text:
\section{Introduction}

Single-electron tunneling \cite{Av-Likh,SCT} in systems of small-capacitance
tunnel junctions has attracted much attention during the last decade because
of both the interesting physics and the possibility of useful devices. Today
the basic physics of single-electron tunneling is sufficiently well
understood, and its possible applications (for reviews see, e.g., Refs.\
\cite{Av-Likh-log} and \cite{Kor-rev}) are becoming an important issue. The
practical value of several analog applications has already been proven: for
example, the single-electron transistor \cite{Ave-Lik-85,Fulton-D} as a
highly sensitive electrometer,\cite{Likh-87} the single-electron pump \cite
{Pothier-pump} as a standard of dc current, \cite{Keller} and the array of
tunnel junctions \cite{Bakh-89} as an absolute thermometer.\cite{Pekola}

In the field of digital electronics, however, only rudimentary devices have
been demonstrated so far. \cite
{LaFarge-trap,Likh-trap,Yano-mem,Nakazato-mem,Min-mem,Fuji-mem,NEC-mem} The
recent invention \cite{Q0indep} of hybrid circuits based on
single-electron-transistor readout from floating-gate memory cells
presumably opens a way to room-temperature {\it memories} with density
beyond $10^{11}$ bit/cm$^{2}$. (This concept has been supported by recent
experiments \cite{NEC-mem} with the first low-temperature prototypes of such
memory cells). The potential of single-electronics in {\it logic} circuits,
however, remains uncertain due to substantial problems which have to be
solved for both types of single-electron logic devices suggested so far.

Devices of the first type use single-electron transistors instead of field
effect transistors in ``voltage-state'' circuits similar to conventional
digital electronics. \cite{Likh-87} In these devices the effects of charge
quantization are restricted to the interior of the single-electron
transistors. As a result, the design of such circuits (including
complementary \cite{Tucker}) is relatively straightforward. They suffer,
however, from a relatively high static power consumption. \cite
{Kor-trans,Chen}

The second possible way (which allows to reduce the power dissipation), is
to code bits directly by single electrons everywhere in the circuit. \cite
{Likh-Sem,Likh-Polon,Naz-Vysh,Nakazato-log,Kor-isl,Param1,Param2,Ancona,%
GSC,Lent-Tou}
(A different, interesting approach based on rf parametric excitation of
single-electron-tunneling oscillations has been suggested by Kiel and
Oshima; \cite{Kiehl} unfortunately their original proposal seems to have run
into considerable implementation problems \cite{Oshima}). It is important
that these ``charge-state'' logic circuits do not necessarily require long
wires and can be implemented using only small conducting islands separated
by tunnel barriers, with the necessary power and timing provided by an
external rf electric field. \cite{Kor-isl} Recently we suggested \cite
{Param1} a new device for charge-state, wireless logic circuits - the Single
Electron Tunneling Parametron (or SET Parametron). In comparison with the
wireless single-electron devices suggested earlier,\cite{Kor-isl} the SET
Parametron may have wider parameter margins and extremely low power
dissipation, lower than the thermodynamic ``limit'' of $k_{B}T\ln 2$ per
bit. \cite{Param2}

In this paper we present the results of a detailed analysis of the SET
Parametron and basic logic circuits using this device. The major
characteristics of the SET Parametron, including its parameter margins,
speed, error rate, and power consumption, will be discussed.

\section{SET Parametron: The Basic Idea}

The basic cell of the new logic family, the SET Parametron, consists of
three conducting islands - see Fig.\ \ref{three-isl}a. (In our numerical
calculations we have assumed the islands to be of spherical shape, with $R$
being the radius of the edge islands 1 and 3, and $r$ the radius of the
middle island 2; this assumption is, however, not important for the device
operation.) The middle island is slightly shifted off the line passing
through the centers of the edge islands. We will identify this line with
$x$-axis, and the direction of the middle island shift with $y$-axis (which
is the symmetry axis of the cell). Electrons can tunnel through small gaps
between the middle and edge islands, but not directly between the edge
islands because of their much larger spacing (Fig.\ \ref{three-isl}a).

Let us assume that the cell as a whole is charged by one uncompensated
electron. (This assumption makes the explanation of the operation principle
simpler; later we will consider the more natural case of an initially
neutral cell.) If the cell is biased with a sufficiently strong ``clock''
electric field $E_{c}>0$ directed along axis $y$, the electron is obviously
located at the central island.\cite{sign} Now let the field be decreased
gradually so that eventually it changes direction to negative. At some
moment the electron will have to tunnel to one of the edge islands because
these states become energetically preferable. Because of the geometrical
symmetry, the choice of island (left or right) will be random, i.e. the
charge symmetry of the system will be broken spontaneously.

However, if there is a weak ``signal'' field $E_{s}$ along direction $x$
(this field may be applied, for example, by the neighboring similar cell),
the final position of the electron will depend on the sign of $E_{s}$. A
natural way to discuss this effect is to say that the signal field $E_{s}$
creates an energy difference $\Delta $ between the electron states in
islands 1 and 3, and that the electron prefers to tunnel into the island
with the lowest energy state (Fig.\ \ref{three-isl}b). If now the clock
field $E_{c}$ becomes negative and large, it creates a high energy barrier
$W$ (see Fig.\ \ref{three-isl}b) between the edge islands, so that the
electron is reliably trapped in the island it has tunneled to, regardless of
further changes of the signal field $E_{s}$.

Thus if fluctuations in the system are low enough, and the clock field
changes slowly enough, even a small field $E_{s}$ of the proper sign at the
decision-making moment (when $W(t)$=0) is sufficient to ensure a certain
robust final polarization of the cell. This process can be interpreted as a
reliable recording of one bit of information; for example, the electron on
the right island may mean logical ``1'' while the electron on the left
island encode logical ``0''. Now the dipole moment of the cell can in turn
be used to produce the signal field to control the other cells during their
decision-making moments, and hence determine their information contents (see
Section V below).

This ``parametric'' amplification of signal, which gave the SET Parametron
its name, is quite similar to the operation of a Josephson junction device
called Parametric Quantron \cite{Likh-PQ,Likh-PQ2} (re-invented later as the
``Flux Quantum Parametron'' \cite{Goto-PQ}), and in a broader sense to
rf-driven parametrons. \cite{Param-book,Kiehl} The main difference is that
all the previously analyzed parametrons are described by a continuous degree
of freedom (e.g., the Josephson phase $\phi $ in the Parametric Quantron).
This variable can take any value, and the discrete information states
correspond to energy minima on the $\phi $ axis. On the other hand, in the
SET Parametron with low tunnel conductances, the possible states are
discrete (the electron has to be definitely on one of the islands at each
particular instant). \cite{higher-states}

\section{SET Parametron: Quantitative Analysis}

Let us consider the operation of one SET Parametron cell using the orthodox
theory \cite{Av-Likh} which is adequate for the description of
single-electron tunneling in systems with many background electrons in each
island and sufficiently low conductance $G$ of tunnel junctions ($G\ll
e^{2}/\hbar $). In this theory the electron is always localized in one of
the islands, and the rate $\Gamma $ of each tunneling event is solely
determined by the corresponding decrease $W=-\Delta \varepsilon $ of
electrostatic energy $\varepsilon $ of the system. Using elementary
electrostatics, we obtain the following expressions for the energy decreases
corresponding to four possible tunneling events in the SET Parametron
(tunneling to/from each of the edge islands is denoted with signs $+$ and
$-$, respectively):

\begin{eqnarray}
W^\pm_l &=& \pm e \, (\phi_2-\phi_1) - W_{12}, \,\,\,
\nonumber \\
 W^\pm_r &=& \pm e \,
(\phi_2-\phi_3) - W_{23} \, ,
\label{gain} \end{eqnarray}

\begin{equation}
\phi_i = \sum_{j=1}^3 \, (C^{-1})_{ij} q_j - {\vec E} {\vec D}_{i} \, ,
\end{equation}
\begin{equation}  \label{Wij}
W_{ij} = \frac{e^2}{2} \left[ (C^{-1})_{ii} + (C^{-1})_{jj} -2 (C^{-1})_{ij}
\right] \, ,
\end{equation}
\begin{equation}
q_i=q_{i0}+n_i e \, .
\end{equation}

Here $l$($r$) means left (right) junction, $\phi _{i}$ is the electrostatic
potential of $i$-th island (for numbering, see Fig.\ \ref{three-isl}a),
$W_{12}$ and $W_{23}$ are the Coulomb blockade energies, and $C^{-1}$
is the inverse capacitance matrix. Vectors
$e{\vec{D}}_{i}=(eD_{ix},\,eD_{iy},\, eD_{iz})$ are the dipole moments
of islands when charged with single
electrons, ${\vec{E}}$ is the external electric field (accepted to be
uniform) and $q_{i}$ is the total electric charge of $i$-th island, while
$q_{i0}$ is the uncompensated part of its background charge.

In the limit when the island radii are smaller than the spacing between
islands, the following simple approximation for the capacitance matrix
elements can be used:
\begin{eqnarray}
&&(C^{-1})_{11}=(C^{-1})_{33}=\frac{1}{4\pi \epsilon \epsilon _{0}}\,
\frac{1}{R}\,;\,\,\,\,(C^{-1})_{22}=\frac{1}{4\pi \epsilon
\epsilon _{0}}\,\frac{1}{r}\,;  \nonumber \\
&&(C^{-1})_{ij}=\frac{1}{4\pi \epsilon \epsilon _{0}}\,\frac{1}{s_{ij}}
\,,\,\,\,i\neq j\,;  \nonumber \\
&&s_{ij}=\left[ (x_{i}-x_{j})^{2}+(y_{i}-y_{j})^{2}+(z_{i}-z_{j})^{2}\right]
^{1/2};\,\,  \nonumber \\
&&{\vec{D}}_{i}={\vec{r}}_{i},  \label{approx}
\end{eqnarray}
where ${\vec{r}}_{i}=(x_{i},y_{i},z_{i})$ is the $i$-th island center, and
$\epsilon $ is the dielectric constant of the dielectric environment. In the
case of comparable radii and island spacing, $C_{ij}$ have to be calculated
numerically, for example, using the method of multiple electrostatic images
(see Appendix A). The results show that approximation (\ref{approx}) gives
accuracy better than 10\% if the spacing between the islands is larger than
the largest island's radius.

In our initial analysis (until Section VII) we will assume that temperature
$T$ is low and that the electric fields are changing slowly (adiabatically).
In this case the full result of the orthodox theory,
\begin{equation}
\Gamma =\frac{G\,W}{e^{2}\,[1-\exp (-W/k_{B}T)]}  \label{Gamma}
\end{equation}
is reduced to the simple rule that the system always follows the local
minimum of the total electrostatic energy.

Figure \ref{diag}a shows the phase diagram of stationary charge states of a
cell charged by one uncompensated electron. Each state is locally stable
within a diamond-shape region corresponding to two conditions:
\begin{equation}
|e(\phi _{2}-\phi _{1})|<W_{12}\,,\,\,\,\,|e(\phi _{2}-\phi _{3})|<W_{23}\,,
\label{diamond}
\end{equation}
being valid simultaneously, so that no tunneling event is possible,
$W_{l,r}^{\pm }<0$. Within the small-island approximation (\ref{approx})
the position of the diamond center is
\begin{eqnarray}
E_{s} &=&\frac{1}{4\pi \epsilon \epsilon _{0}}\,\frac{1}{2}\,\frac{1}{d}
\,(n_{1}-n_{3})\,e\left( \frac{1}{2d}-\frac{1}{R}\right) ,  \nonumber \\
E_{c} &=&\frac{1}{4\pi \epsilon \epsilon _{0}}\,\frac{1}{2}\,\frac{1}{b}
\left[ (n_{1}+n_{3})\,e\left( \frac{2}{s}-\frac{1}{2d}-\frac{1}{R}\right)
\right. \nonumber \\
&& \left. +2n_{2}e\left( \frac{1}{r}-\frac{1}{s}\right) \right] ,
\label{center} \end{eqnarray}
while the diamond width and height are
\begin{eqnarray}
\delta E_{s} &=&\frac{2}{e}\,\frac{1}{d}\,W_{12}\,,\,\,\,\,\,\delta E_{c}=
\frac{2}{e}\,\frac{1}{b}\,W_{12}\,,  \nonumber \\
W_{12} &=&W_{23}=\frac{e^{2}}{2}\,\frac{1}{4\pi \epsilon \epsilon _{0}}
\,\left( \frac{1}{r}+\frac{1}{R}-\frac{2}{s}\right) \,  \label{size}
\end{eqnarray}
(here $s\equiv s_{12}=s_{23}=(d^{2}+b^{2})^{1/2}$ is the distance between
island centers -- see Fig.\ \ref{three-isl}a).

The diamonds are periodic along both axes $E_{s}$ and $E_{c}$, with periods
\begin{eqnarray}
\Delta E_{s} &=&\frac{1}{4\pi \epsilon \epsilon _{0}}\,\frac{1}{d}\,e\left(
\frac{1}{R}-\frac{1}{2d}\right) ,  \nonumber \\
\Delta E_{c} &=&\frac{1}{4\pi \epsilon \epsilon _{0}}\,\frac{1}{b}\,e\left(
\frac{1}{R}+\frac{2}{r}+\frac{1}{2d}-\frac{4}{s}\right) .  \label{period}
\end{eqnarray}
Equations (\ref{center})--(\ref{period}) are valid even if the approximation
(\ref{approx}) is not used; however, in this case $1/R$, $1/r$, $1/s$, $1/2d
$ (divided by $4\pi \epsilon \epsilon _{0}$) need to be replaced by
$C_{11}^{-1}$, $C_{22}^{-1}$, $C_{12}^{-1}$, $C_{13}^{-1}$, respectively,
and also $b$ and $d$ by $D_{2y}-D_{1y}$ and $D_{2x}-D_{1x}$ (the
corresponding
equations are direct consequences of Eqs.\ (\ref{gain})--(\ref{Wij}) and
(\ref{diamond})).

The period along axis $E_{s}$ corresponds to the transformation
$(n_{1},n_{2},n_{3})\rightarrow (n_{1}-1,n_{2},n_{3}+1)$, while the period
along $E_{c}$ axis corresponds to $(n_{1},n_{2},n_{3})\rightarrow
(n_{1}-1,n_{2}+2,n_{3}-1)$. Notice that these transformations allow only
even-number changes at the middle island; the ``odd'' set of diamonds can be
obtained from the ``even'' set by the shift
$(\Delta E_{s}/2,\Delta E_{c}/2)$.

Figure \ref{diag}a shows the results of more exact, numerical calculations
of the phase diagram for a particular cell; however, they are quite close to
the approximate analytical results (\ref{center})--(\ref{period}). (The
approximation accuracy is better than 10\% and it becomes even better than
1\% after the normalization by $\Delta E_{s}$ and $\Delta E_{c}$.) For
example, the minor offset of the diamond corners from the horizontal axis,
which arises due to deviations from the analytical approximation, is hardly
visible.

The most important qualitative feature of the phase diagram is the existence
of bistability regions (shaded in Fig.\ \ref{diag}a) where either of two
charge states is locally stable. We will refer to the SET Parametron in
these regions as being in an ON state, while the remaining part of the phase
diagram corresponds to one of the possible OFF states of the system. If
signal field $E_{s}$ is low (as we suppose in the following), only the set
of diamonds along axis $E_{c}$ may be implemented. The arrow in Fig.\ \ref
{diag}a shows a possible way (described qualitatively in Sec.\ II above) of
switching the cell from a monostable OFF state to a bistable ON state by
changing the clock field $E_{c}$. It is clear that the sign of a small
$E_{s} $ field determines which diamond boundary will be crossed first, and
hence determines the charge state of the system within this bistable region.

Notice that crossing any phase boundary outside of the bistable regions
involves one tunneling event with negligible energy difference $W$. In the
adiabatic limit this transition is reversible, and the associated energy
loss is infinitesimal (see Sec.\ VII). However, leaving the bistable state
from the state with higher energy results in two sequential tunneling events
and leads to a finite energy loss. This irreversible switching should be
avoided in reversible computation. Below we will show that SET Parametron
circuits can operate using exclusively reversible transitions.

\section{Single Exciton Parametron}

While the case of the cell charged by one electron is the simplest for
understanding the device operation, a more natural option is the initially
electrically neutral cell: $n_{1}+n_{2}+n_{3}=0$. (This variety of SET
Parametrons may be called the ``Single Exciton Parametron'', since digital
bits in it are presented by electrostatically bound electron-hole pairs,
although the physics of this bound state is rather different from that of
the usual excitons in semiconductors.) Figure \ref{diag}b shows the phase
diagram of such a cell with the same geometrical parameters as in Fig.\ \ref
{diag}a. The only difference between the diagrams is a change in the charge
states labeling and a fixed shift along $E_{c}$ axis, so that the diagram in
Fig.\ \ref{diag}b is symmetric about both axes. (Actually, {\it any} change
of the initial charge of the cell is equivalent to a fixed offset of the
fields $E_{c}$ and $E_{s}$).

Due to its field sign symmetry, the Single Exciton Parametron allows two
natural modes of operation. The first is illustrated by the arrowed
rectangle in the center of the diagram (instead of the thick line in Fig.\
\ref{diag}a we have drawn the rectangle in Fig.\ \ref{diag}b to emphasize
that $E_{s}$ may shift during the operation). The periodic clock field
$E_{c}(t)$ causes two switchings OFF$\rightarrow $ON and two switchings
ON$\rightarrow $OFF per period. Another possible mode of operation is
shown by
the smaller rectangle centered at $E_{s}$=$\Delta E_{s}/2$. It also provides
two pairs of ON/OFF switchings per period of the clock field $E_{c}(t)$,
with the bistable state implemented at small fields. In our analysis we will
concentrate on the former operation mode because it does not require the
additional dc bias of the signal field, though the latter mode may allow
wider parameter margins.

Figures \ref{diag}a and \ref{diag}b show the phase diagrams of SET
Parametrons for a particular set of geometric parameters. Changing the
parameters may result not only in quantitative but also qualitative changes
of the diagram. In particular, regions with three stable charge states
appear if the ratio $\delta E_{s}/\Delta E_{s}$ of the diamond width and
period becomes larger than 2; if the ratio is larger than 3, four states can
coexist, and so on. Geometrically the multi-stability requires a smaller
middle island to increase the Coulomb barrier for the electron transfer
between the edge islands via the middle island. For the sake of simplicity
we will limit ourselves to the bistable case. \cite{inversion}

\section{Shift register}

Figure \ref{SR-idea} shows the standard scheme of operation of a shift
register using parametron-type binary cells.\cite{Param-book} In this
figure, each symbol represents a parametron cell at some particular phase of
the periodic switching process. Dash means the monostable (OFF) state, while
{\bf I}$_{{\bf i}}$ means the $i$-th data bit which can be either ``0'' or
``1''. Evolution of the symbols shows the bit flow when the cells are
periodically switched ON and OFF using periodic clock signals which are
shifted by $2\pi /3$ for each next stage of the register.

In the initial state (upper line) each bit is encoded by the corresponding
ON state of only one parametron. The signal field created by this cell is
exerted on both neighboring cells, initially in their OFF state. Due to this
field, when the right neighboring cell is switched from OFF to ON by the
clock field (second line in Fig.\ \ref{SR-idea}), its logic state will be
determined by that of the initial cell. Now when the information has been
copied to the right cell, the initial cell can be switched OFF (third line
of Fig.\ \ref{SR-idea}). Thus, the information has been moved by one cell
(one register stage), and the process may be repeated again (lines 4 to 7)
and again. Notice that unidirectionality of the bit propagation is achieved
by the ``running wave'' of the clock while the structure itself is
1D-isotropic.

During each period of the three-phase clock, the information is shifted by
three stages, so that we need 3 cells per bit of information. It is
straightforward to increase the number of phases beyond 3. Typically this
would make the system more robust, but require proportionally more hardware
per bit. (More generally, the number of cells per bit has not to be integer:
by changing the clock phase shift it can have any value larger than 2).

Figure \ref{SET-sr} shows a natural implementation of shift register using
Single Exciton Parametron cells.\cite{Param1} Each next cell, the direction
of the middle island shift is turned by $\pi /3$ (within plane $y-z$). The
system is driven by the clock field vector ${\vec{E}(t)}$ rotating in the
same plane. This rotation provides the shift of $E_{c}$ (which is now the
component of the clock field in the plane of the corresponding cell) by 1/6
of the clock period for each next cell. When a cell is in ON state, its
dipole electric moment creates the signal field $E_{s}$ which is especially
strong for its nearest neighbors, and thus determines the direction of
electron tunneling when one of the neighbors in turned ON.

The operation of the system is illustrated in Fig.\ \ref{sr-diag}. Three
sine lines show the in-plane components of the clock field for each of three
neighboring cells. Since the operation cycle corresponds to the central
rectangle shown in Fig.\ \ref{diag}b, it differs slightly from the
traditional mode shown in Fig.\ \ref{SR-idea}: each cell is switched OFF and
ON twice per clock period.\cite{doubling} In the simplest case of weak
coupling when the signal field $E_{s}$ is much smaller than the clock field
amplitude, switchings happen when the clock field $E_{c}$ crosses one of the
thresholds $\pm \delta E_{c}/2$ and the cell enters or leaves the bistable
region (shaded in Fig.\ \ref{sr-diag}). For correct operation of the shift
register, switching OFF$\rightarrow $ON of a cell (see, e.g., point $S$ at
the thicker middle curve) should occur when the previous neighboring cell is
in ON state while the next neighboring cell is in OFF state, just as shown
in Fig. \ref{sr-diag}.

In order to find the width of parameter window corresponding to correct
operation of the parametron, let us first neglect the inter-cell
interaction. Using the operation diagram shown in Fig.\ \ref{sr-diag} and
the phase diagram of Fig.\ \ref{diag}b it is straightforward to obtain that
the amplitude $A$ of the rotating clock field has to satisfy the following
three conditions:
\begin{eqnarray}
&&A\sin (\frac{\pi }{2}-\frac{\theta }{2})>\frac{\delta E_{c}}{2}\,,
\nonumber \\
&&A\sin (\frac{\theta }{2})<\frac{\delta E_{c}}{2}\,,  \nonumber \\
&&A<\Delta E_{c}-\frac{\delta E_{c}}{2}\,.  \label{amplitude}
\end{eqnarray}
where $\theta $ is the clock phase shift between the adjacent cells. The
first condition is necessary to have the signal source cell still in ON
state when a recipient cell switches from OFF to ON. The second relation
ensures that at that instant the next cell is already in OFF state. Finally,
the third inequality means that the clock field does not reach the next
diamond at the $E_{c}$ axis - see Fig.\ \ref{diag}b and Eqs.\ (\ref{size})
and (\ref{period}), so that no undesirable charge states appear during the
operation.

Equations (\ref{amplitude}) can be reduced to the following equation for the
one-side margin $\xi $ of the field amplitude, $\xi \equiv
(A_{max}-A_{min})/(A_{max}+A_{min})$:
\begin{equation}
\xi =\min \left[ \tan (\frac{\pi }{4}-\frac{\theta }{2}),\,\,\frac{2\Delta
E_{c}/\delta E_{c}-1-1/\cos (\theta /e)}{2\Delta E_{c}/\delta E_{c}-1+1/\cos
(\theta /e)}\right] .  \label{margin}
\end{equation}
Within the approximation (\ref{approx}) the ratio $\Delta E_{c}/\delta E_{c}$
is equal to $2-(1/R-1/2d)/(1/R+1/r-2/s)$; this ratio increases when the
radius of the middle island decreases. In the general case when the terms
$1/R$, $1/r$, $1/2d$, and $1/s$ are replaced for the elements of the inverse
capacitance matrix, the upper bound for $\Delta E_{c}/\delta E_{c}$ is equal
to 2, while the lower bound is equal to 1.\cite{inversion}

For the particular case shown in Fig.\ \ref{SET-sr} we have
$\theta =2\pi /6$, hence, Eq.\ (\ref{margin}) gives the maximum margin
of $\xi =\tan (\pi /12)\simeq 27\%$ for the amplitude $A$ of
the rotating clock field if $\Delta E_{c}/\delta E_{c}>1.5$,
so that the minimum in Eq.\ (\ref{margin})
is determined by the first term. (In order to satisfy this additional
condition the middle island should be sufficiently smaller than the edge
islands.)

The above single-cell analysis is only an approximation, because in the real
structure all the cells interact with each other and also the presence of
neighboring cells somewhat changes the cell electrostatics. This is why we
have carried out extensive numerical simulations of reasonably long shift
registers (18 three-island cells). For a given geometry of the circuit we
first calculated numerically the inverse capacitance matrix $C_{ij}^{-1}$
and the vectors ${\vec D}_i$ (see Appendix A); then these numbers were fed
to a Monte-Carlo program which simulated single-electron tunneling events in
the circuit using the ``orthodox'' theory.\cite{Av-Likh} The logical input
was a relatively long (typically, 16-bit) quasi-random bit sequence,
repeated periodically many times.

The simulations have shown that for the geometry presented in Fig.\ \ref
{SET-sr}, elliptic polarization of the clock field (rather than the simple
circular polarization implied above) is essential to provide broad margins.
More exactly, the out-of-plane component $A_z$ should be larger than the
in-plane component $A_y$, because of the field screening in $z$ direction
due to the finite size of the conducting islands. For example, for the
circuit with $r/R=0.3$, $d/R=1.5$, $b/R=0.7$, and the intercell period in
$y$-direction $l/R=3$, the best ratio $A_z/A_y$ is close to 1.5. If this is
done, sufficiently wide margins for the amplitudes of the bias field are
really achievable. For $A_z/A_y=1.5$, the 18-cell shift register with the
parameters specified above operates correctly (at zero temperature and
sufficiently low clock frequency) within the range $3.25\,<\,A_y/(e/4\pi
\epsilon\epsilon _0R^2)\,<\,5.1$, corresponding to a margin of $\pm 22\%$. If
now $A_y$ is kept constant at $A_y=4.15\,e/4\pi \epsilon\epsilon _0R^2$, the
allowed range for $A_z/(e/4\pi \epsilon\epsilon _0R^2)$ is between $4.6\,$
and $8.55,$ corresponding to a margin of $\pm 30\%$. These margins are much
broader than those for the first generation of wireless single-electron
devices. \cite{Kor-isl}

The margins for parameters which destroy the geometric symmetry of the
parametron cells are much narrower. Numerical simulations show that for a
shift register with the parameters quoted above, the maximum allowable shift
of the edge islands of a cell in the opposite directions (parallel to the
central island shift) is about $\pm 0.010\,R$. This corresponds to the
maximal fluctuation of $\pm 0.4$ degrees of the alignment of the line
connecting the edge islands of the cell and the $x$-axis. (A shift of only
one island leads to the same effect). Possibly the situation may be improved
by using alternative geometries and charge modes.

\section{SET Parametron Logic Gates}

The shift register described in the previous Section is actually a line of
inverters. To have a complete set for the arbitrary logic functions we need
to have other logic gates (e.g., NAND or NOR), and a circuit with a fan-out
more than one (``splitter'').

All these functions can be naturally implemented using the geometry shown in
Fig.\ \ref{OR/AND}. If the clock field rotation causes the signal
propagation from the bottom to the top we get a fan-out-two circuit, because
the dipole moment of cell $F$ (in its ON state) will determine the charge
state of both cell $A$ and cell $B$, set during their OFF$\rightarrow $ON
switching. On the other hand, if the signal propagates from top to bottom,
we get the implementation of a binary logic function
(either $F=A.\mbox{NOR}.B$ or $F=A.\mbox{NAND}.B$,
depending on the asymmetry provided by the background charges or dc
bias field $\langle E_{s}\rangle $ imposed on cell $F$).

In order to verify the operation of this system, we have carried out its
numerical simulations in the symmetric single-exciton mode, using the same
parameters as above ($r/R=0.3$, $d/R=1.5$, $b/R=0.7$, $l/R=3$) for each of
three shift registers, each of them 6 cells long. The $z$-shift between
upper registers was $6R$, while the $y$-spacing between cells $A$ ($B$) and
$F$ was $2R$, i.e. slightly less than the spacing $l=3R$ between cells in
each register.

The simulations have shown the following margins for the amplitude
components $A_{y}$ and $A_{z}$ of the clock field (at zero temperature and
relatively low speed). For the fan-out-two gate, at $E_{z}/E_{y}=1.5$, we
get correct operation at $3.45\,<\,A_{y}/(e/4\pi \epsilon \epsilon
_{0}R^{2})\,<\,4.2$, corresponding to a margin of $\pm 9\%$. For the
constant $E_{y}=4.15\,e/4\pi \epsilon \epsilon _{0}R^{2}$, the $z$-component
should be within the range $4.6\,<\,A_{z}/(e/4\pi \epsilon \epsilon
_{0}R^{2})\,<\,6.3$ (the margins of $\pm 16\%$). For the NOR gate, with
$E_{y}=4.1\,e/4\pi \epsilon \epsilon _{0}R^{2}$, $E_{z}=6.15\,e/4\pi
\epsilon
\epsilon _{0}R^{2}$ (this operating point is within the margins for both the
shift register and fan-out circuits) correct operation is achieved for the
dc bias field $\langle E_{s}\rangle $ equivalent to the background charge
shift in the range $0.034<\,q_{0}/e<0.053$
($q_{0}=q_{0,left}=-q_{0,right}$). For the NAND gate with similar
parameters the range is $0.035\,<\,-q_{0}/e\,<0.069$.
The difference between the results for the
ranges (which should coincide because of the layout symmetry) is explained
by the finite set of tested input signal sequences which did not have a
symmetry between logical zero and unity. Hence, the true range cannot be
wider than the common part of two ranges [0.035,\thinspace 0.053], and thus
the real margin is slightly below $\pm 20\%$.

\section{Energy dissipation during OFF$\rightarrow$ON switching}

\label{EnDis}Let us calculate the energy dissipation during the switching
OFF$\rightarrow $ON of one SET Parametron cell in a fixed signal field
$E_{s}$.
The switching is illustrated in Fig.\ \ref{switching} which shows the
energies of three possible states of the cell as functions of time. For a
cell charged by one electron the letters $l$, $r$, and $m$ correspond to the
location of the extra electron. For the single-exciton case we can use the
same notation, counting one hole or electron as background charge.

Within the framework of the ``orthodox'' theory the switching is described
by the master equation,\cite{Av-Likh}
\begin{eqnarray}
&&\frac{d}{dt}\sigma _{l(r)}=\sigma _{m}\Gamma _{l(r)}^{+}-\sigma
_{l(r)}\Gamma _{l(r)}^{-}\,,  \nonumber \\
&&\frac{d}{dt}\sigma _{m}=\sigma _{l}\Gamma _{l}^{-}+\sigma _{r}\Gamma
_{r}^{-}-\sigma _{m}(\Gamma _{l}^{+}+\Gamma _{r}^{+})\,,  \nonumber \\
&&\sigma _{m}+\sigma _{l}+\sigma _{r}=1\,,\,\,\,\sigma _{m}(-\infty )=1\,,
\label{swit-maseq}
\end{eqnarray}
where $\sigma _{m}$, $\sigma _{l}$, $\sigma _{r}$ are the probabilities of
finding the system in ``$m$'', ``$l$'', and ``$r$'' states. The tunneling
rates $\Gamma _{l(r)}^{\pm }$ are given by Eq.\ (\ref{Gamma}), in which we
now assume the linear dependence of the energies on time:
\begin{equation}
W_{r}^{+}(t)=-W_{r}^{-}(t)\equiv W(t)=\alpha t\,  \label{W(t)}
\end{equation}
\begin{equation}
W_{l}^{+}(t)=-W_{l}^{-}(t)=W(t)-\Delta .  \label{Wswit}
\end{equation}
(This assumption is evidently valid only if the energy difference $\Delta $
due to the signal field in the moment of switching is much less than the
maximal energy due to the rotating bias field.) We also assume that the
signal field makes state ``$r$'' energetically more preferable, $\varepsilon
_{l}-\varepsilon _{r}=\Delta >0$.

If the clock speed and temperature are sufficiently low so that the system
switches correctly from ``$m$'' to ``$r$'' (bit errors will be considered in
Section IX), then the energy dissipation can be calculated considering only
states ``$r$'' and ``$m$'' and neglecting state ``$l$''. In this case the
master equation (\ref{swit-maseq}) is simplified with the condition $\sigma
_{l}(t)=0$,
\begin{equation}
\frac{d}{dt}\sigma _{r}=(1-\sigma _{r})\Gamma ^{+}-\sigma _{r}\Gamma ^{-}\,
\label{red-maseq}
\end{equation}
(here we omit index $r$ in tunneling rates for simplicity), and has an
explicit solution
\begin{equation}
\sigma _{r}(t)=\int_{-\infty }^{t}\Gamma ^{+}(t^{\prime })\exp \left[
-\int_{t^{\prime }}^{t}\Gamma _{\Sigma }(t^{\prime \prime })dt^{\prime
\prime }\right] dt^{\prime }\,,  \label{sigmar(t)}
\end{equation}
where
\begin{equation}
\Gamma _{\Sigma }(t)=\Gamma ^{+}+\Gamma ^{-}=\Gamma ^{+}\left[ 1+\exp
(-W(t)/T)\right] \,.  \label{GammaSigma}
\end{equation}

The statistical average of energy loss by the moment $t$ is given by the
expression
\begin{equation}  \label{dissip}
{\cal E}(t)=\int_{-\infty }^tW(t^{\prime }) {\dot \sigma }_r(t^{\prime
})dt^{\prime }\, .
\end{equation}
Using Eq.\ (\ref{sigmar(t)}) we find, finally:
\begin{eqnarray}  \label{dis-sol}
{\cal E}(t)= && \int_{-\infty }^tW(t^{\prime })\Gamma _\Sigma (t^{\prime })
\left[ \frac 1{1+\exp (-\frac{W(t^{\prime })}T)}
 \right.  \nonumber \\
&&  -\int_{-\infty }^{t^{\prime }}\Gamma _\Sigma (t^{\prime \prime })
\frac 1{1+\exp (-\frac{ W(t^{\prime \prime })}T)}
	\nonumber \\
&& \left. \times \exp [-\int_{t^{\prime
\prime }}^{t^{\prime }}\Gamma _\Sigma (t^{\prime \prime \prime })dt^{\prime
\prime \prime }]\,dt^{\prime \prime }\right] dt^{\prime }\, .
\end{eqnarray}

The solid line in Fig.\ \ref{diss-c-c} shows the total energy loss ${\cal E=}
$ ${\cal E}(\infty )$ as a function of the dimensionless switching speed
\begin{equation}
\beta \equiv \alpha e^{2}/GT^{2}.  \label{beta}
\end{equation}
In the low-speed limit, $\beta \ll 1$, the switching process is almost
adiabatic. It consists of numerous tunneling events (back and forth between
``$m$'' and ``$r$'' states) occurring within the energy interval on the
order of the thermal energy $T$ around the point $W(t)=0$. (Figure \ref
{switching} shows a particular Monte-Carlo realization for $\beta =0.1$.) It
is easy to check that in the purely adiabatic case when $\sigma _{r}$ is
determined by thermodynamics only,
\begin{equation}
\sigma _{r}(t)=\sigma _{r}^{ad}(t)\equiv \frac{\Gamma ^{+}}
{\Gamma _{\Sigma }}=\frac{1}{1+\exp (-W(t)/T)}\,,  \label{sig-ad}
\end{equation}
the total dissipation is zero, because in Eq.\ (\ref{dissip}) the symmetric
function of time ${\dot{\sigma}}_{r}(t)$ is multiplied by the antisymmetric
function $W(t)$.

According to Eq.\ (\ref{red-maseq}), the correction to the adiabatic limit,
$\Delta \sigma _{r}\equiv \sigma _{r}-\sigma _{r}^{ad}$ satisfies the
equation $\Delta \sigma _{r}=-{\dot{\sigma}}_{r}/\Gamma _{\Sigma }$; hence,
as the first approximation in $\beta $ we can use
\begin{equation}
\Delta \sigma _{r}=-{\dot{\sigma}}_{r}^{ad}/\Gamma _{\Sigma }.
\label{Deltasigma}
\end{equation}
After the integration by parts of Eq.\ (\ref{dissip}) the total dissipation
is given by
\begin{equation}
{\cal E}=\int_{-\infty }^{\infty }W(t)\,\frac{d\Delta \sigma _{r}}{dt}
\,dt=-\int_{-\infty }^{\infty }\frac{dW(t)}{dt}\,\Delta \sigma _{r}\,dt\,.
\label{netdis}
\end{equation}
Combining Eqs.\ (\ref{Deltasigma}), (\ref{netdis}), (\ref{W(t)}), (\ref
{GammaSigma}), and (\ref{Gamma}), we obtain the low-speed approximation for
the total dissipation
\begin{equation}
{\cal E}=\kappa \beta T=\kappa \frac{\alpha e^{2}}{GT}\,,  \label{lowspeed}
\end{equation}
\begin{equation}
\kappa =\int_{-\infty }^{\infty }\frac{e^{-x}(1-e^{-x})}{x(1+e^{-x})^{3}}
\,dx\,\simeq 0.426\,.  \label{kappa}
\end{equation}
In this quasi-reversible regime ${\cal E}\ll T$; notice also that in this
limit the total dissipation {\it decreases} when temperature {\it increases}.

In the opposite limit, $\beta \gg 1$, the speed of energy change is so high
that the tunneling occurs only at $W>0$ and only once -- see Fig.\ \ref
{switching}, without numerous back and forth processes. (Actually, this
limit is the only one possible at $T=0$.) Then the solution of Eq.\ (\ref
{red-maseq}) is
\begin{eqnarray}
\sigma _{r}(t) &= &1-\exp \left( -\int_{0}^{t}\Gamma ^{+}(t)dt\right)
	\nonumber \\
& = & 1- \exp
\left( -\frac{\alpha Gt^{2}}{2e^{2}}\right) ,\,\,t>0,
\end{eqnarray}
and the average total dissipation
\begin{equation}
{\cal E}=(\pi \beta /2)^{1/2}T=(\pi e^{2}\alpha /2G)^{1/2}.
\label{highspeed}
\end{equation}
Hence, in the case $\beta \gg 1$ the average energy dissipation is much
larger than (and independent of) the thermal energy, indicating the
thermodynamic irreversibility of the switching process in this limit. In
Fig.\ \ref{diss-c-c} the low-speed and high-speed approximations (Eqs.\ (\ref
{lowspeed}) and (\ref{highspeed})) are represented by dashed lines, while
the solid line shows the result of the exact calculation using Eq.\ (\ref
{red-maseq}), which gives a natural crossover between these two limits.

Equation\ (\ref{Gamma}) is valid only for the case of the continuous
spectrum of electron energies in the conducting islands. It is easy to
consider a different case when the electron energy in the middle island is
strongly quantized so that only one level is involved in tunneling, while
the energy spectrum of the edge island is still continuous. (This situation
is possible when the middle island is much smaller). Then the ``orthodox''
theory should be somewhat modified, \cite{Av-Kor,Av-Kor-Likh,Beenakker}
however, for our purpose the only important change is that Eq.\
(\ref{Gamma}) should be replaced with
\begin{eqnarray}
&& \Gamma (W)=\frac{\Gamma _{0}}{1+\exp (-W/T)},\,\,
	\nonumber \\
&& \Gamma (W)+\Gamma
(-W)=\Gamma _{0}=\mbox{const},  \label{Gamma-discr}
\end{eqnarray}
where $\Gamma _{0}$ is a constant which characterizes the tunnel barrier
transparency. Equation\ (\ref{dis-sol}) yields that the average total
energy loss during one switching is given by a simple formula
\begin{equation}
{\cal E}=\alpha /\Gamma _{0}  \label{diss-discr}
\end{equation}
for arbitrary switching speed (see Fig.\ \ref{fig-discr}). It is evident
that quasi-reversibility (${\cal E}\ll T$) is possible in this case as well,
if the switching speed is low enough: $\alpha \ll T/\Gamma _{0}$.

In both cases considered above, electron energy relaxation in islands with
continuous spectrum (implied by Eqs. (\ref{Gamma}) and (\ref{Gamma-discr}))
is the source of dissipation in the system. In the important case when
electron energy is quantized in {\it all} islands this may not be true, so
that this limit requires a completely different treatment. Our hope is to
complete an analysis of this important case in the near future.

To conclude this section, notice that our model allows not only the total
dissipation ${\cal E}$ to be calculated, but also the time dynamics of the
heat transfer between the system and the environment (``heat bath'') during
the switching process to be followed. Dashed lines in Figs.\ \ref{diss-c-c}
and \ref{fig-discr} show the results of such calculation using Eqs. (\ref
{Gamma}) and (\ref{Gamma-discr}), respectively. During the first part of the
switching process (when $W(t)\leq 0$) the energy ${\cal E}_{1}\equiv -
{\cal E}(0)$ is (on the average) {\it borrowed} from the heat bath which,
hence, is
{\it cooled}. During the second part of the process ($W(t)\geq 0$) the
average energy ${\cal E}_{2}\equiv {\cal E}-{\cal E}(0)>{\cal E}_{1}$ is
{\it returned} back to the heat bath. Notice that in the adiabatic limit
${\cal E}_{1}={\cal E}_{2}=T\ln 2$ independently of the exact model used
for $\Gamma (W)$. This result follows from Eqs.\ (\ref{dissip}) and
(\ref{sig-ad}) after the integration by parts:
\begin{equation}
{\cal E}_{1}^{ad}={\cal E}_{2}^{ad}=\int_{-\infty }^{0}\frac{1}
{1+\exp (-W/T) }\,{\dot{W}}\,dt=T\ln 2.  \label{e1ad}
\end{equation}
Notice that this is valid for any gradual function $W(t)$, if only $W(0)=0$.

The generality of this result is due to the direct relation ${\cal E}
(t)=-T\Delta S_{inf}(t)$ between the energy and the informational
(``Shannon'') entropy $S_{inf}$ of the degree of freedom used to code
information (for a more detailed discussion, see Appendix B). In fact, in
the instant when $W=0$, the system may be in either of two states ($\sigma
_{m}=\sigma _{r}=1/2)$, hence $\Delta S_{inf}=\ln 2$ has been acquired in
comparison with the definite initial state
($\sigma _{m}=1$, $\sigma _{r}=0)$. By the end of the switching
the informational entropy is restored to the
initial value since the state is definite again ($\sigma _{m}=0$, $\sigma
_{r}=1$). Finite switching speed decreases ${\cal E}_{1}$ and increases
${\cal E}_{2}$ (see the dotted lines in Figs.\ \ref{diss-c-c} and \ref
{fig-discr}) leading to a positive total dissipation ${\cal E}={\cal E}_{2}-
{\cal E}_{1}$.

\section{Reversible computation}

The general thermodynamic arguments lead to the conclusion that erasure of
information necessarily requires an energy dissipation of at least $T\ln 2$
per bit (see Refs.\ \cite{infentropy,Landauer,Bennett} and Appendix B).
During the switching OFF$\rightarrow $ON of a cell in any SET-Parametron
circuit, the amount of information is not changed, thus allowing arbitrary
small energy dissipation in the slow-switching limit. However, for switching
ON$\rightarrow $OFF the lower bound on dissipation is determined by logical
reversibility of a particular circuit.

The SET Parametron shift register is obviously a logically reversible
circuit, because during cell switching to OFF the information is preserved
by the next cell. It is easy to check (see Fig.\ \ref{SET-sr}) that the sign
of the energy difference $\Delta =\varepsilon _{l}-\varepsilon _{r}$ between
two digital states does not change during the ON phase because of the back
influence from the next cell. So the cell stays in the lower-energy state
and the analysis of the energy dissipation during switching ON$\rightarrow
$OFF is equivalent to that of the switching OFF$\rightarrow $ON (see Fig.\
\ref{ONOFF}). A similar small-dissipation case is realized in the SET
Parametron fan-out circuit, because during the ON$\rightarrow $OFF switching
of the last cell of the input line (cell $F$ in Fig.\ \ref{OR/AND}) the
proper sign of $\Delta $ is maintained by both first cells of the output
lines.

The situation is different for the NAND/NOR gate because any gate consisting
of two inputs and one output is logically irreversible and, hence, has a
lower bound for dissipation. \cite{infentropy,Landauer,Bennett} For two
uncorrelated input streams of bits with equal probabilities of unity and
zero, the informational entropy before the logic operation is
$S_{inf}^{before}=-\ln (1/4)$ while after the completion of the logic
operation and erasure of the input information it becomes
$S_{inf}^{after}=-\ln (1/2)$. (Notice that the informational entropy
{\it decreases}. This seems to contradict the apparent partial loss of
information at computing. Actually the {\it uncertainty} is partially lost,
not the information, because in the Shannon formalism we should treat the
input data as unknown, and the data bit count is decreased by the gate.) The
entropy difference determines the lower bound for the average dissipation
${\cal E}$ per logic operation ${\cal E}\geq
T(S_{inf}^{before}-S_{inf}^{after})=T\ln 2$.

Actually, in the SET Parametron realization shown in Fig.\ \ref{OR/AND} the
average energy dissipation is much larger than this lower bound. If two
input bits are different, the energy difference $\Delta $ changes its sign
during ON state of either cell A or B. In this case the energy dissipation
during switching to OFF is comparable to $|\Delta |$ (see Fig.\ \ref{ONOFF})
which should be much larger than the thermal energy because the condition
$|\Delta |\gg T$ is necessary to ensure small error probability (see next
Section).

To realize {\it reversible} NOR and NAND operations (which would provide
small dissipation) using SET Parametron cells, gates with two inputs and
three outputs can be used (see Fig.\ \ref{revers}). This idea was suggested
\cite{Likh-PQ2} for the Parametric Quantron logic gates and can be directly
applied to the SET Parametron. The input information is copied to the first
cells of two additional shift register lines. If their coupling to the last
cells of input lines is stronger than input-output coupling, the proper sign
of $\Delta $ is always maintained, and the energy dissipation is arbitrarily
small in the slow switching limit.

\section{Bit error rate}

Kinetic equation (\ref{swit-maseq}) allows the calculation of the rate of
``classical'' digital errors during the SET Parametron cell switching (later
we will briefly discuss also the ``nonclassical'' errors due to cotunneling
\cite{Av-Odin}). The error probability $P$ is given by $\sigma _{l}
(\infty )$. Let us first assume $T=0$ and calculate the ``dynamic''
error which occurs
when the switching speed $\alpha $ is too high, and the system remains in
the initial (symmetric) state up to the moment when tunneling to the upper
energy level becomes possible (see Fig.\ \ref{switching} and Eqs.\ (\ref
{W(t)}) -- (\ref{Wswit})). Since there is no tunneling back and forth at
$T=0 $, the error probability can be found simply as the time integral of
the rate of erroneous tunneling $\Gamma _{l}^{+}$ multiplied by the
probability $\sigma _{m}$ that no tunneling has yet occurred:
\begin{equation}
P_{dyn}=\int_{0}^{\infty }\Gamma _{l}^{+}(\varepsilon )\,\sigma
_{m}(\varepsilon )\,\frac{d\varepsilon }{\alpha }\,,  \label{dyn-gen}
\end{equation}
\begin{eqnarray}
\sigma _{m}(\varepsilon ) =&& \exp \left( -\int_{0}^{\Delta }\Gamma
_{r}^{+}(\varepsilon ^{\prime })\frac{d\varepsilon ^{\prime }}{\alpha }
\right)
	\nonumber \\
&& \times  \exp \left( -\int_{0}^{\varepsilon }\left( \Gamma
_{l}^{+}(\varepsilon ^{\prime })+\Gamma _{r}^{+}(\varepsilon ^{\prime
}+\Delta )\right) \frac{d\varepsilon ^{\prime }}{\alpha }\right) .
\label{dyn-gen2}
\end{eqnarray}

For the ``orthodox'' model of the tunneling rate given by Eq.\
(\ref{Gamma}),
\begin{equation}
P_{dyn}=K\gamma \exp (-\frac{1}{2\gamma })\,,  \label{dyn}
\label{Pdyn}\end{equation}
\begin{eqnarray}
K &=&\frac{1}{2\gamma }-\frac{\sqrt{\pi }}{4\gamma ^{3/2}}\exp (\frac{1}
{4\gamma })[1-\mbox{Erf}(\frac{1}{2\sqrt{\gamma }})]  \nonumber \\
&=&1+\sum_{n=1}^{\infty }\frac{(2n+1)!}{n!}\,(-\gamma )^{n},  \label{dyn-K}
\end{eqnarray}
where $\gamma \equiv \alpha e^{2}/G\Delta ^{2}$. In order to keep
$P_{dyn}\ll 1$, $\gamma $ should be much less than 1, then $K\approx 1$.
Equation (\ref{Pdyn}) shows that the dynamic error decreases
exponentially with the
decrease of the switching speed and even faster than exponentially with the
increase of $\Delta $ (factor $\Delta ^{2}$ in the exponent).

For sufficiently small $\alpha $ and/or large $\Delta $ the main
contribution to the error probability will be due to the thermally activated
processes which populate the symmetrical state ``$m$'' during the passage of
energy $\varepsilon _{m}$ across $\varepsilon _{l}$. The probability of this
``thermal'' error is given by the simple formula
\begin{equation}
P_{therm}=\exp (-\Delta /T)\,  \label{therm-err}
\end{equation}
and it prevails over $P_{dyn}$ when $T\gg \alpha e^{2}/G\Delta $. In the
case when both errors are of the same order, the result can be found by the
numerical solution of Eq.\ (\ref{swit-maseq}). The total error probability
can be estimated as the maximum of the two analytical results presented
above: $P\simeq \max (P_{dyn},\,P_{therm})$.

If instead of the ``orthodox'' model we assume that only one discrete energy
level of the middle island participates in tunneling, then using Eq.\ (\ref
{Gamma-discr}) for the tunneling rate we obtain from Eqs.\ (\ref{dyn-gen})
and (\ref{dyn-gen2}) the following probability of the dynamic error ($T=0$):
\begin{equation}
P_{dyn}=\frac{1}{2}\exp (-\frac{\Delta }{\alpha }\Gamma _{0})\,.
\label{dyn-discr}
\end{equation}
The thermal error is still given by Eq.\ (\ref{therm-err}), and it prevails
over the dynamic error if $T\gg \alpha /\Gamma _{0}$.

One more possible source of errors is the higher-order quantum process of
cotunneling \cite{Av-Odin} when two or more electrons tunnel simultaneously
through different junctions. For illustration, the lowest energy diagram in
Fig.\ \ref{three-isl}b shows the situation when the charge state with higher
energy is occupied, and the digital information in the cell is preserved by
the energy barrier (higher energy of the symmetric state) due to the bias
field. According to the orthodox theory, single-electron tunneling in this
case is impossible (at sufficiently low temperature). However, the
second-order cotunneling, i.e. simultaneous tunneling of two electrons
(through both junction) brings the system into the lower energy state and,
hence, is energetically allowed. This process changes the sign of the cell
dipole moment and can lead to the digital error.

This type of error can occur, for example, in the 3-phase shift register
during the phase when the bit is stored by only one cell, and the long-range
interaction with cells carrying other bits (nearest cells are OFF) provides
uncontrolled sign of the energy difference between ``$l$'' and ``$r$''
states. The erroneous bit will then propagate along the shift register.

Though a detailed analysis of cotunneling was not a goal of this work, we
should notice that several means are readily available to reduce the
resulting error probability. First, because the rate of $m$-electron
cotunneling scales as $(GR_{Q})^{m}$ (where $R_{Q}$ $\approx 6.5$ $k\Omega $
is the quantum unit of resistance) while the single-electron rate is
proportional to the first power of $G$, the decrease of $G$ decreases the
relative importance of the cotunneling processes. Another, more powerful
method is to increase the smallest order $m$ of possible cotunneling
processes. This can be done, for example, by increasing the number of
islands per cell. If the cell consists of 5 islands and the ON state
corresponds to an electron on one of the outer islands, then at least the
4-th order cotunneling ($m=4$) is necessary to switch between logical zero
and unity; a further increase of the number of islands per cell makes the
cotunneling rate negligible even for relatively large tunnel conductance.
Finally, it is possible to increase the minimal cotunneling order while
still using three-island cells, by increasing the number of cells which
store the same bit. This can be done, for example, by the increase of the
number of phases in the operation of the shift register. In the realization
shown in Fig.\ \ref{SET-sr} this may easily be achieved by a decrease of the
angle $\theta $ between the planes of neighboring cells. If the bit is
stored by $k$ neighboring cells then the error can occur only if all these
$k $ cells will simultaneously change their polarizations and if the final
state has a lower energy (any ``partial'' switching would cost at least one
cell-cell interaction energy and, hence, is thermodynamically forbidden at
least for not too large $k$). So, the lowest order of erroneous cotunneling
is $2k$, and the linear increase in ``hardware'' allows the exponential
reduction of the error probability. This method is applicable to any logic
gates which use shift registers as their input and output lines.

\section{Discussion}

In this paper we have presented a functionally complete logic family based
on the SET Parametron cells, including inverter, fan-out-two, NAND and NOR
gates. All the circuits may operate correctly in a common range for the bias
field amplitude. The important advantages of the SET Parametron logic are
wireless operation and extremely low power dissipation possible in the
quasi-reversible mode of operation, with the energy loss much less then
$k_{B}T\ln 2$ per bit.

While the realization of room temperature operation of the SET parametron
logic requires sub-one-nanometer fabrication technology which is hardly
available at the present time, the operation of simple SET Parametron
circuits (with clock wires) can be readily demonstrated experimentally at
lower temperatures. An obvious choice is the aluminum shadow-mask
evaporation technology, widely accepted for singe-electron device
fabrication (see, e.g., the collection \cite{SCT}) . Figure \ref{alumin}
shows the sketch of a possible layout of the two-cell SET Parametron shift
register-inverter. (For the sake of simplicity, the artifact islands typical
for this technology are not shown). Each cell consists of three islands. The
capacitive gates are used for the application of rf ``clock'' fields which
cause the switching processes, and simultaneously for the application of dc
fields to compensate random background charges. Input gates A and B (for the
initial demonstration, one gate is sufficient) determine the polarization of
the first cell during its OFF$\rightarrow $ON switching. This polarization
in turn determines the polarization of the next cell during its
OFF$\rightarrow $ON switching. The final polarization of the latter cell
is sensed by a capacitively coupled single-electron transistor. (If a
multilayer fabrication is available, this layout may be further improved to
provide wider parameter margins: an overlap (without tunneling) of the edge
islands of two cells would increase their capacitive coupling, while a
similar overlap of the bias gates with the islands would allow smaller
cross-talk.) The operation temperature of such a SET-Parametron circuit with
100-nm-scale tunnel junctions will be in sub-1-K range.

Coming back to the wireless realization, let us estimate the parameters of a
possible implementation of the device using the conducting (e.g., metallic)
clusters as islands. For a cluster diameter $2R$ about 5 nm (which is at the
limit of present-day direct e-beam writing techniques) the charging energy
$E_{c}\sim e^{2}/8\pi \epsilon \epsilon _{0}R$ is about $0.15eV$ (where
$\epsilon \sim 2$ is taken as a typical dielectric constant for the organic
materials which are the natural candidates for the cluster environment). For
the layouts considered in this paper the typical energy difference $\Delta $
between ``$l$'' and ``$r$'' states is about $0.2E_{c}$ leading to $\Delta
\sim 0.03$ eV. Requiring the probability of the thermal error to be less
than $10^{-10}$ per switching, Eq.\ (\ref{therm-err}) yields the maximal
operation temperature of about 15 K. Assuming the same value for the dynamic
error (then $\gamma \simeq 0.025$ -- see Eq.\ (\ref{dyn})) and taking into
account the particular geometry (Fig.\ \ref{SET-sr}), we obtain the maximum
clock frequency $\nu _{max}\sim 5\times 10^{-4}G\Delta /e^{2}$ that
corresponds to about $10^{9}$ Hz for our parameters and $G\sim $(10$^{5}$
Ohm)$^{-1}$ (higher $G$ would make the cotunneling a problem). In this case
the power dissipation (see Eq.\ (\ref{highspeed})) is about $4(\pi \gamma
/2)^{1/2}\nu \Delta \sim \nu \Delta \sim 5\times 10^{-12}$ W per cell. This
extremely low dissipation would make possible an integration level up to
10$^{11}$ cells per cm$^{2}$ (i.e.\ 10$^{3}$ nm$^{2}$ per cell), limited by
the cell size, since at 15 K the heat flux about 1W/cm$^{2}$ can be easily
managed without the circuit overheating. To achieve the quasi-reversible
mode of operation the frequency should be even lower: $\nu \ll 5\times
10^{7} $ Hz for our set of parameters at $T=15$ K. Accepting, for example,
$\nu =10^{6}$ Hz we get a power dissipation of only about $5\times 10^{-18}$
W per cell. This figure indicates that as far as power dissipation is
concerned, three-dimensional integration of SET Parametron circuits is quite
feasible. Despite the not very spectacular clock frequency in this regime,
the total computing performance of a 3D system can be very large.

The largest problem with SET Parametron circuits (besides their fabrication)
is that their operation requires well-defined background charges. The
allowed fluctuations are only on the order of $0.01e$ (this number
corresponds to the maximum tolerated angle of the cell tilt -- see Section
V). This is a common problem for any single-electron logic (see for example
Refs.\ \cite{Kor-rev,Kor-trans,Chen}). However, if/when a molecular technology
becomes available for the implementation of single-electron and other
nanoscale devices, SET Parametron cells may be reproducible on the molecular
level, and well defined background charges seem to be achievable in
principle.

From the estimates above we see that in order to increase the operation
temperature of SET Parametron circuits up to 300 K or even up to 77 K,
sub--nanometer-scale islands are necessary. In this case the energy level
discreteness \cite{Av-Kor,Av-Kor-Likh,Beenakker} may result in radically new
features of the SET Parametron operation, and should be taken into account
at its quantitative analysis. Such analysis is outside the scope of the
present paper. We would just like to notice in passing that the operation of
SET Parametron circuits in that mode would be rather close to the recently
proposed new version \cite{Lent-Tou} of the so-called ''Quantum Cellular
Automata''.\cite{GSC} This new version, put forward under the keywords of
``adiabatic switching'' and ``pipelining'', may remove the principal
difficulties \cite{Kor-isl} of the initial suggestion. \ We are not,
however, aware of any detailed analysis of this new family of logic devices.

\acknowledgements
We would like to thank D. V. Averin and T. Usuki for useful discussions. The
work was partially supported by AFOSR Grant No. F49620-95-1-0044, Russian
RFBR Grant No. 97-02-16332, and Russian Program on
Nanoelectronics Grant No. 039-03-232/78/4-3.

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text:
Polymerelektronik.org
Home » Health News » FAST Score Appears Accurate for Diagnosis of Fibrotic NASH
FAST Score Appears Accurate for Diagnosis of Fibrotic NASH
The FibroScan-aspartate aminotransferase (FAST) score shows high sensitivity and specificity for noninvasive identification of patients with fibrotic nonalcoholic steatohepatitis (NASH), according to a new systematic review and meta-analysis.
The FAST score had an overall sensitivity of 89% and an overall specificity of 89% with a defined rule-out cutoff of .35 or lower and rule-in cutoff of .67 or higher, respectively, Federico Ravaioli, MD, PhD, a gastroenterologist at the University of Modena & Reggio Emilia in Italy, and colleagues, wrote in Gut.
"These results could be used in clinical screening studies to efficiently identify patients at risk of progressive NASH, who should be referred for a conclusive liver biopsy, and who might benefit from treatment with emerging pharmacotherapies," the authors wrote.
The research team analyzed 12 observational studies with 5,835 participants with biopsy-confirmed nonalcoholic fatty liver disease (NAFLD) between February 2020 and April 2022. They included articles that reported data for the calculation of sensitivity and specificity of the FAST score for identifying adult patients with fibrotic NASH based on a defined rule-out cutoff of .35 or lower and rule-in cutoff of .67 or higher. Fibrotic NASH was defined as patients with NASH plus a NAFLD activity score of 4 or greater and fibrosis stage 2 or higher.
The pooled prevalence of fibrotic NASH was 28%. The mean age of participants ranged from 40 to 60, and the proportion of men ranged from 23% to 91%. The mean body mass index ranged from 23 kg/m2 to 41 kg/m2, with a prevalence of obesity ranging from 23% to 100% and preexisting type 2 diabetes ranging from 18% to 60%. Nine studies included patients with biopsy-proven NAFLD from tertiary care liver centers, and three studies included patients from bariatric clinics or bariatric surgery centers with available liver biopsy data.
Fibrotic NASH was ruled out in 2,723 patients (45.5%) by a FAST score of .35 or lower and ruled in 1,287 patients (21.5%) by a FAST score of .67 or higher. In addition, 1,979 patients (33%) had a FAST score in the so-called "grey" intermediate zone.
Overall, the FAST score pooled sensitivity was 89%, and the pooled specificity was 89%. By the rule-out cutoff of .35, the sensitivity was 89% and the specificity was 56%. By the rule-in cutoff of .67, the sensitivity was 46% and the specificity was 89%.
At an expected prevalence of fibrotic NASH of 30%, the negative predictive value of the .35 cutoff was 92%, and the positive predictive value of the .67 cutoff was 65%. Across the included studies, the negative predictive value ranged from 77% to 98%, and the positive predictive value ranged from 32% to 87%.
For the rule-in cutoff of .67, at a pretest probability of 10%, 20%, 26.3%, and 30%, there was an increasing likelihood of detecting fibrotic NASH by FAST score at 32%, 52%, 60%, and 65%, respectively. For the rule-out cutoff of .35, at the same pretest probability levels, the likelihood of someone not having fibrotic NASH and not being detected by FAST score was 2%, 5%, 7%, and 8%, respectively.
In subgroup analyses, the sensitivity of the rule-out cutoff was significantly affected by the study design. In addition, age and BMI above the median both affected pooled sensitivity but not pooled specificity. On the other hand, the rule-in cutoff was significantly affected by study design, BMI above the median, and presence of preexisting type 2 diabetes above the median.
"Today, we stand on the cusp of a revolutionary time to treat NASH. This is due in part to the fact that many exciting, novel precision metabolic treatments are in the pipeline to combat this disease," said Brian DeBosch, MD, PhD, associate professor of cell biology and physiology at the Washington University in St. Louis, who was not involved with this study.
"A major barrier in clinical NASH management is a rapid, noninvasive, and precise means by which to clinically stage such patients," Dr. DeBosch said. "We now approach as closely as ever the sensitivity and specificity required to stratify the highest-risk patients, identify candidates for advanced therapy, and meaningfully reduce biopsies through using noninvasive testing."
Dr. DeBosch noted the importance of pretest probability and specific subpopulations when deciding whether to use the FAST score. For instance, he said, a tertiary academic liver transplant center will see a different patient population than in a primary care setting. Also, in this study, the presence or absence of diabetes and a BMI above 30 significantly altered sensitivity and specificity.
"One important remaining question stemming from these data is whether FAST can also be used as a surrogate measure to follow disease regression over time following intervention," Dr. DeBosch said. "Even if FAST is not useful in that way, defining individuals who most need to undergo biopsy and/or those who need to undergo treatment remain important uses for this test."
The study authors did not declare a specific funding source or report any competing interests. DeBosch reported no relevant disclosures.
This article originally appeared on MDedge.com, part of the Medscape Professional Network.
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redpajama_set_name: RedPajamaCommonCrawl


What is a TeachMeet? A fun, informal event for sharing great ideas for teaching and learning with opportunities to network with other educators.
Read more about this FREE event and for details of how to book click here.
Tickets are moving quickly so book now and pass on to colleagues who may be interested.


Social anxiety can be difficult to manage on your own, which is why having a compassionate counselor on your side can help you learn how to get over social anxiety. CBT and Acceptance and Commitment Therapy counselors have many tools at their disposal that can help you cultivate your social anxiety toolkit. how to get spore for free mac 2017 If you're depressed, nervous and don't know how to overcome social anxiety, it's because you're stuck in your own head and can't identify thoughts outside of your "never-good-enough" self.
If your social anxiety, in general, is severe and self-help strategies are not sufficient to reduce your fear, consider contacting a mental health professional or your doctor for a referral. There are effective treatments for SAD, such as cognitive-behavioral therapy (CBT) and medication , that can make a difference in your life.
Step 1: Get to know your social anxiety better To face your fears, it is helpful to know what your specific fears are about social or performance based situations. For example, are you afraid of saying "hi" to a co-worker or asking a stranger for directions?
Social anxiety can be difficult to manage on your own, which is why having a compassionate counselor on your side can help you learn how to get over social anxiety. CBT and Acceptance and Commitment Therapy counselors have many tools at their disposal that can help you cultivate your social anxiety toolkit.


More than 125 local freelance broadcast workers at the Big Ten Network ratified the first ever college sports network union contract with the International Alliance of Theatrical Stage Employees (IATSE).
Broadcast workers at the University of Wisconsin and University of Minnesota campuses will receive guaranteed rate increases, health contributions, and eventually pension and annuity contributions under the new contract. These workers produce telecasts of events ranging from Championship Women's Volleyball to Big Time College Football, featuring some of the top ranked teams in the nation.
Negotiated by the IATSE, IATSE Local 745 in Minnesota, and IATSE Local 414 in Wisconsin, the contract is the result of months of bargaining that began after broadcast workers in Minnesota and Wisconsin voted overwhelmingly to be represented by the IATSE in the summer of 2014. After often going for years without raises and working with no guaranteed overtime or holiday pay, workers will now be paid fair, market-based rates for the work they do in helping to make the Big Ten Network one of the most profitable sport networks.
The four-year contract, with wage retroactivity to September 1, 2015, was ratified in a five-day voting period that ended November 5th. All work conducted after November 5th will be under the full terms of the contract, including the newly negotiated wage and benefit contributions.
IATSE Local 745 and IATSE Local 414 are local unions representing skilled broadcast professionals, specializing in sports and entertainment television production. Local 745 represents broadcast workers in the Minneapolis/St. Paul metro area, and Local 414 represents workers in the Greater Milwaukee area.


Home / Blogging and Admin / Science and Technology / eNidhi.net now available as Nokia ovi store app!
eNidhi.net now available as Nokia ovi store app!
Long time since I've done anything remotely geeky. Even this one isn't, still I can claim I've an app of mine in the world of smart phone apps.
eNidhi.net is now available as an App (short for Application) in Nokia Ovi Store. What does this app do? It fetches latest posts from RSS and lets you read them from within your nokia smart phone. Nothing greater than that.
Is the app really useful?
Not sure. It isn't interactive as many of the apps such as games, stock quotes or social media apps. It only fetches blog's RSS feed and provides it for the consumption of mobile users.
How to submit one's blog as an App for Nokia Ovi store?
Nice to know about this.. Good one attempt..
Love the ICON Design with your Pic!
Loggy: Thanks. You're the first person to say "I've downloaded it"
Recruitment Frauds: Job Aspirants beware!
Backlong Post: Transfer in IT Companies!


Each ticket holder goes home with a bottle of wine and a MOSAIC wine glass! As tickets are drawn, each ticket holder will pick a bottle from the selection of local wines, wrapped in children's art.
WINE TASTING, MUSIC, RAFFLE PRIZES, FOOD AVAILABLE.


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Most people are quite passionate about maintaining the beauty of their skin and hair. To the people who have a true passion for staying beautiful and always looking their best, the quest to have strikingly elegant hair and beautiful skin is never really ending. A lot of time and energy is being put into taking adequate care of the hair and skin by these people.There is no limit to the quest for more products that are able to deliver benefits. Many people have spent a significant amount of their time and money trying to find the most suitable products. For those that can afford it, the related expenses are not a big problem. But for those that don't have an unlimited supply of resources, it is comforting to know that nature has provided a lot of pure and natural alternatives to chemical laden cosmetics out there.
Everyday, more and more beauty products are being introduced into the market, with the promises and claims to provide an effortlessly glossy, and well-conditioned smooth looks to your skin and hair. Unfortunately though, not all these products have the capacity to deliver their promises. But beauty does not have to be painful or overly expensive. We can also not not discount the benefits of beautiful hair and skin as it does wonders to ones confidence and self esteem so, if you are reading this blog post, you are in luck as we will highlight a few things about this wonderful butter that would help you achieve the perfect hair and skin you have always dreamt about.
Cupuacu butter is extracted from the Cupuacu seed which is obtained from a tree that grows in the Amazon rainforests of some countries in South America like Brazil. It is related to the family of cocoa butter and has a characteristic aroma that slightly resembles that of cocoa butter. Cupuacu butter has an impressive lineup of great beneficial components for the skin and hair. It contains linoleic, lauric, myristic and oleic acids. All of these amazing omega 3 fatty acids make its moisturizing and hydrating properties absolutely outstanding.
Fuller and softer hair: applying hair products that contain a high content of cupuacu butter will help your hair to become softer. It penetrates the hair shaft to smoothen and lay down the hair shaft. As such, it is a great natural straighter for the hair. If you are battling hair dryness and hair brittleness, you can rely on this butter for its powerful hydrating capabilities. Cupuacu butter is known to work wonders particularly on ethnic hair and can restore its natural smoothness and soft texture.
Hydrated and moisturized skin: people who are suffering from dry skin issues often use this butter to keep their skin moisturised and hydrated, seeing that the butter has a high level hydration capacity. You can also use the butter as a cream supplement to maintain your skin's tenderness and moisture.
Hair Growth: regular massage of the cupuacu butter into the hair scalp as a form of hair mask works effectively to boost hair growth, especially for people who have slow hair growth. The rich nutrients contained in cupuacu butter feeds the hair follicles and allows it to grow more healthy hair at a faster rate.
Younger looking skin: with frequent use, and over time, cupuacu butter has proven to be an amazing anti-aging skin care product. The high anti-oxidant nutrients of the butter work to eliminate wrinkles that appear on the skin, thereby renewing and rejuvenating skin and keeping it younger looking.
Cupuacu butter can be used as key ingredient in a number of skincare products. It can be used in making body butters, skin care cremes, hair butters, salves, deodorants, hair masks, hair styling creme, moisturizing lotion, general hair care and cosmetics. It is also used extensively in the field of aromatherapy. Cupuacu butter also serves as a great source of nourishment to boost the immune system of both the hair and the skin, prohibiting the proliferation of skin and scalp diseases.There are so many benefits that this great unrefined butter provides for skin and hair but they are far too many for us to mention.
We encourage you to order yours to see the amazing rewards it offers. Please note that we carry the unrefined version of this butter which is the most potent form you will find. Refined cupuacu butter does not have the same properties as the unrefined version so we advise you to use the unrefined version. The strong aroma of unrefined cupuacu butter can be slightly overpowering but this is no match for the great benefits you will enjoy. Simply mask or complement the aroma using essential oils and enjoy.
Let's meet you at Vendors block 2017.
The secret of fluffy whipped Shea Butter: making your own skin butters at home.


This luxury detached property is located in a prime location of Limassol in Ayios Athanasios area. On one side there is a beautiful view of the Sea and other side the view of mountain slopes. The villa is in a peaceful residential area, which is just 15 minutes away from the sea.
All materials used in building this property are of a very high standard offering luxury and comfort throughout this property. In the entrance hall there are two winding staircases completed with beautiful granite, the best quality tiles have been used in the bathrooms, and then best wooden material has been used everywhere in the house.
The house comprises 4 large bedrooms, 3 bedrooms with en suite bathroom and jacuzzi, and a separate maid's quarters outside of the main building. Outside is the large yard, swimming pool and there is big parking spaces underneath the house.
Other features include central heating and security alarm system.
Supermarkets and schools are nearby, and it is also close to the shopping center and night life of Limassol.


At MIE we put the student at the centre of all our activities. We are committed to providing courses that challenge and ultimately prepare our students to be the leading educators of tomorrow.
Below you will see some of the views and opinions from our students on their time at MIE.
make again in a heartbeat."
which will make you feel at home in no time!"
community, you'll love every aspect of life here."
representing the college in a very positive light."
you will get to know everyone very quickly."
and you get to know people so well."
but we made it thanks to the support given to us."
students and one can easily make life-long friends."
experience due to the backup given to us."
which resulted in me fulfilling my dream."
always responded to my queries."


When Fabienne is not on location, she assists in wardrobe planning and revamps her client's entire look by adding new articles to old favorites. After accessing the body shape, color palette and lifestyle of her client, she ads her personal touch by putting together unforgettable ensembles. Some clients have ended up with a new wardrobe as well as a new interior for their homes.


two cpu's started up again.
>> within the node management window. Is there a step I am missing?
>>> newly saved node configuration?
>>> - Do the new hostnames properly resolve from the display machine?
>>>> neither pc can find each other within the Access Grid software.
>>>> changes the name/IP to the name used prior to the network change.
>>>> software so that they recognize each other?


From music tours to a leisurely stroll through the rose gardens, Shreveport and Bossier City offer must-see attractions and fun things to do for the entire family. Book at tour at the Backstage Music Tour at the Shreveport Municipal Auditorium, use your wits to unlock clues at the Red Herring Escape Rooms, or catch an independent movie and sit on the balcony for dinner and cocktails at the Robinson Film Center. The sister cities offer so many fun things to see and do through the performing arts, museums, art galleries and historic places. Don't forget to take advantage of free offerings, too.


I have long considered starting a conservative blog. Like many Americans, I want to voice my opinions, make criticisms, and offer solutions to what I see going on in America. There are so many of them though, and the idea of putting my thoughts in writing for everyone to see was worth careful consideration. In the days just before and after the passing of the Affordable Care Act aka Obamacare, conservative and libertarian organizations and blogs sprang up like wildflowers in the summertime. These ranged in quality and content from the ranting of conspiracy theorists, to slick, professional journals. I was not sure that in this bumper crop of libertarian/conservative leaning blogs that my voice might not get lost. If I was going to start a blog, it could not be just another conservative blog, by another guy venting his frustrations at the government from behind a keyboard. It would have to be something a little different, have a different angle. My blog would be where my fellow Americans could learn, or relearn about the cause of liberty.


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When it's winter outside in Warkworth, air conditioning might not be the most urgent thing on your priority list. However, it's important to anticipate rising temperatures that come along with a steamy summer. You do not want to be stuck with a faulty air conditioner when the time comes to turn on your air conditioner. Trust us, we've seen plenty of warm and miserable homeowners who wish they had their AC checked sooner!
No problem, we can help. D & K Heating Service Experts in Warkworth offers a 100% Satisfaction Guarantee*, we're certified to service each and every brand of air conditioner, and our experts are available every hour of the day to help you find the right solution for your AC. The bottom line? We believe that you should be happy inside your own home, and proper temperature control is an important feature of personal comfort.
For many Warkworth homeowners, cost plays a role in whether or not they choose to upgrade their furnace or air conditioner. In fact, updating your air conditioner or furnace can actually be more accesible than you might think. Begin with our no-cost estimate, and we'll work with you on the basis of your need to find the right choice for your home. Once your AC or furnace is updated, you may even see your energy bills lower. Even if your thermostat is programmed correctly, inefficient systems can result in pricey end-of-the-month surprises. Give us a call and we can help you find a solution that won't be too expensive.
Our experience has shown us that heating and cooling solutions can make a true difference in the experience of homes in Warkworth. In addition, if you worry about the environment and list sustainability as a priority, you should understand that solar air conditioning is surprisingly affordable as well – in addition to making your home more efficient. If you're interested in decreasing your carbon footprint, choosing one of our ENERGY STAR qualified air conditioners will do the trick. Discussing your lifestyle, preferences, and interests with one of our qualified technicians might reveal options you didn't know existed.
Come spring, heat isn't the only change in your home. Spring in Warkworth is notorious for provoking allergies, spreading pollen, and reinvigorating allergens that could cause a nasty allergic reaction. Many homeowners constantly inhale chemical vapors, microbes, mildew, viruses, bacteria, dust, dirt, pollen, allergens, and more! Indoor air quality is crucial, and you can control it by using air filtration systems, humidifiers and dehumidifiers, duct cleaning, and ventilation. Therefore, working with our experts to improve your air quality can, quite literally, make your air healthier!
Air filtration and air conditioning are just part of the services we offer: 24/7 heating and cooling, commercial HVAC systems, and more are all in our wheelhouse. Give us a call at 613-707-2421 anytime, and we'd be happy to talk through ways that you can make your home in Warkworth healthier and happier.


In Absentia, created for The Art of Lost Words has been compiled. 24 printed pages, with 8 full-colour photographs tipped in and printed in an edition of 200. The book explores the word 'skirr', its imminent removal from the dictionary and other themes surrounding absence of flight. For six weeks only, from March 5th, copies are available to purchase from text/gallery for £5 and all proceeds from the sales will be donated to the National Literacy Trust.


text:
Visit Chesterfield
Welcome to Chesterfield County, a first choice community for residents, businesses and visitors.
If you are a Chesterfield County resident, you can take pride in the recognition we have already received, such as "The 17th Best Place to Live in America;" "One of the 100 Best Communities in America for Young People;" the lowest crime rate in the Richmond Metropolitan region and many other kudos. Providing you with the best possible quality of life is our main mission as a local government.
If you operate, or are contemplating operating, a business in the county, you'll find that we are business friendly, from fast tracking new business site development to support of existing business programs of all sizes. We also have one of the lowest machinery and tools tax rates of any developed community in Virginia.
A Historic Treasure
There is so much to see and do in Chesterfield County. Its rich history includes the Native Americans who lived here for thousands of years prior to the arrival of the first English settlers in 1611 to establish the second permanent settlement in the New World. That story is told at Henricus Historical Park, where Pocahontas lived before marrying John Rolfe. Tobacco was first cultivated at historic Bermuda Hundred and exported back to England as a cash crop. The first iron furnace was established in the New World at Falling Creek, and the first commercially-mined coal in North America was at Mid-Lothian Mines. Thomas Jefferson's brother-in-law, Francis Eppes, build his Georgian-designed plantation house, known as Eppington, in 1768. The Historic Courthouse Green was the site of Colonial militia encampment and also the Baptist preacher trials in late 1700s, which resulted in religious freedom and liberties. The county also is the place of significant Revolutionary War and Civil War engagements. Magnolia Grange's distinctive Federal-style architecture and rich history interprets life in a county mansion of the early 19th century. Find historic sites and programs.
A Special Place
For residents, businesses and visitors alike, what makes us such a special place is our people, both in our communities and in our local government, and the way in which everyone works together. It's that teamwork that makes us what we are, and that will carry us into the future as we mold the Chesterfield County of tomorrow. I welcome your comments on our Website, and your suggestions for how we should move forward as a community.
Email Communications and Media
TTY / TDD Phone: 804-717-6700
Chesterfields Location
Directions to Chesterfield County
History in Chesterfield
Athletics in Chesterfield
Things to do in Chesterfield
Welcome to Chesterfield Today


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Hmm, I haven't done a nice thing for myself in ages, I'm run ragged. I guess I could say I clipped my nails yesterday so I would type faster. Nice enough?
I will reach my goals.
resting from a very eventful week.
Going for a daytime trip.
Not really doing anything today except .
Giving myself a movie afternoon today.
Going to buy me a pair of new sneakers .
I finally got around to ordering myself some loose tea. I can't wait to try it.
Bad movie night with friends tonight!!
I am not doing anything today for myself. Maybe tomorrow.
I bought myself a new pair of work shoes. The old pair were worn out and no longer provided any support.
"Seven days without exercise makes one weak."
I am going to give myself a high five for sticking with my program for the majority of the days this week. .
I'm going to love myself by buying myself my gift for reaching below 160 even if I'm not still below 160 tomorrow. I'm also going to love myself by doing Sparkcoach first thing in the morning. I often only allow myself to do it when I'm fished everything else, as a reward, and then I never get to it because there's always another email, another important thing to do. I'll do it when I wake up, whether or not I have any exercise to report.
Today I start a 3 month licensing class that will move me forward in my job, While it's work it is something I am doing to better my life.
Today I am giving myself a big'ol mental pat on the back for keeping up with my program.
I am saying positive things to myself to show that I do love ME!
To treat myself to a day out.
OooOOooh Diane that sounds lovely!
Today I am having a glass (ok probably 2) of red wine with my big sis!
I am going to take a long bubble bath and light some of my favorite candles and make a sparkling non-alcoholic drink to drink while I am in the tub and just relax. .
I have the night to myself so I am going to stop on the way home and grab some veggies go home, do yoga then make myself a ridiculous packed full of goodness salad. Then I'll light some candles, watch a bunch of episodes of Being Human and knit.
Side note - a "great night" means something much different than it used to LOL!
Wow, I've been neglecting this thread, but I promise I'm not neglecting myself. I shopped on Saturday because Dillard's was having a super great markdown sale. I got my first Spanx! Oh my goodness they are like magic. I now know what the fuss is about. They really smooth you out and they really are comfortable. I would never buy them not on sale, but I got lucky. I also got a new wallet and a new blouse and I didn't even feel bad spending money on just me and nobody else!
Just had some me time. Went out shopping.
I spent the evening with my hubby watching the Olympics. I enjoyed our time together.
today I did the 5 mile challenge and loved it, I also spent the rest of the day home alone with my husband which is the absolute most fun thing I can think of to do, we laugh like children together!
Today I will read my Harry Potter book for 1 hour.
I laid down and took an early evening snooze.
I bought book 5 of the immortal instruments series and pre-ordered book 6 (it comes out in May). I also purchased The Book Thief and The Orphan Trains. Not that I have a lot of time thread, but at least when I do, I will have something good to read.
Black truffle oil... I have heard wonderful things about it but have never tried it.
Wow, never heard of black truffle oil. Sounds chocolatey or mushroomy. I also bought myself a kindle book but it's required reading for teaching the acting class. Even so I don't know when I'll find time to read it. Third night since this challenge began I've been up 24 hours. Losing sharpness, lol.
sounds good Tiff what did you get? I need to start reading more again, I'll put that on the nice things to do list.
starting Jan 13 I have put my workout times as the number 1 priority. That is the most love I have shown myself in ages! And I love love love kickboxing so I am even happier when I walk in the door for the evening!
Keelie and Transformers,I'm so sorry I haven't been here yet. I've barely slept a wink since this challenge began, working day and night on the acting class I'm teaching, so all the nice stuff I do for myself is stuff like reading Harry Potter, but that's my job. I've barely had time to breathe. It's 6:10 am and I didn't sleep last night at all, second night since this challenge began. I guess I should do something nice for myself now, but sleep won't be one an option for a while yet. I guess it's nicest for me to just regard this as Me Time because I'm teaching this class for experience that will help me, and looking it as something I Choose to do, rather than Have to do (though now that I'm committed, it's a choice to dedicate myself for the coming while, 100%. I don't feel I can even take the time to meditate, and yesterday I didn't even spin the bonus wheel by midnight though I had 25 points. Wow! I thought the last challenge was tough! I guess I will finish the water that's in front of me and get my bonus points and see where that takes me.
Instead of eating leftovers I took the time to cook some chicken just for me and made a really yummy chicken taco salad for lunch.
Spent 37 minutes doing isometric exercise for my upper body. . Feeling good.
Velvet - thanks for reminding me I have a ball in the closet in a box better blow that thing up!
I got a fitness ball over the weekend and for starters I'm going to do a couple of the seated workouts from SP on it. This morning after I got my daughter off to school I listened to a meditation audio. I really enjoyed it!
I have done a couple of things today, took 45 minutes closed up away from the men folk to do a 3 mile walk with Leslie Sansone. Another thing I did which I've really been trying to do more of is, to try to be more present in the moment. Michael took the boys to visit their grandparents (conveniently located right around the corner) I stayed home to start a beef stew I got the recipe for in Spark Recipes. Anyway instead of just trying to quickly get through the preparation I tried to be present in the moment and enjoy the process. It felt really good.
I took time to exercise and felt much better. My spirits were lifted after the 40 minute workout. That was my time for me today.
~~"It is better to conquer 'yourself' than to win a thousand battles."
Hey there Transformers!! Since February is a month for celebrating L O V E we wanted to remind everyone to show love to yourself as well.
So this months challenge is to do one kind thing for YOU per day, and post it on this thread. Be it taking time for meditation, a mani/pedi, or even just watching a favorite movie. I bet a lot of us will find this challenge a real eye opener.


text:
Models don eye-popping looks in tape-only swimsuit show
Gypsy bail is truly golden, jewelry appraiser testifies in New York court
By Shayna Jacobs
Avner Rubinov, president of NY Estate Buyers, holds up some of the ancestral gold, which he appraised, that Tom Eli's family is attempting to put up for Eli's bail. (Jefferson Siegel/New York Daily News)
A midtown jewel appraiser vouched for more than $100,000 in solid gold jewelry and heirlooms that a family of Gypsies are trying to use to bail out their son.
Avner Rubinov examined the riches — which have been in defendant Tom Eli's family for generations — on the witness stand before Manhattan Supreme Court Justice Charles Solomon, who will decide whether to approve the bizarre form of bond on Thursday.
Solomon asked him if he had "any doubt" about a gold rope and coin piece he valued at over $27,000.
Some of the gold that the family of Tom Eli hopes to put up for his bond in a felony assault case. (Jefferson Siegel/New York Daily News)
"Yes, I guarantee it's gold," said Rubinov, who testified in a thick Soviet accent as he held up the illustrious chains.
He said his nearly 30 years of experience dealing with precious metals means he knows the real thing when he sees it, but said the Elis' gold was also tested through various means at his W. 47th St. shop Sept. 5.
Tom Eli, shown in Manhattan Supreme Court on Tuesday, is charged with assaulting another Gypsy despite video evidence to the contrary. His family wants to use ancestral gold coins to pay his bail. (Jefferson Siegel/New York Daily News)
"I'm telling you, it's just knowledge, it's feelings," Rubinov said. "It's feeling. You know what you're doing."
Solomon had told Eli's attorney, Thomas Kenniff, that he would need to hear testimony from the appraiser before ruling on whether the riches could be used as collateral to back a bail bond.
NY Estate Buyers president Avner Rubinov on Wednesday holds up gold coins in court. He appraised the ancestral gold that Tom Eli's family is attempting to put up for Eli's bail. (Jefferson Siegel/New York Daily News)
A bondsman is expected to return to court with the family on Thursday to complete the process, but prosecutors can then investigate the ownership of the valuables.
Eli, 41, who is being held on $50,000 bail on felony assault charge for allegedly slashing a man in the chest outside a Flatiron District club on April 14, was not produced for the hearing. His family previously tried to post properties in Florida and cash belonging to a nonrelative, but those forms of collateral were denied.
The defendant's father, Mike Eli, griped that "everything we give, they deny" and said the process has been frustrating.
"It's prejudice on Gypsies, whatever it is," he said. "We tried everything."


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Last week, a student attending Seattle University was suspended from the fall and spring terms for selling medical marijuana brownies through her job at a dispensary. The student has decided to remain unidentified for now, but she did say that she was only selling her brownies to sick patients and only for the purpose of earning money to pay for her nearly $40,000 a year in tuition. She claims to have never sold to students or on campus.
Washington state has legalized the use of marijuana for both medical and recreational use, so the student wasn't aware that she was doing anything wrong. The issue stemmed from one of her roommates selling one of her brownies to a freshman student who then got sick after ingesting it.
University administrators were then notified and the student was promptly suspended for a full academic year and lost her tuition. She will now be unable to graduate on time.
Seattle University does have a drug policy in place which states that it, "prohibits the use, possession and or distribution of marijuana on campus". There university's policy is in line with that of the Safe and Drug Free Schools and Communities Act.