Insets of (a) and (b) show entropies (black dots) of the first few
states of the corresponding subspaces. (c) and (d) show entropies of the
first few states using filled circles (for even spins) and open
circles (for odd spins). Inset of (d) shows how entropies fluctuate about a
mean value. Solid lines represent plots for gerade ($g$) spaces and broken
lines represent plots for ungerade ($u$) spaces.}
\label{entr_ico}
\end{center}
\end{figure}

Since the entropy profiles fluctuate (see inset of Fig. \ref{entr_ico} d),
we take averages to analyze the general features. The averaging is done in
the following way: the first and last few states in the energy spectrum are
comparatively well-separated from each other, we leave five of them
from both sides with their actual values (which are zoomed in the insets of
Fig. \ref{entr_ico} a and b). Since the rest of the points from both
sides of the spectrum are closely placed, we average the entropy over sets
of four consecutive states. This is done for up to 40 states from both
ends of the spectrum. Since the middle part of the spectrum is highly dense
\cite{note1}, we average the entropy values over 10 consecutive states.
We find that the entropies for the lowest states in different symmetrized
subspaces, for a given spin, do not seem to have any special features
(see insets of Figs. \ref{entr_ico} a and b). However, for a fixed spin,
the maxima of the entropy profiles (see the middle portions of Figs.
\ref{entr_ico} a and b) are higher for degenerate spaces, such as $T$,
$G$, and $H$ compared to the non-degenerate $A$ spaces. In fact, the higher
the degeneracy in a space, the higher is the entropy maximum;
for example, the $H$ space has a higher maximum entropy compared to, say,
the $T$ space. This fact can be partially explained by the fact
that spaces with a higher maximum entropy have a higher dimensionality (see
Table \ref{tab_ico}). But this does not explain why the entropy of a
non-degenerate space is much lower compared to the degenerate ones,
while the degenerate ones are very close in entropy. Its explanation lies in
the fact that entropy increases with DoS (see Sec 3.3) and DoS is much lower
for non-degenerate spaces \cite{sahoo1}. We also note that for
a subspace with a particular spatial symmetry, the maxima of the entropy
profiles is higher for lower spin spaces (see Figs. \ref{entr_ico} c and d).
This is also generally true for the entropy of the lowest states of different
spins in a given spatial symmetry subspace. This can be qualitatively explained
by the dimensionalities of the spaces. However, there must be other factors
contributing to this observation since, in general, the entropy for triplet
states is lower than that of the singlet states even though the dimension of
the triplet space is higher than that
of the singlet space. This fact can be explained by noting that the
low-spin states are made up of more singlet pairs (lines) than the
high-spin states, and we are only considering states with the highest
$M_S$ value (i.e., $S$) which are least entangled. This leads to a higher
entropy for states with a lower total spin. If we had worked with the
$M_S =0$ state of the triplet states (which is a linear combination of
two configurations), we would have expected a higher entropy for the states.

The entropy profiles are not monotonically increasing in each symmetry
subspace; each profile reaches a maxima and then decreases. This can be
explained by considering the properties of the VB basis. Initially, for the
low-energy eigenstates, the VB states like Fig. \ref{vbbasis} a appear with
larger weights. This is because these VB states have nearest-neighbor
singlets. These VB states would contribute less towards the entropy of an
eigenstate, as the boundary plane crosses a smaller number of lines on the
average. In higher energy eigenstates, more and more VB states, like
Fig. \ref{vbbasis} b where distant sites form singlets, acquire a significant
weight in the eigenstates. Now, as more states get involved, the entropy of
the eigenstates starts to increase since the type (b) VB basis states have a
larger entropy (since the boundary plane crosses a larger number of lines on
the average). As we move to even higher energy eigenstates, the entropy
saturates (reaches a maxima) due to the finite number of basis states, since
we are working
with a finite system. If we move to the highest energy part of a spectrum,
more and more ionic VB states like Fig. \ref{vbbasis} c appear and
the type (b) VB states reduce in number. Now due to the reduced number of
the covalent basis states involved and as ionic VB basis states contribute
less towards the entropy, the entropy of these states starts to decrease.

\subsection{Comparison of Entropy and DoS profiles}

We note that the entropy profiles and corresponding DoS profiles within a
given symmetry and spin subspace bear an interesting similarity. Using the PPP
Hamiltonian, we first calculate the eigenvalues and eigenvectors for a given
spin and spatial symmetry adapted space. We then calculate the entropy
corresponding to each eigenvector in that space. Using this data, we plot the
entropy and logarithm of the DoS across the energy spectrum for a few spaces.
For a chain the results can be seen in Fig. \ref{entr_dos_chain}, while
for the icosahedron the results can be seen in Fig. \ref{entr_dos_ico}. In
this study the DoS is calculated by histogramming a number of states within
an energy gap of $0.5$ eV. To reduce the fluctuation in the entropy profiles,
we have averaged the entropy of the states in successive energy gaps of $0.5$
eV. The entropy is seen to be proportional to the logarithm of the DoS, i.e.,
$S \propto log (DoS)$. Qualitatively, the reason for this can be that
the higher the DoS, the larger is the number of basis
states which have a significant weight for a given state in this
energy range, hence, the higher is the entropy. Since the entropy scales as
the logarithm of the number of states involved, the observed relation
between the entropy and DoS profiles follows.

\begin{figure}[]
\begin{center} {\includegraphics[width=16.0cm]{fig10_entr_dos_chain.eps}}
\caption{\small For two spin and spatial symmetry adapted subspaces we compare
the entropy profiles with the logarithm of DoS profiles. The system is a
10-site half-filled chain.} \label{entr_dos_chain} \end{center} \end{figure}

\begin{figure}[]
\begin{center}
{\includegraphics[width=16.0cm]{fig11_entr_dos_ico.eps}}
\caption{\small For four spin and spatial symmetry adapted subspaces we
compare the entropy profiles with the logarithm of DoS profiles. The system is
a 12-site half-filled icosahedron.} \label{entr_dos_ico} \end{center}
\end{figure}

\section{Conclusion}
To summarize, we have studied the effect of long-range interactions on
the entanglement of strongly correlated systems. We find that the diagonal
interactions do not increase the entropy of the states, even if they are
long-ranged. The behavior of the entropy in correlated
models can be understood from a VB picture of the eigenstates. The even-odd
alternation in the entanglement entropy for even/odd block sizes can also
be understood based on such a VB picture and was illustrated by
analyzing the spin-1 Heisenberg antiferromagnet. We also studied the
effects of spin and spacial symmetry on the entropy of states by examining
the correlated icosahedral cluster. We showed an interesting similarity
between the profiles of the entropy and the corresponding profiles of
the logarithm of the DoS.

\section{Acknowledgment}
S. R. is thankful to the Department of Science and Technology (DST), India for
financial support and Professor Steve White for a helpful discussion. D. S.
thanks DST, India for support under SR/S2/JCB-44/2010.

redpajama_set_name: RedPajamaArXiv


Yogaholics United are open-minded & dedicated people. We love yoga and offer different traditions under one roof. You'll find all the Yoga stages from purification to strengthening, meditation and illumination on our schedule. Our motto is: "come as you are – leave as you wanna be". Find more info about the different styles we offer by cruising through our webpage, but best is to simply come by and practice with us.


text:
Q: Cake Pattern: How to share an instance? I have a configuration component in my Scala project.
Obviously I don't want to have more than one instance of this component. I'm using the cake pattern, but I'm not sure how to tweak it to fit my requirements:
// Library
// =================================================
trait ConfigComp {

  trait Config {
    def get(k: String): String
  }

  def config: Config
}

trait QueueComp {
  self: ConfigComp =>

  class Queue {
    val key = config.get("some-key")
  }

  lazy val queue = new Queue
}

// Application
// =================================================

trait MyConfig extends ConfigComp {

  lazy val config = new Config {
    println("INITIALIZING CONFIG")

    def get(k: String) = "value"
  }
}

object Frontend extends QueueComp with MyConfig
object Backend  extends QueueComp with MyConfig

Frontend.queue.key
Backend.queue.key

prints:
INITIALIZING CONFIG
INITIALIZING CONFIG

How to make the cake pattern share the anonymous instance of Config?

A: Something like this ?
// Library
// =================================================
trait Config {
  def get(k: String): String
}

trait ConfigComp {
  def config: Config
}

trait QueueComp {
  self: ConfigComp =>
  class Queue {
    val key = config.get("some-key")
  }
  lazy val queue = new Queue
}

// Application
// =================================================

object SingleConfig extends ConfigComp {
  lazy val config = new Config {
    println("INITIALIZING CONFIG")
    def get(k: String) = "value"
  }
}

object Frontend extends QueueComp with ConfigComp {
  val config = SingleConfig.config
}
object Backend  extends QueueComp with ConfigComp {
  val config = SingleConfig.config
}

Frontend.queue.key
Backend.queue.key

If your Config trait is placed inside ConfigComp, I could not workaround these type errors:
error: type mismatch;
 found   : MyConfig.Config
 required: Frontend.Config
    (which expands to)  Frontend.Config
                override def config = MyConfig.config

error: type mismatch;
 found   : MyConfig.Config
 required: Backend.Config
    (which expands to)  Backend.Config
                override def config = MyConfig.config

A: As om-nom-nom mentioned, you're looking to use a singleton, and thus should make MyConfig use a config that is initialized in an object. To the second question, in your gist, the following error:
[error] overriding method config in trait ConfigComp of type => MyConfig.this.Config;
[error]  lazy value config has incompatible type
[error]   lazy val config = MyConfig.config
[error]            ^
[error] one error found

essentially tells you exactly the problem. MyConfig.this.Config is not equal to the object MyConfig.this.Config. To make it more clear, let's change the code to the following:
object MyConfigSingleton extends ConfigComp {
  val config = new Config {
    println("INITIALIZING CONFIG")
    def get(k: String) = "value"
  }
}

trait MyConfig extends ConfigComp {
  lazy val config = MyConfigSingleton.config
}

Here, the type MyConfig.this.Config != MyConfigSingleton.this.Config

redpajama_set_name: RedPajamaStackExchange


I can't stop picking my nose!
I've been a chronic nose-picker since eighth grade, and now I'm in graduate school.
3) Stop picking my nose."
The third is actually now heavily scratched out because I was horrified someone would find the journal, and that might be the most embarrassing piece of vulnerability in there.
I have lots of seasonal allergies, but I don't think that's the cause.
As you can somewhat see from my other eighth-grade goals, I'm a huge perfectionist with a tendency toward depression and mild anxiety. I like to fidget with my hands -- I think the nose-picking is like a nervous twitch. Once I wore gloves to bed to keep me from picking my nose. But I've given up on tricks like gloves, spicy sauce on my fingers or sheer willpower because I've decided I must cure it by examining the underlying causes. I've been in a lot of therapy already -- I wonder if the nose-picking is the remnants of other addictions I've dealt with successfully, including eating disorders and alcoholism. I'm a strong person! I just can't kick this one! Any advice before my boyfriend dumps me because of the boogers on the sheets?
It has been said recently that I often wax poetic where a straightforward response is called for. That is a fair observation. In fact, early in life this tendency was noted by the adult couple into whose care I had been entrusted (called, in those days, "parents") who sent me to a specialist to test my hearing. The test revealed that I could hear just fine. The truth was that I was not interested in answering questions in a straightforward manner. So I would pretend that I had not heard the question correctly. I preferred to live in a world of my own. Things have not changed much.
What child does not want to live in a world of his own?
But what does that have to do with nose-picking?
Therefore, this response attempts to take on the subject of fixing bad habits in a straightforward manner. This is accomplished at some cost in grace -- look closely and you will see where the prose is stretched, bruised, a bit frayed or sprained as it has been agonizingly contorted into appearing natural -- but it is nevertheless an important step in my continued struggle to serve my many and varied readers.
Nose-picking has a technical name of relatively recent provenance, Rhinotillexomania, and is honored with an entry in Wikipedia. It was even the subject of an award-winning humorous song in the category of filk music.
I have also been accused of stating the obvious. But I am comfortable knowing that no one can state the obvious with greater aplomb than professional researchers in the area of human behavior, as demonstrated by the conclusion of this survey of adolescent behavior abstracted from the Journal of Clinical Psychiatry: "Conclusion: Nose picking is common in adolescents."
Having amply demonstrated my detractors' thesis, let me now offer a little bit of practical advice. I would suggest, for starters, the About.com Web site entry on breaking bad habits.
This is good general advice. It suggests we break bad habits by becoming conscious of the choice being made, and then making different choices. So recognize what benefit you are getting from picking your nose and then consider at what cost you are achieving this benefit.
If you can do that, you may be well on your way to a life free of nose-picking.
However -- and this is a distinction familiar to those whose habits are more deeply entrenched -- some benefits are not available to consciousness. Some habits exist precisely to cover over or keep from consciousness their actual benefits. For instance, if a habit exists to hide pain, then it will be difficult or impossible for a person in the grip of this habit to identify the pain that the habit is masking.
When getting falling down drunk to avoid thinking about one's mother, for instance, one does not know that one is avoiding thinking about one's mother. So it is more complicated.
So why are you picking your nose? Are you avoiding thinking about your mother? Stop picking your nose!
We're back at the beginning.
There are many sensible approaches to changing bad habits.


text:
Module 1: Introduction & Overview
Ch. 1: Psychoactive Substances
Ch. 2: Who (Mis)Uses These Substances?
Ch. 3: A Brief History of Substance Use and U.S. Policy Responses
Ch. 4: Considering the Language That We Use
Module 1: References
Module 2: Introducing Theories of Addiction
Ch. 1: Substance Use & Misuse versus Substance Use Disorders
Ch. 2: Diagnosing Substance Use Disorders
Ch. 3: Epidemiology of Substance Use Disorders
Ch. 4: Classifying Theories
Ch. 5: The Science of Addiction from NIDA
Modules 3 & 4: Biological Models of Addiction
Modules 3 & 4: Introduction
Ch. 1: Introduction to Biological Models of Addiction
Ch. 2: Brain and Behavior
Ch. 3: Biology of Addiction
Ch. 4: More about Neurotransmitters and How Neurons Communicate
Ch 5: Summary
Modules 3 & 4: Key Terms
Modules 3 & 4: References
Module 5: Psychological Theories of Addiction
Ch. 1: Introduction to Psychological Models of Addiction
Ch. 2: More about Psychological Models of Addiction
Ch. 3: Addiction and Cognition
Ch. 4: Implications of Cognition and Learning Theories for Intervention
Ch. 5: Expectancies Theory
Module 6: Social Context Theories
Ch. 1: Social Context and Physical Environment
Ch. 2: Social Contexts
Ch. 3: Family
Ch. 4: Applying Content About Family
Module 7: Prevention, Vulnerability, Risk Resilience, and Protection Theories
Ch. 1: Integrating Our Theories
Ch. 2: Prevention Strategies
Ch. 3: Motivation and Readiness to Change
Module 8: Alcohol
Ch. 1: Setting the Stage
Ch. 2: Alcohol Initiation Before and During Adolescence
Ch. 3: The Role of Social Media (Twitter)
Ch. 4: The Role of Drinking Context
Module 9: Sedative/Hypnotics and CNS Depressants
Ch. 1: Introducing Sedative/Hypnotics and CNS Depressants
Ch. 2: Club Drugs
Ch. 3: More About Sedative/Hypnotic and CNS Depressant Drugs
Module 10: Stimulant Substances
Module 10: Introduction
Ch. 1: Introduction
Ch. 2: Cocaine
Ch. 3: Methamphetamine
Ch. 4: Tobacco and Nicotine
Ch. 5: Caffeine
Ch. 6: Energy Drinks and Alcohol
Module 10: Key Terms
Module 10: References
Module 11: Opioids
Ch. 1: The Opioid Epidemic
Ch. 2: Introduction to Opioids
Ch. 3: Heroin
Ch. 4: Neonatal Abstinence Syndrome (NAS)
Ch. 5: Alcohol versus Opioid Deaths
Module 12: Marijuana, Hallucinogens, Inhalants, and Steroids
Ch. 1: Introduction to Marijuana/Cannabis
Ch. 2: Marijuana in the Community
Ch. 3: Introducing the Other Hallucinogens
Ch. 4: More Club Drugs
Ch. 5: Introducing Inhalants
Ch. 6: Introducing Anabolic Steroids
Module 13: OTC and Rx Abuse and Pharmacotherapy and Detox
Ch. 2: Pharmacotherapy
Ch. 3: Detoxification and Stabilization
Ch. 4: Policy Considerations
Ch. 13: References
Module 14: Co-Occurring Problems
Ch. 1: What Are Co-Occurring Problems?
Ch. 2: Comorbidity with Addiction
Ch. 3: More About Post-traumatic Stress Disorder (PTSD)
Theories and Biological Basis of Addiction
abstinence: restraining from consuming a particular substance.
binge drinking: In the NSDUH surveys, this is defined as five or more drinks on the same occasion on at least one day. The NIAAA definition is a pattern of drinking alcohol that brings a person's blood alcohol concentration (BAC) to or above the 0.08 gram percent (legal level for driving). Risky single occasion drinking (RSOD) is another term for describing this pattern or drinking. Discussed in greater detail in our course Module 8.
blood alcohol concentration: defined in terms of grams (weight) of alcohol per 100 milliliters of blood, for example 0.08 means 80 milligrams (.08 grams) per 100 milliliters (100 ml=1 deciliter, dL) blood, and can be estimated in breath or urine tests; discussed in greater detail in our course Module 8.
cannabinoids: substances that interact with cannabinoid receptors in the brain to affect neurotransmitter release, such as the compounds in cannabis (marijuana); the subject of our course Module 12.
Centers for Disease Control and Prevention (CDC): operating through the Department of Health and Human Services (DHHS) to protect America from health and safety threats, respond to health threats, and support communities in protecting health.
decriminalization: the act of repealing, removing, or reducing legal restrictions or criminal penalties associated with a previously illegal act.
depressants: substances that reduce (depress) one's state of mental arousal, stimulation, or anxiety, as well as slowing the rate of body functions; the subject of our course Module 9, but also includes alcohol (Module 8).
dissociatives: substance that induce a state of relaxation and calm by detaching the conscious mind from perception brain functions, including pain perception—which is why it can be used in medical anesthesia; discussed in our course Module 9.
hallucinogens (psychotomimetics): substances that induce distortions in the sensory system perceptions of reality (hallucinations); discussed in our course Module 12.
harm reduction: practical strategies for reducing negative consequences from substance use, may or may not involve abstinence.
harmful use of alcohol: the World Health Organization definition involves consuming alcohol in a manner "that causes detrimental health and social consequences for the drinker, the people around the drinker and society at large, as well as the patterns of drinking that are associated with increased risk for adverse health outcomes" (WHO, p. 2).
heavy drinking: Defined in the NSDUH surveys as a pattern of consuming five or more drinks containing alcohol on the same occasion, on each of five or more days in a month; discussed in greater detail in our course Module 8.
inhalants: chemically volatile substances producing vapors that can be inhaled, and have a psychoactive effect; discussed in our course Module 12.
National Institute on Alcohol Abuse and Alcoholism (NIAAA): an institute of NIH charged with supporting and conducting research on the impact of alcohol use on human health and well-being, and leading the nation's efforts to reduce alcohol-related problems.
National Institute on Drug Abuse (NIDA): an institute of NIH charged with advancing science concerning the causes and consequences of drug use and addiction, as well as applying that knowledge to improve public health.
National Institutes of Health (NIH): comprised of 27 institutes and centers, operating through the U.S. Department of Health and Human Services to seek knowledge about the nature and behavior of living systems and application of that knowledge to health enhancement.
National Institute on Mental Health (NIMH): an institute of NIH leading research into mental disorders, as well as discovery in the science of brain, behavior, and experience toward the goal of prevention and cure of mental disorders.
National Survey on Drug Use and Health (NSDUH): an annual study sponsored by SAMHSA providing national and state-level data concerning mental health status in the United States, and the use of tobacco, alcohol, illicit drugs, and prescription drug misuse.
opiates: substances containing or derived from opium, reduce pain, and induce sleepiness; the subject of our course Module 11.
opioids: substances the mimic the effects and properties of opiates, but are synthetically derived (not necessarily containing opium); the subject of our course Module 11.
psychoactive (psychotropic) substances: These are substances that, when consumed, have a significant effect a person's mental processes, mind, mood, and behavior.
Substance Abuse and Mental Health Services Administration (SAMHSA): the federal agency in the Department of Health and Human Services (DHHS) charged with leading public health efforts to advance the nation's behavioral health and reduce the impact of substance abuse and mental disorders on communities.
steroids (anabolic & androgenic): manufactured substances that mimic the effects of the naturally occurring hormone testosterone; discussed in our course Module 12.
stimulants: substances that have the effect of increasing alertness, attention, energy, blood pressure, heart rate, and breathing rate; the subject of our course Module 10.
War on Drugs: the label applied in 1971 by President Nixon to a campaign of United States government policy actions directed toward controlling trade in illegal drugs.
World Health Organization (WHO): part of the United Nation's system, headquartered in Geneva, and leading global efforts to promote health and responses to global health concerns.
Previous: Summary
Next: Module 1: References
Theories and Biological Basis of Addiction by Audrey Begun is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to count the number of records in MySQL by month for the last 12 months including the current month? I have found several answers for questions similar to this one, but none of then exclusive for MySQL. I have a table like this
+-----------+---------------------+
| requestor | request_date        |
+-----------+---------------------+
| email1    | 2015-08-02 01:03:51 |
----------------------------------
| email2    | 2015-08-01 11:24:32 |
-----------------------------------
| email3    | 2015-07-01 07:35:32 |
-----------------------------------
| email4    | 2015-06-01 16:24:32 |
-----------------------------------
| ...       | ...                 |
-----------------------------------
| email100  | 2014-09-01 22:45:04 |
+-----------+---------------------+

I need and output:
+----------+-------+
| Months   | Count |
+----------+-------+
| Aug-2015 | 2     |
--------------------
| Jul-2015 | 1     |
--------------------
| Jun-2015 | 1     |
--------------------
| ...      | ...   |
--------------------
| Sep-2014 | 1     |
+----------+-------+

I tried with this code
SELECT *
 FROM(SELECT DATE_FORMAT(now(), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 1 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 2 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 3 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 4 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 5 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 6 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 7 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 8 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 9 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 10 MONTH), "%b %Y") as Month
 UNION
 SELECT DATE_FORMAT(DATE_SUB(now(), INTERVAL 11 MONTH), "%b %Y") as Month) AS Months
  LEFT JOIN (SELECT DATE_FORMAT(utilization.request_time, "%b %Y") AS Month,      requestor, COUNT(request_time)
        FROM utilization
        WHERE utilization.request_time > DATE_SUB(now(), INTERVAL 12 MONTH)
        GROUP BY request_time) AS Datas
     ON Months.Month = Datas.Month

A: SELECT CONCAT(SUBSTRING(DATE_FORMAT(`request_date`, '%M'),1,3),DATE_FORMAT(`request_date`,'-%Y')) as dateName, COUNT(*)
FROM foo
WHERE PERIOD_DIFF(DATE_FORMAT(NOW(), '%Y%m'), DATE_FORMAT(`request_date`, '%Y%m'))<12
GROUP BY YEAR(`request_date`), MONTH(`request_date`)

Result:
dateName    COUNT(*)
Sep-2014    1
Jun-2015    1
Jul-2015    1
Aug-2015    2

A: SELECT requestor, id
FROM tbl_data JOIN
(
    SELECT COUNT(requestor), id
    FROM tbl_data
    GROUP BY DATE_FORMAT(request_date,'%y-%m')
) AS temp
ON temp.id = tbl_data.id

A: Try this:
SELECT MAX(EXTRACT(YEAR_MONTH FROM request_date)) AS Months, COUNT(*) AS Count
FROM table
WHERE request_date > '2015-01-01 01:01:01'
GROUP BY EXTRACT(YEAR_MONTH FROM request_date);


text:
package com.intellij.codeInsight.template.emmet.nodes;

import com.intellij.codeInsight.template.CustomTemplateCallback;
import com.intellij.codeInsight.template.emmet.ZenCodingUtil;
import com.intellij.codeInsight.template.emmet.tokens.TemplateToken;
import com.intellij.codeInsight.template.emmet.tokens.TextToken;
import com.intellij.codeInsight.template.impl.TemplateImpl;
import org.jetbrains.annotations.NotNull;
import org.jetbrains.annotations.Nullable;

import java.util.Collections;
import java.util.List;

/**
 * @author Eugene.Kudelevsky
 */
public class TextNode extends ZenCodingNode {
  private final String myText;

  public TextNode(@NotNull TextToken textToken) {
    final String text = textToken.getText();
    myText = text.substring(1, text.length() - 1);
  }

  public String getText() {
    return myText;
  }

  @NotNull
  @Override
  public List<GenerationNode> expand(int numberInIteration,
                                     int totalIterations, String surroundedText,
                                     CustomTemplateCallback callback,
                                     boolean insertSurroundedTextAtTheEnd, GenerationNode parent) {
    final TemplateToken templateToken = new TemplateToken("");
    final boolean containsSurroundedTextMarker = ZenCodingUtil.containsSurroundedTextMarker(myText);

    final String text = ZenCodingUtil.replaceMarkers(myText.replace("${nl}", "\n"), numberInIteration, totalIterations, surroundedText);
    final TemplateImpl template = new TemplateImpl("", text, "");
    templateToken.setTemplate(template, callback);

    final GenerationNode node = new GenerationNode(templateToken, numberInIteration, totalIterations,
                                                   containsSurroundedTextMarker ? null : surroundedText,
                                                   insertSurroundedTextAtTheEnd, parent);
    return Collections.singletonList(node);
  }

  @Override
  public int getApproximateOutputLength(@Nullable CustomTemplateCallback callback) {
    return myText.length();
  }

  @Override
  public String toString() {
    return "Text(" + myText + ")";
  }
}

redpajama_set_name: RedPajamaGithub


Investigators from Brigham and Women's Hospital are developing an automated, low-cost tool to predict a woman's ovulation and aid in family planning. Capitalizing on advancements in several areas, including microfluidics, artificial intelligence (AI) and the ubiquity of smartphones, the team has built an ovulation testing tool that can automatically detect fern patterns - a marker of ovulation - in a saliva sample. The team evaluated the performance of the device using artificial saliva in the lab and validated results in human saliva samples from six subjects, observing greater than 99 percent accuracy in effectively predicting ovulation. The team's results are published in Lab on a Chip.
Potluri V, Kathiresan PS, Kandula H, Thirumalaraju P, Kanakasabapathy MK, Kota Sai Pavan S, Yarravarapu D, Soundararajan A, Baskar K, Gupta R, Gudipati N, C Petrozza J, Shafiee H.
An inexpensive smartphone-based device for point-of-care ovulation testing.
Lab Chip. 2018 Dec 18;19(1):59-67. doi: 10.1039/c8lc00792f.


text:
Mossberg®-Sponsored WILDCraft Video Series Now Available
North Haven, CT – Mossberg is pleased to announce the recent release of the video series, WILDCraft, which takes viewers on a journey through the eyes of hunters in remote, wild locations. In Season One, a group of renown editors and writers travel to Fort Richmond Safaris in the rugged mountains of South Africa's Northern Cape for free-ranging kudo and other local species with Mossberg PatriotTM bolt-action rifles in hand. WILDCraft: South Africa, Episodes One through Four, is now available through Amazon® Prime Instant Video at https://www.amazon.com/Wildcraft-South-Africa/dp/B07ZDLMGFW.
Not-your-typical hunting series, WILDCraft: South Africa goes beyond the hunt; addressing the challenges of each hunter's adventures in the field and sharing their successes and failures around the campfire at the end of the day. The captivating series also focuses on the culture, the people and the positive impact of hunting in the local community.
Mossberg Patriot bolt-action rifles were the perfect accompaniment for the hunters in the wilds of South Africa. Rugged, dependable and accurate, the Patriot series of mag-fed, bolt-action rifles combine the most requested features of Mossberg's field-proven centerfire rifles in a premium bolt-action platform. Available in 15 calibers ranging from 6.5mm Creedmoor to 375 Ruger, there is a Patriot to meet your needs. Classically-styled options include choice of Premier 2.0 Grade European walnut to durable synthetic to field-ready scoped combo versions with Vortex® Crossfire II 3-9x40mm riflescopes. The Patriot also offers Mossberg's user-adjustable LBA trigger system for a clean, crisp trigger break; streamlined bolt handle; aggressively-checkered bolt knob and spiral-fluted bolt. Select models are available with fiber optic rifle sights; suppressor-ready, threaded barrels; and Cerakote® finishes.
Hunting in remote locations may not be on your bucket list, but after experiencing the journey through the eyes of hunters, Joe Arterburn, Luke Hartle, Richard Mann and Alfredo Rico, in WILDCraft: South Africa, you may change your mind. Why not be ready for your next hunt or the hunt of a lifetime with a Mossberg Patriot bolt- action rifle? For more information on the complete line of Patriot rifles, please visit www.mossberg.com.
WILDCraft is a trademark of Wildcraft Entertainment, LLC. Amazon® is a registered trademark of Amazon Technologies, Inc. Vortex® is a registered trademark of Sheltered Wings, Inc. Cerakote® is a registered trademark of NIC Industries, Inc.
About O.F. Mossberg & Sons, Inc.
Founded in 1919, O.F. Mossberg & Sons, Inc., is the oldest family-owned firearms manufacturer in America, and is the largest pump-action shotgun manufacturer in the world. Celebrating 100 years of innovation, Mossberg leads the industry with over 100 design and utility patents to its credit and stands as the first ISO 9001 Certified long-gun manufacturer. Complete information on commercial, special purpose, law enforcement and military shotguns, rifles, handguns and accessories are available at mossberg.com or by calling 1-800- 363-3555. Mossberg can also be found on Facebook, Instagram, Twitter and YouTube.
Safety and safe firearms handling is everyone's responsibility.


is designed for all levels of fitness. The Lagree Method has over 200 exercises and over 1,000 ways to perform each of them, which means that we can modify each exercise that is performed in class to your level of fitness by adjusting your position on our state-of- the-art Megaformer M3S's and the springs to a beginner, intermediate or advanced level to ensure your success in each class that you take at Wicked Core. As you get stronger, we will continue to modify and adjust your position and springs accordingly. This class is a High Intensity, low impact & safe 45 minute core workout that is equally effective for Men & Woman of ALL ages. It strengthens, lengthens & tones your muscles more effectively and efficiently than any other workout. It is the ultimate in core strengthening, cardio, stretching & conditioning providing you with a Full Body Transformation in a minimal amount of time.
It is our commitment to you that every time you come to our studio, you will feel welcomed, supported, motivated, and challenged. We will push you, sweat with you, empathize with you, motivate you and applaud you for getting stronger with each class.


He is gearing up to be the performer for the halftime of the Super Bowl this weekend but he is spends a lot of time in the Big Sky state. So it is not surprising that a track on his new album is title 'Montana'.
Pitchfork released the tracklist and sure enough 'Montana' was on there! He is really gearing this one towards his love of the outdoors and in particular the woods. "man of the Woods" is his new album that just dropped. Love the shout out JT.


text:
Melba Pattillo Beals and the courage of the Little Rock Nine
All things being equal, a student's first day at a new school is supposed to be exciting. There's the prospect of building new, long-lasting friendships, meeting your new teachers and getting acclimatized to your new home-away-from-home. And, on that fateful September morning in 1956, 16-year-old Melba Pattillo Beals was excited.
She was excited, not to meet new people and make new friends, but to finally enjoy the incalculable benefits of a better-quality education. But Melba's quest for personal development is just a side story, for the impact of Melba's enrollment to the Central High School in Little Rock extended far past the borders of Arkansas.
They inspired millions of African-American students across the U.S. to demand equality and freedom from oppression.
Up until a few years prior, Little Rock's Central High School was designated as "white-only". But history and the United States Supreme Court had decided that racial segregation was a thing of the past. Two years earlier, in 1954, the highest courtroom in the country ruled that the segregated US school system was unconstitutional. Effectively opening the doors of all-white schools to African American students.
Melba Beals, along with 8 other, previously banned African American students, expressed their right to equal education and vowed to be the first to enroll at Little Rock's Central High school.
Much of the country was watched anxiously as many others banded together in protest. Fearing trouble, then President Dwight D. Eisenhower asked the 101st Airborne Division for help. And, as if young Melba's first day at school couldn't get any stranger, she was forced to share her ride to school with a rifle-toting armed guard.
When they arrived at Central High, the students were greeted by an angry mob of white protestors waving signs, shouting epithets and telling the students (some as young as 14-years-old) that they didn't belong.
For their courage in the face of hate and ignorance, Melba Patillo Beals and her friends earned their place in the annals of history as "The Little Rock Nine." They inspired millions of African-American students across the U.S. to demand equality and freedom from oppression.
However, Beals' contribution to the fight for African-American civil rights didn't end at graduation. Her book, "Warriors Don't Cry: A Searing Memoir of the Battle to Integrate Little Rock's Central High" has been translated into over 30 languages and has become a favourite text taught in middle and high school social studies across the United States. She, along with the rest of the Little Rock Nine, was awarded the Congressional Gold Medal.
Melba Beals was reunited with her high-school tormentors in search of closure and clarity on an episode of the Oprah Winfrey show in 1996. Melba preached unity and compassion to a crowd of appreciative onlookers at the 50th anniversary of the Little Rock Nine's ordeal. Melba also wrote two more books, detailing her life before the Central High ordeal (March Forward, Girl) and detailing her relationship with God (I Will Not Fear).
For her entire life, Melba Pattillo Beals has championed equality, compassion, education and faith. You can learn more about her harrowing fight for equality by watching her recent appearance on Your Story with Melinda.
Watch Elias Dummer Perform Live Version of "1914 (Christmas Truce)"
DC Talk Celebrates 25th Anniversary of 'Jesus Freak' Album


Embassy of Sweden and the Swedish Institute representing the exhibition "Puzzle of life." The role of the family in Sweden.
The exhibition will run from 17 to 27 September 2015.
Master class by art school "SOLOMRIA"
Movie showing by project "Open Ukraine!"
Hrystyna Lulchenko, Olia Herus, Polina Shtern, Nastia Melnichenko are presenting films made by schoolchildren for the project "Open Ukraine"
Master class by modern сhoreography school "Totem"
The animated films show by studio "Borysphen"
Theatrical walk-adventure "Lost in time" (separate route from Sophyivska square)"
Musical by modern сhoreography school "Totem"
The program for children: "Preschoolers - Education for Sustainable Development"
Children Kinofest presents a special program: the selection of films by legendary director Georges Méliès and contemporary remakes of his films shot by young participants of Shoot like Méliès! contest. Incredible tricks and mysterious disappearances, witty tricks and breathtaking illusions: the program is designed for young viewers by direct descendants of the famous filmmaker.
Presentation of Halyna Maniv book "Kvartyria"
During the lecture we'll discuss the most common barriers, which prevent pleasant creative process of home-drawing. How to understand your small artist?Which supplies are better to use?During the practice you will able to feel yourself as a child, who draws under the supervision of grown-ups.
Master Class "How to make a plane"
Academy of non-classical music "Nota Bene"
Lecture: How to become a movie star!
Lecture: How to become a movie star! for children and parents about children's casting.
Animated films showing by studio "Red dog"
Children Kinofest presents a special program! Shoot like Méliès!
The age of puppet animation is more than a hundred years! Oksana Karpus will tell you about secrets, traditions and practices of this classic animation.
She is the director, who produced dozens of cartoons! Children will become masters of puppets for some time in this express school of animation!
Master class from famous director Tatiana Polyanskoyi. Showing her video works.
Tatiana Poljanskaya - directed by animator, who founded the nursery anymatstsiynu studio "Hundred fantasies."
It domozhe kids of all ages to dip into the world of ideas, through plastylyn. Children plastylynovyy multfiilm Create your own!
"The heat makes your palms miracle - plasticine characters come alive on the screen" - T. Poljanskaya.
Writers and publishers recall and read their favorite fairy tales.
Discussion "What should be done in the education of the child in order to avoid the problems of drug and alcohol dependence in the future"
Children's performance "Nylka i vylka"
Entrance fee - 200 UAH for adults 100 UAH. for children.
Laboratory drama for children and adolescents.
How you do not love my Kiev!
Concert of the winners of the International festival "Chestnut piano"
How can I not love you, my Kyiv!
Studio of creative practice "Expressive things"
Events for children under "Garage sale"
Evening tales, star reading («Видавництво Старого Лева»).
Participants of the master class will become familiar with ancient national art paper decorations (paper cutting) and own cut-paper decorations delicate silhouettes.
Showing full-length animated film "Bogeyman" from Ukranimafilm.
Meeting with the director and actors.
Laboratory of drama for children and adolescents.
Presentation of adventure magazine for children "Krylatie"
Dmitry Cherednichenko, Vasiliy Gerasimiuk, Tatiana Savchenko, Kornelia Koliadzhin (writers).
Creative meeting with children's writer Larisa Nitsoy (winner of the International literary competition "Coronation of Word"), game for preschool children and their fathers.
Master class from the Museum of the Book and printing "Scriptorium"
Master class from Julia Stakhovskaya, illustrator of the book by Sergei Uhachevsky "Tale of an old miller"
Julia Stakhovskaya - Sergei Uhachevskoho illustrator of the book "The Tale of the old miller"
Hand-drawn animation. Master class from animation studio "Borisfen"
Game-presentation by the author of children's books, Valentina Zaha-Bura, winner of the international literary contest "The Coronation of Word"
Interactive play based on the "Carnival of the Animals"
Presentation of the book by Tatiana Vinnik "Echo of our house"
Children's performance "Nylka i Vylakа"
Presentation of information resources, current events and areas of work of the State Library of Ukraine for Youth.
Master-class "How to build a car"
Performance of a marching drums school "ArtDrums"
Children's exemplary theater of the young actor "FantaziaNew"
Imagination is hungry. Traveling in time.
Master class "How to build a car"
Project of a publishing house "Vydavnytstvo Starogo Leva"
Flashmob of extreme reading ReadInExtreme.


text:
One for the history books-why Rugby League need more Rabbitohs
Joseph Del Duca writes passionately about his beloved Rabbitohs. Fate had better bring triumph or...well, you ask him what.
Recently I've been forced to eat my own words but in a very happy way. In April this year, at the start of the rugby league season, I said: "I wasn't sure how many more seasons of pain," I could endure as a Rabbitohs supporter on my biography page. Fast forward to September, and the mighty Red and Green are just one game away from playing in their first grand final in 41 years.
Saturday night, against Canterbury-Bankstown is the game in question. So far an estimated crowd of between 65,000 – 80,000 people are expected. This makes it the biggest game this season. So what is it that makes this game such a sell a huge event compared to all the others? In my opinion there are two figures that cause this, 1908 and 1935. 1908 is the year South Sydney Rabbitohs were founded, and 1935 is the year Canterbury-Bankstown began its side.
Many have tried and failed to tell us that we need to be passionate about a sporting team. In the dark days of the Super League War we were given the Hunter Mariners, the South Queensland Crushers and the Adelaide Rams. The NBL has tried to convince us to follow the Western Sydney Razorbacks and the A League tries valiantly to convince us that we have an immense rivalry with people from the Central Coast. In spite of this we still see the NBL sail to the edge of bankruptcy. The A League continuously struggles to find relevance, and the NRL consistently fails to achieve impressive crowd figures. The reason is simple; you can't buy history.
Continue reading "One for the history books-why Rugby League need more Rabbitohs" »
By Geoff Crocker
21/09/2012 4:41:25 PM | Joseph Del Duca, Sport
Andy's 2011 Melbourne Cup Tips
The Emirates Melbourne Cup is being held today at Flemington Race course.
I have a limited knowledge of horse racing and the purpose of this article is primarily fun.
My top picks are Dunaden, Niwot, Americain, Jukebox Jury, Drunken Sailor and Illo.
The best way to implement this strategy is via a 'box trifecta' on the top 6 horses (see your local bookie for a description of this bet).
Good Luck and gamble responsibly.
01/11/2011 10:49:33 AM | Andy Semple, Sport
The rotting state of the gentleman's game
The ICC's refusal to accept John Howard's nomination as its Vice President raises questions about the integrity of the Council, writes Joshua Bell.
With great dismay, I have been following the debacle surrounding the International Cricket Council's rejection of former Prime Minister John Howard's nomination to be its vice-president (and therefore future president).
These events expose a grim reality that has been kept under the radar for some time and, to paraphrase Marcellus' famous statement in Hamlet, something is rotten in the world of cricket.
Allow me to start by setting the scene.
Continue reading "The rotting state of the gentleman's game" »
06/07/2010 9:00:00 AM | International, Joshua Bell, Sport
Victoria needs a serious look at Mixed Martial Arts
Legalising MMA is a good thing, writes Clinton Gale.
On Sunday February 21st this year Sydney hosted Australia's first ever visit from American based institution Ultimate Fighting Championship, commonly known as the UFC. Drawing an attendance of 17,831, tickets for the Acer Arena's show sold out within an hour, making it the second fastest sell out time for a UFC event. The sport known as mixed martial arts (or MMA) is sweeping the world in popularity. UFC President Dana White stated he wishes to bring the event to Australia annually after the highly successful Sydney event, but due to current state regulations Melbourne is unable to host the UFC.
Continue reading "Victoria needs a serious look at Mixed Martial Arts" »
28/02/2010 8:30:00 PM | Clinton Gale, Sport, Victoria


But in terms of .
And Lee is tremendous, like an encyclopedia of every bass part of every song that ever written, I think. Adidas Yeezy Collection He got a photographic memory. I gone on tour with him, literally, with no rehearsal. He just knows everything he supposed to do. Unfortunately, working with great people means they always busy. But that a nice problem to have. You been collaborating with your wife as a songwriting partner for the past several years. Does Jo have a fixed role in your collaborative process? How does that process work? Does that bring you closer together as a couple?I think she starting to attract attention in her own right with this. She very positive, and she very passionate about music. She written books on psychology and history. She a great Grecophile.
remotely friendly for a violinist to play. To be honest, I wanted to able to use more real time orchestra instruments on the album, but as ever, time constraints meant that at times we had to use samples of things like, for instance, trombones, french horns and many other things. But as you layer up, you realize the tools are getting better and better all the time. The difference between and is there are times when only a real players will do it. But there a ton of technology out there that really come into its own. For example, the choir we used on Fire sounds absolutely real. You can see them standing in front of you. You can believe people aren actually singing in front of you. It a mixture of ancient Greek and Latin, a phonetic approach.
been between Nick Beggs and Lee Pomeroy, both of whom are great players and lovely guys. So, sometimes it one, sometimes it the other. And it may be that this year I have to work with some other player live, because they much in demand. I share Nick Beggs with Steven Wilson so, some years, Steven gets the priority, and other years, I get the priority. I think Nick probably the most brilliant stick player out there. His unaccompanied stick playing, harmonically, is worthy of the work of Bill Evans on piano.