text:
\section{Introduction}

A {\em ranking/unranking} function defined on a data type is a
bijection to/from the set of natural numbers (denoted $\mathbb{N}$).
When applied to formulas or proofs, ranking functions are usually called
{\em G\"{o}del numberings} as they have originated in arithmetization
techniques used in the proof of G\"{o}del's incompleteness results
\cite{Goedel:31,conf/icalp/HartmanisB74}.
In  G\"{o}del's original encoding \cite{Goedel:31}, given that
primitive operation and variable symbols in a formula are mapped to exponents of
distinct prime numbers, factoring is required for
decoding, which is therefore intractable for formulas of non-trivial size.
As this mapping is not a surjection, there are codes that decode
to syntactically invalid formulas. This key difference  also applies to
alternative G\"{o}del numbering schemes (like G\"odel's beta-function), while
ranking/unranking functions, as used in combinatorics, are bijective mappings.

Besides codes associated to formulas,
a wide diversity of common computer operations, ranging
from data compression and serialization to
data transmissions and cryptographic codes
are essentially bijective encodings between
data types. They provide a variety of services ranging from
free iterators and random objects to data compression and succinct
representations. Tasks like serialization and persistence are facilitated
by simplification of reading or writing operations without the need of
special-purpose parsers.

The main focus of this paper is designing an efficient bijective G\"odel
numbering scheme (i.e. a ranking/unranking bijection) for {\em term algebras},
essential building blocks for various data types and programming language constructs.

The resulting G\"odel numbering algorithm, the main contribution of the paper,
enjoys the following properties:
\begin{enumerate}
\item the mapping is bijective
\item natural numbers always decode to syntactically valid terms
 \item it works in time low polynomial in the bitsize of the representations
 \item the bitsize of our encoding is within
 constant factor of the syntactic representation of the input.
\end{enumerate}

These properties ensure that our algorithm can be applied to derive compact
serialized representations for various formal systems and programming language
constructs.

\section{Tuple Encodings} \label{tuple}
We will now define a few primitive operations in terms of a small
set of bitwise primitives with known asymptotic complexity.
Assuming a copying implementation of arbitrary size integers
each of the following operations are at most linear in the bitsize
of their operand {\tt N} and some can be considered constant time
when this operand fits in a machine word as well as when
an efficient mutable implementation of arbitrary length integers is used.
\begin{code}
first_bit(N,Bit):- Bit is 1 /\ N.
times_exp2(N,K,R):-R is N << K.
div_by_exp2(N,K,R):-R is N >> K.
predecessor(N,R):-R is N-1.
successor(N,R):-R is N+1.
\end{code}

First we define the {\tt k\_deflate} and {\tt k\_inflate} operations.
{\tt k\_deflate} can be seen as collecting each k-th bit
from a number's binary representation and aggregates the result
into a new natural number. {\tt k\_inflate} can be seen as building
a new natural number by inserting {\tt 0}s in every position
except in each k-th position where the bits of its argument {\tt N}
are placed. However, we avoid direct bitlist manipulation by
expressing them in terms of the previously defined
arbitrary length integer operations.

\begin{code}
k_deflate(_,0,0).
k_deflate(K,N,R):-N>0,
  div_by_exp2(N,K,A),
  k_deflate(K,A,B),
  times_exp2(B,1,C),
  first_bit(N,D),
  R is C\/D.
\end{code}
\begin{code}
k_inflate(_,0,0).
k_inflate(K,N,R):-N>0,
  div_by_exp2(N,1,A),
  k_inflate(K,A,B),
  times_exp2(B,K,C),
  first_bit(N,D),
  R is C\/D.
\end{code}
The following example illustrates their use:
{\small \begin{verbatim}
?- k_inflate(3,42,X),k_deflate(3,X,Y).
X = 33288,
Y = 42 .
\end{verbatim}}

We can define a bijective decomposition of a natural number {\tt N}
as a tuple of {\tt K} natural numbers in terms of {\tt k\_deflate}
and our primitive bitwise operations.

The function {\tt to\_tuple:} $Nat \rightarrow Nat^k$ converts a natural
number to a $k$-tuple by splitting its bit representation into $k$ groups,
from which the $k$ members in the tuple are finally rebuilt. This operation
can be seen as a transposition of a bit matrix obtained by expanding
the number in base $2^k$:
\begin{code}
to_tuple(K,N,Ns):-K>0,
  predecessor(K,K1),
  numlist(0,K1,Ks),
  maplist(div_by_exp2(N),Ks,Ys),
  maplist(k_deflate(K),Ys,Ns).
\end{code}
Note the use of the SWI-Prolog library predicates {\tt numlist} that generates
a list of integers in increasing order and {\tt maplist} that applies a closure to
lists of corresponding arguments.
To convert a $k$-tuple back to a natural number we will merge their
bits, $k$ at a time. This operation can be seen as the transposition of a bit
matrix obtained from the tuple, seen as a number in base $2^k$, but we
implement it more efficiently in terms of bitwise operations
on integers. Note the use of the SWI-Prolog library predicate {\tt sumlist}
that computes the sum of a list of numbers.
\begin{code}
from_tuple(Ns,N):-
  length(Ns,K),K>0,
  predecessor(K,K1),
  maplist(k_inflate(K),Ns,Xs),
  numlist(0,K1,Ks),
  maplist(times_exp2,Xs,Ks,Ys),
  sumlist(Ys,N).
\end{code}
The following example shows the mapping of {\tt 42} to a $3$-tuple and the encoding
back to {\tt 42}.
{\small \begin{verbatim}
?- to_tuple(3,42,T),from_tuple(T,N).
T = [2, 1, 2],
N = 42 .
\end{verbatim}}
Fig. \ref{isot42} shows multiple steps of the same decomposition,
with shared nodes collected in a DAG. Note that
markers on edges indicate argument positions.
\FIG{isot42}{42 after repeated 3-tuple expansions}{0.50}{isot42.pdf}

Note that one can now define {\em pairing functions}, i.e. {\em bijections between
natural numbers and pairs of natural numbers},
as specializations of the tupling/untupling
predicates:
\begin{code}
to_pair(N,A,B):-to_tuple(2,N,[A,B]).
\end{code}
\begin{code}
from_pair(X,Y,Z):-from_tuple([X,Y],Z).
\end{code}
One can observe that {\tt to\_pair} and {\tt from\_pair} are the same as the
functions defined in Steven Pigeon's PhD thesis
on Data Compression \cite{pigeon} and also known as Morton-codes
with uses in indexing of spatial databases \cite{lawder99}.

\section{G\"odel numberings of a term algebra with finite signature}

Traditionally a term algebra is defined over a
finite set of functions symbols of given arities.
Constants can be singled out as a special set
or considered function symbols of arity 0.
Term algebras are
{\em free magmas\footnote{See \url{http://wikipedia.org/wiki/Free_object}}}
induced by a set of variables and a
set of function symbols of various arities (0 included), called {\tt signature}, that
are closed under the operation of inserting terms as arguments of function
symbols. In various logic formalisms a term algebra is called a Herbrand
Universe.

Having a bijective encoding over a signature and a (finite) set  of
variables (seen as input ``wires") is also useful for synthesizing
code over a set of functions -
for instance a library of
logic gates, in the case of circuit synthesis, as well as for
generating random terms
of a given signature for testing purposes.

Besides being bijective, it is useful if the mapping
relates terms to numbers of comparable representation size
and if it works in linear or low polynomial time to
be useful for practical applications.

We will denote {\tt Vs, CSyms, FSyms} the sets of variables, constant symbols and
function symbol/arity pairs, respectively, that parameterize
the converter from terms to codes {\tt term2nat/5} and the converter
from codes to terms, {\tt nat2term/5}.

Given that {\tt Vs, CSyms} are finite, we map them bijectively to
the ranges {\tt [0..LV-1]} (variables), {\tt [LV..LV+LC-1]} (constants).
The predicate {\tt term2nat} precomputes these values and
then calls the recursive converter {\tt t2n}.

\begin{code}
term2nat(Vs,CSyms,FSyms,T, X):-
  length(CSyms,LC),
  length(FSyms,LF),
  length(Vs,LV),
  LVC is LV+LC,
  LVC>0,
  t2n(LV,LC,LF,LVC,Vs,CSyms,FSyms,T, X).
\end{code}
The predicate {\tt t2n} uses {\tt lookup\_var} and the built-in {\tt nth0/3}
to look-up indices associated to
variable, constant and function symbols.
For compound terms, these values are combined with
values computed recursively on their arguments
and then merged using {\tt from\_tuple} into
natural numbers.

Note that the index {\tt L}
of the function symbol {\tt F/K} computed by {\tt nth0/3}
is multiplied with the length {\tt LF} of
the list of function
symbols {\tt FSyms}. This operation will
be reversed using modulo and quotient
when converting back.
\begin{code}
t2n(LV,_LC,_LF,_LVC,Vs,_CSyms,_FSyms,V, X):-var(V),!,
  lookup_var(I,Vs,V),
  I>=0,I<LV,X=I.
t2n(LV,_LC,_LF,_LVC,_Vs,CSyms,_FSyms,C, X):-atomic(C),!,
  nth0(I,CSyms,C),
  X is I+LV.
t2n(LV,LC,LF,LVC,Vs,CSyms,FSyms,T, X):-compound(T),
  T=..[F|Ts],
  nth0(L,FSyms,F/K),
  K>0,
  length(Args,K),
  P=..[t2n,LV,LC,LF,LVC,Vs,CSyms,FSyms],
  maplist(P,Ts,Args),
  from_tuple(Args,N),
  X is LVC+LF*N+L.
\end{code}
\begin{code}
lookup_var(N,Xs,X):-lookup_var(X,Xs,0,N).
\end{code}
\begin{code}
lookup_var(X,[Y|_],N,N):-X==Y.
lookup_var(X,[_|Xs],N1,N3):-
  N2 is N1+1,
  lookup_var(X,Xs,N2,N3).
\end{code}
The predicate {\tt nat2term} reverses the process,
using the same lists {\tt Vs,CSyms,FSyms} to map
variables, constants and function symbols to
natural number codes, by calling the recursive
converter {\tt n2t/8}.
\begin{code}
nat2term(Vs,CSyms,FSyms,X, T):-X>=0,
  length(CSyms,LC),
  length(FSyms,LF),
  length(Vs,LV),
  LVC is LV+LC,LVC>0,
  n2t(LV,LC,LF,LVC,Vs,CSyms,FSyms,X, T).
\end{code}
The recursive converter {\tt n2t} uses dictionaries
{\tt Vs, CSyms, FSyms} to map natural numbers
to the corresponding, functions, constant and variable
terms, uniformly. Note the use of the library
predicate {\tt nth0} that associates an index, starting at 0,
to a term on a list. It also uses Prolog's {\tt univ} to
build a closure {\tt P} that with help from
{\tt maplist} applies it recursively.
\begin{code}
n2t(LV,_LC,_LF,_LVC,Vs,_CSyms,_FSyms,X, V):-X<LV,!,
  nth0(X,Vs,V).
n2t(LV,_LC,_LF,LVC,_Vs,CSyms,_FSyms,X, C):-LV=<X,X<LVC,!,
  X0 is X-LV,
  nth0(X0,CSyms,C).
n2t(LV,LC,LF,LVC,Vs,CSyms,FSyms,X, T):-X>=LVC,
  X0 is X-LVC,
  N is X0 // LF,
  L is X0 mod LF,
  nth0(L,FSyms,F/K),
  K>0,
  to_tuple(K,N,Args),
  P=..[n2t,LV,LC,LF,LVC,Vs,CSyms,FSyms],
  maplist(P,Args,Ts),
  T=..[F|Ts].
\end{code}
Note the use of the predicate {\tt to\_tuple} with
length {\tt K} based on the arity of each function symbol,
which splits the natural number {\tt N}
in a list of codes {\tt Args} to be used
recursively to build the subterms associated
to the function symbol {\tt F/K}.

A first example shows that starting from a term {\tt T} we obtain a
natural number from which the same term {\tt T} is recovered.
Note that the two side of the transformer are parameterized
by the same lists of variables, constants and function symbols.
{\small \begin{verbatim}
?- T=f(a,f(X,g(Y))),Vs=[X,Y],Cs=[a],Fs=[f/2,g/1],
   term2nat(Vs,Cs,Fs,T,N),nat2term(Vs,Cs,Fs,N,T_again).
T = f(a, f(X, g(Y))),
Vs = [X, Y],
Cs = [a],
Fs = [f/2, g/1],
N = 17439,
T_again = f(a, f(X, g(Y))) .
\end{verbatim}}

The next example shows that starting from any natural number e.g. {\tt 2012}
we obtain a term that in turn is converted back to the same number.
{\small \begin{verbatim}
?- N=2012,Vs=[X,Y],Cs=[a,b],Fs=[f/2,g/1],
   nat2term(Vs,Cs,Fs,N,T),term2nat(Vs,Cs,Fs,T,N_again).
N = 2012,
Vs = [X, Y],
Cs = [a, b],
Fs = [f/2, g/1],
T = f(f(Y, b), f(b, a)),
N_again = 2012 .
\end{verbatim}}

Finally, the following example (where {\tt '->'} is seen as logical implication),
hints towards an application to circuit synthesis. When combined with a fast
bitstring-based boolean evaluator (see \cite{iclp07}) terms associated
with natural numbers can be tried out to see if the result
of their boolean evaluation matches a given specification.
{\small \begin{verbatim}
?- N=2012,Vs=[A,B],Cs=[0],Fs=['->'/2],
   nat2term(Vs,Cs,Fs,N,T),term2nat(Vs,Cs,Fs,T,N_again).
N = 2012,
Vs = [A, B],
Cs = [0],
Fs = [ (->)/2],
T = (((B->A)->0->A)-> (0->A)->B),
N_again = 2012 .
\end{verbatim}}

\begin{comment}
\begin{code}
t(N,Vs-T):-Vs=[_,_],nat2term(Vs,[0],['->'/2],N,T).

n(Vs-T,N):-term2nat(Vs,[0],['->'/2],T,N).

t1(N,Vs-T):-length(Vs,3),nat2term(Vs,[0,1],['+'/2,'*'/2],N,T).

n1(Vs-T,N):-term2nat(Vs,[0,1],['+'/2,'*'/2],T,N).

t2(N,Vs-T):-length(Vs,2),nat2term(Vs,[a,b,c],['f'/2,'g'/3,'h'/1],N,T).

n2(Vs-T,N):-term2nat(Vs,[a,b,c],['f'/2,'g'/3,'h'/1],T,N).

test:-between(0,100,I),t(I,X),n(X,N),portray_clause([I=N,X]),fail.

\end{code}
\end{comment}

One can generate random terms with a given signature based on a
natural number of a given bitsize as follows.
\begin{code}
ranterm(Bits,Vs,Cs,Fs, T):-
  N is random(2^Bits),
  nat2term(Vs,Cs,Fs,N,T).
\end{code}
This can be useful in generating random
arithmetic expressions or boolean functions for
testing purposes.
{\small \begin{verbatim}
?- Vs=[A,B,C],ranterm(100,Vs,[],['+'/2,'*'/2],T).
Vs = [A, B, C],
T = (B+ (C+A))* ((A+B)*A* ((A+A)*C))+ (A+B+A*A+ (B+ (A+A))*(B+A))+
    (B*A*B* (B+B)* (C+ (C+B))+ (A* (A+A)+C*A)* ((B+A)* ((A+A)*C))) .

?- Vs=[A,B,C,D],ranterm(50,Vs,[0,1],[and/2,or/2,not/1],T).
Vs = [A, B, C, D],
T = and(not(not(or(or(not(0), A), or(and(B, B), A)))),
    or(or(and(A, A), or(D, A)), not(or(C, not(B))))) .
\end{verbatim}}

\section{Bijective encodings of Prolog atoms}
Prolog provides a mapping between its symbols and their
character codes. To obtain an encoding of strings linear in their bitsize
we need a general mechanism to map arbitrary combinations
of {\tt k} symbols to natural numbers.

\subsection{Encoding numbers in bijective base-k} \label{bijnat}

The conventional numbering system does not provide a bijection between
arbitrary combinations of digits and natural numbers, given that leading 0s are
ignored. For this purpose we need to use {\em numbers in bijective
base-k}\footnote{We refer to
\url{http://en.wikipedia.org/wiki/Bijective_numeration} for the
historical origins of the concept and the
properties of this number representation.}.
First we start with the mapping from list of digits in {\tt [0..k-1]}
to a natural number defined by the predicate {\tt from\_bbase/3}
\begin{code}
from_bbase(Base,Xs,R):-
  maplist(successor,Xs,Xs1),
  from_base1(Base,Xs1,R).
\end{code}
\begin{code}
from_base1(_Base,[],0).
from_base1(Base,[X|Xs],R):-X>0,X=<Base,
  from_base1(Base,Xs,R1),
  R is X+Base*R1.
\end{code}

\begin{code}
to_bbase(Base,N,Xs):-
  to_base1(Base,N,Xs1),
  maplist(predecessor,Xs1,Xs).

to_base1(_,0,[]).
to_base1(Base,N,[D1|Ds]):-N>0,
   Q is N//Base,
   D is N mod Base,
   (D==0->D1=Base;D1=D),
   (D==0->Q1 is Q-1;Q1=Q),
   (Q1==0->Ds=[];to_base1(Base,Q1,Ds)).
\end{code}
Note that the predicates {\tt from\_bbase} and {\tt to\_bbase} are
parametrized by the base of numeration which
should be the same when encoding and decoding.
{\small \begin{verbatim}
?- to_bbase(7,2012,Ds),from_bbase(7,Ds,N).
Ds = [2, 6, 4, 4],
N = 2012 .
\end{verbatim}}
This encoding will turn out to be useful for
symbols of a finite alphabet.

\subsection{Encoding strings}
Strings can be seen just as a notational equivalent
of lists of natural numbers written in bijective base-$k$.
For simplicity (and to avoid unprintable characters as a result of applying the
inverse mapping) we will assume that our strings naming
functions are built only using lower case ASCII characters.
\begin{code}
c0(A):-[A]="a".
c1(Z):-[Z]="z".

base(B):-c0(A),c1(Z),B is 1+Z-A.
\end{code}
Next, we define the bijective base-k encodings
\begin{code}
string2nat(Cs,N):-
  base(B),
  maplist(chr2ord,Cs,Ns),
  from_bbase(B,Ns,N).
\end{code}
\begin{code}
nat2string(N,Cs):-N >= 0,
  base(B),
  to_bbase(B,N,Xs),
  maplist(ord2chr,Xs,Cs).
\end{code}
\begin{code}
chr2ord(C,O):-c0(A),C>=A,c1(Z),C=<Z,O is C-A.
ord2chr(O,C):-O>=0,base(B),O<B,c0(A),C is A+O.
\end{code}
We obtain an encoder for strings working as follows:
{\small \begin{verbatim}
?- Cs="hello",string2nat(Cs,N),nat2string(N,CsAgain).
Cs = [104, 101, 108, 108, 111],
N = 7073802,
CsAgain = [104, 101, 108, 108, 111] .

?- nat2string(2012,Cs),string2nat(Cs,N).
Cs = [106, 121, 98],
N = 2012 .
\end{verbatim}}
And finally we can obtain a bijective encoding of Prolog atoms as
\begin{code}
atom2nat(Atom,Nat):-atom_codes(Atom,Cs),string2nat(Cs,Nat).

nat2atom(Nat,Atom):-nat2string(Nat,Cs),atom_codes(Atom,Cs).
\end{code}

\section{``Catalan skeletons" of Prolog terms} \label{termenc}

We will now turn to encodings focusing on the separation
of the structure and the content of Prolog terms.
The connection between balanced parenthesis languages and
a large number of different data types (among which we find
multi-way and binary trees)
in the {\em Catalan family}
is known to combinatorialists
\cite{berstel2002formal,liebehenschel2000ranking}.
We will start by mapping a term to a ``skeleton"
representing its structure as a list of
balanced parentheses.

\subsection{An injective-only structure encoding}

We sketch here an encoding mechanism that might also be useful to Prolog
implementors interested in designing alternative heap representations for new
Prolog runtime systems or abstract machine architectures as well as hashing mechanisms
for ground terms or variant checking for tabling.

First we provide an encoding that separates the ``structure" of a term {\tt T},
expressed as a balanced parenthesis
language\footnote{A member of the {\em Catalan family} of combinatorial objects.}
representation
{\tt Ps} and a list of atomic terms and Prolog variables {\tt As},
seen as a symbol table that stores the ``content" of the terms:
\begin{code}
term2bitpars(T,[0,1],[T]):-var(T).
term2bitpars(T,[0,1],[T]):-atomic(T).
term2bitpars(T,Ps,As):-compound(T),term2bitpars(T,Ps,[],As,[]).
\end{code}
\begin{code}
term2bitpars(T,Ps,Ps)-->{var(T)},[T].
term2bitpars(T,Ps,Ps)-->{atomic(T)},[T].
term2bitpars(T,[0|Ps],NewPs)-->{compound(T),T=..Xs},
  args2bitpars(Xs,Ps,NewPs).
\end{code}
\begin{code}
args2bitpars([],[1|Ps],Ps)-->[].
args2bitpars([X|Xs],[0|Ps],NewPs)-->
  term2bitpars(X,Ps,[1|XPs]),
  args2bitpars(Xs,XPs,NewPs).
\end{code}
The encoding is reversible, i.e. the term T can be recovered:
\begin{code}
bitpars2term([0,1],[T],T).
bitpars2term([P,Q,R|Ps],As,T):-bitpars2term(T,[P,Q,R|Ps],[],As,[]).
\end{code}
\begin{code}
bitpars2term(T,Ps,Ps)-->[T].
bitpars2term(T,[0|Ps],NewPs)-->
  bitpars2args(Xs,Ps,NewPs),{T=..Xs}.
\end{code}
\begin{code}
bitpars2args([],[1|Ps],Ps)-->[].
bitpars2args([X|Xs],[0|Ps],NewPs)-->
  bitpars2term(X,Ps,[1|XPs]),
  bitpars2args(Xs,XPs,NewPs).
\end{code}
The two transformations work as follows:
{\small \begin{verbatim}
?- term2bitpars(f(g(a,X),X,42),Ps,As),
   bitpars2term(Ps,As,T).
Ps = [0,0,1,0,0,0,1,0,1,0,1,1,1,0,1,0,1,1],
As = [f,g,a,X,X,42],
T=f(g(a,X),X,42) .
\end{verbatim}}
By using this encoding one can further aggregate bitlists into
natural numbers with {\tt term2inj\_code}
by converting the resulting bitlists seen as
bijective-base 2 digits and then convert
them back with {\tt inj\_code2term}.
\begin{code}
term2inj_code(T,N,As):-
  term2bitpars(T,Ps,As),
  from_bbase(2,Ps,N).
\end{code}
\begin{code}
inj_code2term(N,As,T):-
  to_bbase(2,N,Ps),
  bitpars2term(Ps,As,T).
\end{code}
working as follows:
{\small \begin{verbatim}
?- term2inj_code(f(a,g(X,Y),g(Y,X)),N,As),inj_code2term(N,As,T).
N = 131364115,
As = [f, a, g, X, Y, g, Y, X],
T = f(a, g(X, Y), g(Y, X)) .
\end{verbatim}}

\begin{comment}
One can complete the encoding by hashing the symbol table into a
list of small integers that can be encoded as a natural number
and then aggregated with the result of {\tt term2inj\_code} using a pairing function.
\end{comment}
Note however that this encoding is injective only i.e. not every natural number
is a code of a term.

We will next describe a bijective encoding to ``Catalan skeletons"
which abstract away the structure of a Prolog term as a unique natural
number code.

\subsection{A Diophantine decomposition of natural numbers}
First, we need a mechanism to bijectively encode/decode
the actual information content of term as well as
the arities associated to its function symbols.

As an immediate consequence of the unique decomposition
of natural numbers in prime factors,
the Diophantine equation
\begin{equation}
2^x(2y+1)=z
\end{equation}
has, for any positive natural number {\tt z} a unique solution {\tt  (x,y)}.

Using the {\tt lsb/1} function that returns the least significant bit of a
natural number (available, for instance, in SWI-Prolog
and easy to emulate in other Prologs) one can define:
\begin{code}
cons(X,Y, Z):-Z is ((Y<<1)+1)<<X.

decons(Z, X,Y):-Z>0, X is lsb(Z), Y is Z>>(X+1).
\end{code}
We will use these predicates to decompose a natural
number {\tt Z>0} into {\tt X} and {\tt Y} such that
{\tt X} is well suited to work as the length of a tuple
and {\tt Y} to provide the members of a tuple of length {\tt X},
in a reversible way.

\subsection{A bijection between natural numbers and lists}

By combining {\tt cons/3} and {\tt decons/3} (which aggregate/separate ``length'' and ``content'')
with {\tt to\_tuple} and
{\tt from\_tuple} (which aggregate/separate a ``content'' of fixed ``length''),
we obtain an bijection between lists of numbers
and numbers of size proportional to the bit representations
of the operands.
\begin{code}
nat2nats(0,[]).
nat2nats(N,Ns):-N>0,
  decons(N,L1,N1),
  L is L1+1,
  to_tuple(L,N1,Ns).
\end{code}
\begin{code}
nats2nat([],0).
nats2nat(Ns,N):-
  length(Ns,L),
  L1 is L-1,
  from_tuple(Ns,N1),
  cons(L1,N1,N).
\end{code}
The following example illustrates that this encoding is a bijection:
{\small \begin{verbatim}
?- nat2nats(2012,Ns),nats2nat(Ns,N).
Ns = [7, 7, 2],
N = 2012 .
\end{verbatim}}

\subsection{A bijection between natural numbers and lists of balanced parenthesis}
We can build a bijection between lists of balanced parenthesis and
natural numbers
by encoding sublists, recursively with {\tt nats2nat/1}
while parsing them with a DCG.
\begin{code}
pars2nat(Xs,T):-pars2nat(0,1,T,Xs,[]).
\end{code}
\begin{code}
pars2nat(L,R,N) --> [L],pars2nats(L,R,Xs),{nats2nat(Xs,N)}.

pars2nats(_,R,[]) --> [R].
pars2nats(L,R,[X|Xs])-->pars2nat(L,R,X),pars2nats(L,R,Xs).
\end{code}
The inverse mapping works in a similar way, using {\tt nat2nats}
to recursively generate the lists of balanced parenthesis using
a DCG.
\begin{code}
nat2pars(N,Xs):-nat2pars(0,1,N,Xs,[]).
\end{code}
\begin{code}
nat2pars(L,R,N) --> {nat2nats(N,Xs)},[L],nats2pars(L,R,Xs).

nats2pars(_,R,[]) --> [R].
nats2pars(L,R,[X|Xs])-->nat2pars(L,R,X),nats2pars(L,R,Xs).
\end{code}

The following example illustrates that the two mappings
are indeed invertible.
{\small \begin{verbatim}
?- nat2pars(2012,Ps),pars2nat(Ps,N).
Ps = [0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,0,1,1,1],
N = 2012 .
\end{verbatim}}

\subsection{Bijective Catalan skeletons of Prolog terms}

By combing the converters between terms to lists of parenthesis
with a bijection provided by {\tt pars2nat} and {nat2pars}
we obtain:
\begin{code}
term2code(T,N,As):-
  term2bitpars(T,Ps,As),
  pars2nat(Ps,N).
\end{code}
\begin{code}
code2term(N,As,T):-
  nat2pars(N,Ps),
  bitpars2term(Ps,As,T).
\end{code}

As as the following example shows the encoding is indeed reversible:
{\small \begin{verbatim}
?- term2code(f(a,g(X,Y),g(Y,X)),N,As),code2term(N,As,T).
N = 786632,
As = [f, a, g, X, Y, g, Y, X],
T = f(a, g(X, Y), g(Y, X)) .
\end{verbatim}}
Not also the succinctness, by comparison to the usual Prolog heap representations,
of the ``Catalan structure" of the term.

\section{Related work} \label{related}

This paper can be seen as an application to the data transformation framework
\cite{ppdp09pISO} which helps gluing together the pieces
needed for the derivation of our bijective encoding of term algebras,
including algebras with finite signatures,
the novel contribution of this paper.

We have not found in the literature an encoding scheme
for term algebras that is {\em bijective}, nor an encoding that
is computable both ways with effort proportional to the
size of the inputs.

On the other hand, {\em ranking} functions for sequences
can be traced back to G\"{o}del numberings
\cite{Goedel:31,conf/icalp/HartmanisB74} associated to formulas.
Together with their inverse {\em unranking} functions they are also
used in combinatorial generation
algorithms
\cite{conf/mfcs/MartinezM03,knuth_trees}.
Pairing functions have been used in work on decision problems as early as
\cite{robinson50}. A
typical use in the foundations of mathematics is
\cite{DBLP:journals/tcs/CegielskiR01}.
An extensive study of various pairing functions and their
computational properties is presented in
\cite{DBLP:conf/ipps/Rosenberg02a}.

The closest reference on encapsulating bijections
as a programming language data type is \cite{bijarrows}
and Conal Elliott's composable
bijections Haskell module \cite{bijeliot}.
\cite{Kahl-Schmidt-2000a} uses a similar category theory inspired framework
implementing relational algebra, also in a Haskell setting.

\section{Conclusion} \label{concl}
We have described a compact bijective G\"odel numbering scheme for term
algebras. The algorithm can be made to work in linear time and has applications
ranging from generation of random instances to exchanges of structured data between
declarative languages and/or theorem provers and proof assistants.
We foresee some practical
applications as a generalized serialization mechanism
usable to encode complex
information streams with heterogeneous subcomponents -
for instance as a mechanism for
sending serialized objects over a network.
Also, given that our encodings are {\em bijective}, they can be used to generate
random terms, which in turn, can be used to represent
random code fragments. This could have applications ranging from
generation of random tests to representation
of populations in genetic programming.

\section*{Acknowledgment} We thank NSF (research grant 1018172) for support.

\bibliographystyle{INCLUDES/splncs}

redpajama_set_name: RedPajamaArXiv


text:
Home Blog The plan to merge the Family Court of Australia and the Federal Circuit courts before the federal election will not happen.
The plan to merge the Family Court of Australia and the Federal Circuit courts before the federal election will not happen.
Admin 05/04/2019 Uncategorized
The proposed Family Court and Federal Circuit Court merger bills have not won support of the Senate and will not be passed into law (at least before the next election).
Attorney-General Christian Porter was not able to win crossbench senators' support by Wednesday this week which was the final sitting day of the Senate before the federal election.
The Law Council of Australia and its Family Law Section opposed a merger of the Family Court and Federal Circuit Court of Australia. They support a stand-alone and specialised Family Court.
Law Council President, Arthur Moses SC said:
"Merging one court with another does not address significant underlying issues, including chronic underfunding and under-resourcing, which have led to crippling delays, pressures and costs."
"There is no doubt the family law system is in need of reform but this was not the way forward…"
The public is awaiting the release of a Australian Law Reform Commission review of the family law system which was delivered to the government on March 31.
#familylawnews

redpajama_set_name: RedPajamaCommonCrawl


text:
Kunst im Untergrund. 60 Jahre Art in the Underground. 60 years
Presentation of submissions to the 2018 competition and anniversary exhibition
5 August–8 September 2018
Opening: 4 August 2018
station urbaner kulturen, Auerbacher Ring 41, 12619 Berlin (Entrance: Kastanienboulevard, next to Lebenshilfe e.V.)
Project group Kunst im Untergrund
Feben Amara, Jochen Becker, Eva Hertzsch, Constanze Musterer, Adam Page
Christian Hanussek
"Kunst im Untergrund" celebrates its 60th anniversary this year, with a new edition of the public art event launched in 1958 on the theme of "Posters for Peace" at the U-Bahnhof Alexanderplatz [underground station] in what was then the GDR. Since 1992, the annual international art competition has been organized by the nGbK (formerly NGBK).
The anniversary exhibition at the station urbaner kulturen in Hellersdorf turns the spotlight on the 60-year history of "Kunst im Untergrund," particularly the years before the political turnaround of 1989/90. Likewise on display are all of this year's competition entries. Juxtaposing the public art event's past and present in this way vividly brings to light the continuities and breaks in artistic positions and their implementation.
In the early years after 1958, the production of posters for the underground station walls behind the tracks was regulated by the East German state. Subsequent shifts both in subject matter and style attest artists' endeavors to gradually transform the U-Bahnhof Alexanderplatz from a platform for propaganda into one for artistic positions on socially relevant issues. In 1991 the working group "Kunst statt Werbung" [Art instead of Advertising] was founded. In 1993 the nGbK realized the group exhibition "Hund ist extra" in the U-Bahnhof Alexanderplatz. Until 2008 the annual exhibition and art actions were shown both behind the tracks and on the central platform of the U2 underground line.
Once the BVG [transport authority] sold all its underground station billboards to a advertising company, the Alexanderplatz platform was lost to art and artists. The competition duly changed: exhibition areas were sought now throughout the entire underground network—and no longer solely underground—while the permissible project format was broadened to encompass art of a more strongly conceptual or interventionist nature. In 2014 the station urbaner kulturen in Berlin-Hellersdorf was secured as a permanent venue where artists can continue to confront the general public with sociopolitical and aesthetic questions.
2018: Plakat politisch machen [Posters made political]
The focus of this year's competition is the connection between the outlying district of Berlin-Hellersdorf and the Alexanderplatz—the latter being an emblem of the urban downtown hub as well as the original competition venue. Under the motto "Recht auf Stadt" [Right to the City], artistic projects examine the relationship between urban policy and civic participation, and ask: What is the city? Who does it belong to?
Selected Artists 2018: Stephan Kurr, mark, Mio Okido, Felix Pestemer und GloReiche Nachbarschaft, Lars Preisser (from the open competition) and Sven Johne, Katharina Sieverding (from the "Kooperative Verfahren")
Financed by
Kunst im Untergrund. 60 Jahre (2018)
Exhibition view "Kunst im Untergrund [Art in the Underground], 60 years", 2018
Author: nGbK (Foto)


Moon filters at 25% and 13% light transmission.
1.25" Moon Filters for reducing the glare of the Moon. High quality optical glass is used with anti-reflection coating having been applied on both sides of the filter to reduce glare.
The filters are mounted in a machined aluminium cell which is threaded to accept additional filters. Choice of filter with 25% or 13% light transmission with a clear aperture of 26mm.


text:
The Mabinogion Cottages Nr Snowdon
Ref: MABX4
MABX4
No. PETS
STS Grade 2 & 3
MABX4 is a combination of 3 properties that sleep 12 people in 6 bedrooms, set within the same grounds Math Cottage (ref 2134 sleeps 4, Pwyll Cottage ref 2135A sleeps 4 & Branwen Cottage ref 2138A sleeps 4). The photos seen here are of the lounges, kitchens and bedrooms and outlying grounds and views of the properties. For all the pictures, we thought it would be easier to refer you to the inudvidual properties as shown above (click on the link to see each individual property). Please do not book this reference number - it is just to direct you to the three cottages. You will have to book the cottages individually:
On the northern ridge of the Nantlle valley, facing south towards the sea, amazing views await you on top of the Snowdonia mountains. Situated within 5 minutes walk to the village of Fron and five mile drive from Caernarfon the properties provides a relaxing retreat and a convenient base for exploring Snowdonia mountains and coast. Wonderful views from most rooms of the Eifl mountains, Caernarfon bay and Nantlle valley. Snowdon can be seen from the bottom of the lane at the head of the Nantlle valley. Plenty of inspiring walks from the doorstep; one of the most interesting walks takes you through the Old Dorothea slate quarry, shrubs and trees are taking over now but abandoned historic machinery and slate mounds have become an intergrated part of this dramatic and beautiful landscape. The award winning sandy beach at Dinas Dinlle (3ml) nearby has three miles of gently sloping sandy beach, sand dunes and rock pools. The iron age fort is long gone but the ramparts are still there whilst the sea eats at the base of it's boulder clay mound. A small airfield just outside Dinas Dinlle has a museum and offers flights over Snowdon. Caernarfon (5ml) is an interesting harbour town dominated by its castle and town walls with small shops in the old narrow streets, boat trips, roman museum and fort. Interesting choice of restuarants in the old town. The Welsh Highland Railway trains now start from Caernarfon and pass the foot of Snowdon and then onward to Porthmadog. Ffestiniog railway at Porthmadog (17ml) up the valley to Blaenau Ffestiniog (28ml) and the Titan ZipWire. Choice of pony trekking locally.
Electricity and Gas included.
Property ref 2134:
2 BEDROOMS: One double bedroom with views and one twin bedroom. Bed linen provided.
WiFi: Included
PETS: No pets under ANY circumstances.
EXTRA: The bungalow is totally self contained and private with its own seperate access. Access to the front door from the carparking area is via four easy rise steps down to the front of the house and then just one into the house.
2020 Price Group: 8
Property ref 2135A:
2 BEDROOMS: One double bedroom with views and one with two single beds. Bed linen provided.
PETS: Two.
WiFi: included.
EXTRA: The bungalow is totally self contained and private with its own seperate access. Access to the front door from the carparking area is via 6 easy rise steps up to the front of the house and then just two into the house.
2 BEDROOMS: One double bedroom with views and 1 bedroom with two Single beds. Bed linen provided
PET: Maximum two pets.
TOWELS: At this time , due to Covid regulations, we are asking Guests bring their own TOWELS and TEA TOWELS.
We strongly recommend that you take our Cancellation Protection (see Terms & Conditions). If you continue you will notice that during the next booking steps this will automatically be selected for you and the price will increase, so simply de-select them on the bookings screen if you already have holiday insurance or if you do not want any cover.
The Pet Charge for all properties accepting pets is £20 per pet.
After your stay, we ask you kindly to please leave the property as it is found, in a clean and tidy manner. This includes replacing the furniture if you have moved them, emptying all internal bins, clean and put away plates etc., clean work tops and surfaces and hoover the floors.
No Smoking: We want all our guests to enjoy an odour free environment when they arrive at their property. We therefore prohibit smoking within the premises in ALL our properties. A 'Refreshing Charge' will be levied on guests who smoke in properties. A No Smoking Policy may form part of a property's statutory Fire Risk Assessment.
Mini-breaks & Weekends: In most cases, bookings that are for less than 7 nights in the season (Easter to the end of October) are only bookable at short notice. Out of season (November to last week before Easter) is more flexible. The mini-break rules for each property is stated on the description. Weekend booking requests that do not start or end on a property's change-over day or cross over more than 1 week, are at the discretion of the property owner. Please feel free to call us to discuss your requirements.
2130 & 2134 don't have an Access Statement as of yet
This is a single level dwelling that has been newly refurbished. The building comprises of two bedrooms, one twin and one double, which include overhead and bedside lighting.
Good size bathroom with shower over bath. Large kitchen/diner is well appointed with all modern appliances. Comfortable lounge with overhead lighting and additional lamp.
Electric sockets are all switched and at varying heights. Door widths are approximately 730 mm.
Access: The car park is private and capable of accommodating a number of vehicles and is reasonably level.
Acess to the property is down 3 easy steps with handrail to level patio, with one step into the property. The rise of the 3 steps are 5 inches each and the distance between the steps is 13 inches, The hand rail can be on either side depending upon which steps are used.
Valley View "Branwen" is a recently refurbished two-storey house. Access is by a sloping pathway to the front door with a step.
The spacious ground floor consists of entrance hall, leading to fitted kitchen, large lounge/diner, incorporating colour television with video remote control and CD/Radio.
The dog leg staircase leading off the lounge is not steep and has full hand rail, this leads to a small landing, two bedrooms and shower room.
All floors are carpeted with full central heating and good lighting throughout.
A slate patio to the rear, with access through a patio door and step down with table and chairs outside.
Week Price
02 January 2021 to 08 January 2021 £ 1537 £ 1230
09 January 2021 to 05 February 2021 £ 1137 £ 910
06 February 2021 to 12 February 2021 £ 1197 £ 958
13 February 2021 to 19 February 2021 £ 1257 £ 1006
27 February 2021 to 26 March 2021 £ 1137 £ 910
27 March 2021 to 02 April 2021 £ 1377 £ 1102
03 April 2021 to 16 April 2021 £ 1407 £ 1126
01 May 2021 to 28 May 2021 £ 1377 £ 1102
29 May 2021 to 04 June 2021 £ 1537 £ 1230
05 June 2021 to 02 July 2021 £ 1467 £ 1174
03 July 2021 to 09 July 2021 £ 1527 £ 1222
24 July 2021 to 20 August 2021 £ 1767 £ 1414
21 August 2021 to 27 August 2021 £ 1587 £ 1270
28 August 2021 to 03 September 2021 £ 1527 £ 1222
04 September 2021 to 17 September 2021 £ 1407 £ 1126
25 September 2021 to 15 October 2021 £ 1197 £ 958
16 October 2021 to 29 October 2021 £ 1377 £ 1102
30 October 2021 to 10 December 2021 £ 1137 £ 910
11 December 2021 to 17 December 2021 £ 1377 £ 1102
30 April 2022 to 30 December 2022 £ To be confirmed £ To be confirmed
Select your holiday dates here
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Or call us on 01766 51 38 29.
January 2021 February 2021 March 2021 April 2021 May 2021 June 2021 July 2021 August 2021 September 2021 October 2021 November 2021 December 2021 January 2022 February 2022 March 2022 April 2022 May 2022 June 2022 July 2022 August 2022 September 2022 October 2022 November 2022 December 2022
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* Please check the property description if there is a cot and/or high chair
0 1 2 3 4 5 6 7 8 9 10 11 12 How many pets? (£20 per pet) 0 1 2 3 4


The beloved Defender returns in 2020.
Launched in the '80s, the Land Rover Defender became a huge hit from the beginning. In 2016, the company broke the hearts of many automotive fans when it announced the end of the Defender era. Now, Land Rover has decided to reconsider that decision, as the beloved model will make a triumphant comeback in 2020. The recently announced Land Rover Defender 2020 brings back the popular boxy shape of the original, with an upgraded silhouette and a range of cutting-edge features. While the details remain firmly under wraps, the company has offered some hints about their latest SUV.
Apart from the expected off-road capabilities and rugged build, the Land Rover Defender 2020 will also feature state-of-the-art technology. The company has claimed that it will withstand extreme temperatures of -40 and up to 120 degrees. Which means that this Defender will be able to take on any (off-)roads, even at altitudes above 13,000 feet, in style. Land Rover fans will have to wait to find out more details about the new Defender. The company has announced that the vehicle will make its debut in 2020 in the US. Until then, fans should watch out for the car's big reveal, expected at one of this year's auto shows.


text:
Girls soccer: Can't-miss games across state this week, Nov. 2-Nov. 8
Updated Nov 02, 2020; Posted Nov 02, 2020
Cranford celebrates after 1-0 win during the girls soccer game between No. 14 Westfield and No. 13 Cranford at Gary Kehler Stadium in Westfield, NJ on Thursday, October 8, 2020. Cranford won 1-0.Scott Faytok | For NJ Advance Media
By Brandon Gould | NJ Advance Media for NJ.com
The first week of girls soccer action in November is coming up and there is another collection of must-see games, including a few Top 20 showdowns.
Check out the list below to see some games to keep an eye on.
Monday, Oct. 2
Matawan at Wall, 2 p,m.
Wall brings a 10-game winning streak into this game and will match its offensive prowess against Matwan's tough defense. Senior forward Olivia Ramiz is on pace to score more than 20 goals in this shortened season. Megan Stuart has been great in net for Matawan though and will be tough to beat.
East Brunswick at Ridge, 3 p.m.
East Brunswick hasn't given up a goal all season, but this is going to be one of its toughest games to date. The Bears come in on a 20-game unbeaten streak. East Brunswick has given up one goal during that stretch, which started on Sept. 24 of last year. Ridge is a defensive team itself, but does have a pair of Division-I bound forwards on its squad to lean on.
Brick Township at Toms River North, 10 a.m.
Toms River North still has not lost a game this season, but will have its hands full against a talented Brick Township squad. Brick Township hasn't lost since its season-opener and looks better now that we're a month into the season. It will be hard to get the best of Toms River North though, especially with its defense playing lights out lately.
Cranford at Immaculate Heart, 3:30 p.m.
Cranford is going to test itself right before starting its Union County title defense. The Cougars are the No. 3 seed in the Union County Tournament and will have tough challenges ahead with Scotch Plains-Fanwood and Westfield standing in the way of a repeat. Immaculate Heart is one of the top teams in Bergen County and one of the state's best non-public programs.
Montclair Kimberley at West Orange, 4 p.m.
Montclair Kimberley has a great group of young players who have helped this program get back on its feet after a down year last fall. The Cougars only loss so far came against Montclair in a 1-0 battle. West Orange is a tough squad in its own right and will challenge this squad in a game that could help better depict the hierarchy in Essex County this fall.
Monroe at Old Bridge 4 p.m.
The last time these two teams met, Old Bridge won in double overtime. It should be fun to see the rematch this week. These Middlesex County squads lean on their defense, so expect another low-scoring game. If Monroe is going to even the season series, it will need South Carolina commit Brigitte Bussiere to make some big plays.
Demarest vs. Ramapo, 5 p.m.
This will be Ramapo's first game in three weeks and it's a tough matchup to come back to. Carly Sherman and Emily Holzer are a tough duo that will really challenge Ramapo's defense. That pair has a combined 31 points for Demarest, which also has a tough game against Wayne Hills this weekend. Ramapo has a good offensive duo of its own and will be led by midfielders Mary Cochran and Mia Suchora.
Wednesday, Oct. 4
Princeton Day at Pennington, 3:30 p.m.
This is always a good game to watch when you have the best Prep B team in the state playing the best Prep A squad. These two teams have not been able to play many games, but when they do take the field, the talent is undeniable. Kelly Beal leads a balanced offense at Princeton Day, while Rutgers commit Kylie Daigle leads a strong attack at Pennington.
Science Park at Technology, 4 p.m.
This game was supposed to be last week, but the weather pushed it back. It will be an interesting matchup with Technology forward Neli Velasquez going up against and Science Park's offensive duo of Briana Esteves and Jessica Brahnan. With those three playmakers all on the field at the same time, watch out.
Gloucester Tech at Rancocas Valley, 6 p.m.
Gloucester Tech is having one of the best seasons in program history and is led by New Hampshire commit Meghan Guarente. The South Jersey squad feels really good about its depth and isn't afraid to play anyone. Rancocas Valley will test Gloucester Tech, especially with sophomores Kennedy Garcia and Olivia Sweeney out there. Senior Rachel Satchell is another player to keep an eye on when these two squads go toe to toe.
Kearny at West Essex, 4 p.m.
Kearny is doing a good job of testing itself outside of Hudson County, with the postseason coming up fast. The Kardinals played DePaul last weekend and will also play Lyndhurst next week. This particular matchup with West Essex will be a good indicator as well of what kind of team Kearny has. West Essex is a tough team and will battle all game.
Ramapo at DePaul, 7 p.m.
It's going to be quite the week back for Ramapo. The Raiders next test will come in a night game at DePaul. These are two of the best teams in the state. Ramapo won the Bergen County title last year and played in the Group 3 final. DePaul won the Passaic County championship and played in the Non-Public A title game. These are championship-caliber programs and it will be fun to see them go head to head.
Livingston at Montclair, 4 p.m.
Last year, these two teams met in the Essex County final. That was no surprise. These are two elite programs that have been loaded with talent for years. This season, Montclair is led by Division-I bound midfielders Sydney Masur and Claire Manning. Livingston, meanwhile, has an ace of its own in Villanova commit Lauren Belcuore.
North Hunterdon at Pingry, 11:30 am
The weekend schedule is a little light, but the Skyland matchup puts two talented squads up against each other. Pingry has won its last four games and is led by senior midfielder Sophia Cavaliere. North Hunterdon has a good core and will be tough to beat.
Union County semifinals
The state's lone county tournament will have its semifinals played this weekend. If the bracket goes chalk, that will mean a big-time game between defending co-champs Cranford and Westfield.
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Brandon Gould may be reached at bgould@njadvancemedia.com. Follow him on Twitter at @BrandonGouldHS.


Redwater ISD is committed to making every child feel welcome and safe every day. One of the steps we are taking to ensure that bullying does not take place in our district is to establish an anonymous reporting system for students and their parents.
"The District prohibits bullying, including cyber-bullying, as defined by state law. Retaliation against anyone involved in the complaint process is a violation of District policy and is prohibited." False reports of bullying will result in disciplinary action.
On each school's web page you will see a link called Safe2Say. You may anonymously report bullying using the link on the campus page or one of the links at the top of this page. This is not the only way to report bullying. Students and parents may contact teachers, counselors or the principal about any bullying incident.


text:
Lustbader, Victoria 1947-
Born November 11, 1947, in New York, NY; daughter of Rubin and Dorothy Schochet; married Eric Van Lustbader (an author). Education: State University of New York at Stony Brook, B.A.
Home—Southampton, NY; New York, NY. Agent—Laurie Liss, Sterling Lord Literistics, 65 Bleecker St., New York, NY 10012. E-mail—[email protected]
Harper & Row (publishers), New York, NY, began as manuscript reader, became assistant to the editor for fantasy and science fiction, beginning 1969; freelance editor; Nature Conservancy, began as development staff worker, became board member for New York State chapter.
WRITINGS:
Hidden, Forge (New York, NY), 2006.
SIDELIGHTS:
With a background in fiction publishing and a husband who is a novelist, Victoria Lustbader was very familiar with the art of writing by the time she decided to try it for herself. Her first published work is the historical novel called Hidden. The story of the ties between two families from very different worlds, the novel is set during World War I and the Roaring Twenties. The pivotal characters in the tale are Jed Gates, the son of a wealthy New York City businessman, and David Warshinsky, who comes from a poor Jewish family. Both men leave their families to enlist in World War I, and here they meet and become fast friends. When they return home, David does not want to go back to his old life and instead gets Jed's help to join Gates's company. He changes his name to David Shaw and denies his Jewish background. Meanwhile, Jed is also in denial of his true identity as a gay man. Lustbader follows the two families through this connection as they live through drastically changing times, see family members die tragically, and try to face down villainous characters.
Reviewers commenting on Hidden were impressed by its historical detail and well-rounded characters, but also found some flaws in Lustbader's debut. For example, Washington Post critic Brigitte Weeks felt the author was guilty of some stereotyping, especially of the female characters, adding that "Lustbader's skill in making us genuinely interested in these characters does make her tendency to bump them off when they get in the way of the plot sometimes aggravating." Weeks, however, commented that these were small flaws in a novel that "delivers robustly on its promise to take readers into another era." Marianne Fitzgerald, writing for the Library Journal, enjoyed the "fully dimensional and deftly drawn characters" in this "hard-to- put-down, historically accurate tale."
BIOGRAPHICAL AND CRITICAL SOURCES:
Library Journal, June 15, 2006, Marianne Fitzgerald, review of Hidden, p. 58.
Washington Post, July 6, 2006, Brigitte Weeks, "Characters from Both Sides of the Tracks Mingle in a Tale of Early 20th-Century New York," review of Hidden.
Bookreporter.com,http://www.bookreporter.com/ (November 13, 2006), Carole Turner, review of Hidden.
Fantastic Fiction,http://www.fantasticfiction.co.uk/ (November 13, 2006), review of Hidden.
"Lustbader, Victoria 1947- ." Contemporary Authors. . Encyclopedia.com. 28 Dec. 2021 <https://www.encyclopedia.com>.
"Lustbader, Victoria 1947- ." Contemporary Authors. . Encyclopedia.com. (December 28, 2021). https://www.encyclopedia.com/arts/educational-magazines/lustbader-victoria-1947
"Lustbader, Victoria 1947- ." Contemporary Authors. . Retrieved December 28, 2021 from Encyclopedia.com: https://www.encyclopedia.com/arts/educational-magazines/lustbader-victoria-1947
Meg Cabot , Cabot, Meg 1967-(Meggin Cabot, Patricia Cabot, Jenny Carroll) Cabot, Meg 1967-(Meggin Cabot, Patricia Cabot, Jenny Carroll) Personal Born February 1,… James Stevenson , Stevenson, James 1929– Personal Born 1929, in New York, NY; son of Harvey (an architect) and Winifred (Worcester) Stevenson; married Jane Walker, 195… Katherine Applegate , Applegate, Katherine (Alice) 1956– (K. A. Applegate) Personal Born 1956, in MI. Hobbies and other interests: Playing the cello, traveling, reading, g… Robert Newton Peck , Peck, Robert Newton 1928- PECK, Robert Newton 1928- Personal Born February 17, 1928, in Vermont; son of Haven (a farmer) and Lucile (maiden name, Dor… Joyce Carol Oates , OATES, Joyce Carol 1938- (Rosamond Smith, a pseudonym) PERSONAL: Born June 16, 1938, in Lockport, NY; daughter of Frederic James (a tool and die desi… Ray Bradbury , Bradbury, Ray 1920– Bradbury, Ray 1920– (D.R. Banat, Ray Douglas Bradbury, Leonard Douglas, William Elliott, Douglas Spaulding, Leonard Spaulding, Br…
Quin-Harkin, Janet 1941–
Bradley, Marion Zimmer 1930–1999
Balogh, Mary 1944-
Jakes, John 1932- (William Ard, John William Jakes, Alan Payne, Jay Scotland)
Anderson, Kevin J. 1962- (Kevin James Anderson)
Charyn, Jerome 1937–
Deitz, Tom 1952-
Lustbader, Eric Van 1946–
Lustbader, Eric Van
Lust, Caution
Lust in the Dust
Lust for Gold
Lust for Freedom
Lust for Dracula
Lust for a Vampire
Lust and Revenge
Lussu, Joyce Salvadori (1912–1988)
Lussan, Marguerite de (1682–1758)
Lussali, Zélie de
Lussac, Elodie (1979–)
Luso-Brazilian
Luso-American Education Foundation
Luskin, Fred 1954-
Lusk, John 1969(?)-
Lusk, Graham
Lusk, Grace (1878–1938)
Lusk, Georgia Lee (1893–1971)
Lusitanus, Amatus (Rodrigues, Joāo)
lusingando
lusing.
Lusinchi, Jaime Ramón
Lusted, Marcia Amidon
Lusted, Marcia Amidon 1962-
Lustig, Aaron 1956–(Aaron Luftig)
Lustig, Alessandro
Lustig, Arnost
Lustig, Moses
Lustig, Nora Claudia
Lustig, T(imothy) J(ohn)
Lustige Witwe, Die
Lustigen Weiber von Windsor, Die
Lustiger, Jean-Marie Aron
lustral
lustrate
Lustratio
lustre mottling
lusty
Lusus Naturae
Lutayeva-Berzina, Valentina (1956–)
lute harpsichord
lutefisk
Luteinizing Hormone Test


This is not a standard PSC Kit, rather an OPW specific kit that we have put together based on our years of competition experience.
This kit includes a number of upgrades and also components that others class as extras all added to improve strength and ensure high performance.
Note - as a guide 6" stroke ram suits Suzuki and Hilux Diffs - you will need to confirm the stroke you require though for your specific set up as it will depend on the specific steering arms you are using.


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Dr. Pimple Popper Has Switched to Paid Video
The famed dermatologist explains why she made the move.
By Kaleigh Fasanella
Sandra Lee (a.k.a. Dr. Pimple Popper) is currently in hot water with her fans for making the move to paid video. Now, instead of being able to tune in to all of the pimple-popping fun for free, subscribers will have to shell out $2.99 per month in order to watch some of the famed surgeon's content. While she still posts frequent teasers on Instagram, some of Lee's full videos are now only available to her All Access Subscribers.
In the comment section of a recent teaser, fans expressed their frustration with having to pay to see the full duration of their beloved popping videos. One fan wrote, "So no more free videos huh? Nice 😒," while another offered, "So access..pay to see you pop spots...no way...was and am a fan but your milking this now for profit..not gonna follow you now on here anymore...#scottishfan."
What's more, some folks chimed in about the quality of the video. "Not great video, need to be closer pls," wrote one user. "The camera is too far!!!" added another. Additionally, one person said, "If she's going to charge people to watch the videos she at least needs good video quality."
Other longtime fans of Lee's expressed their unhappiness with the pivot. A user by the name of xxcheryl17xx2019 wrote: "I've been a loyal Dr. Pimple Popper fan on YouTube from the start. Now we hardly get any videos. You're also wanting us to pay for the ones you do make. I understand you want to make money, but you're already rich. Can't the TV show be enough and you still post on YouTube for your followers and fans? I feel it does us a disservice."
Due to the slew of negative feedback she received, Lee posted a YouTube video explaining why she made the switch. In the video, she says that because her gory content gets flagged and removed so often, YouTube restricted ads from running on her content, which in turn costs her business a boatload of revenue because ads are a major way YouTubers make money.
Put simply, by charging for some of her content Lee is earning the money she's no longer receiving from YouTube. "This subscription is really to help cover the cost of everything, really," she explains. And it makes perfect sense, considering how costly video production can be — that, and the fact that she doesn't charge her patients who agree to be filmed. Oh yeah, and she doesn't get paid for her TLC show, either.
What she does earn revenue for, however, is her book, her skin-care line SLMD, and her merchandise. Lee puts a ton of hard work into making these videos for her loyal fans, so it's not at all crazy to ask for some compensation. Here's hoping that people can come to understand that.
Want more from Teen Vogue? Check this out: How to Watch the Secret Videos That Dr. Pimple Popper Doesn't Instagram
KeywordsDr. Pimple Poppersandra lee


The band led by Cristopher Johnsson is one of the most spectacular musical acts of all time. The way in which they melt orchestral elements, choirs and symphonic metal is unique and has garnered them a rabid fan base absolutely dedicated to the creative universes that Johnsson proposes. Records such as "Secret of the Runes", "Theli" and most recently the impressive record "Les Fleurs du Mal" have helped them to have their own and untouchable niche in heavy metal.


Solar panels cost thousands of dollars to install and, because of this, they usually come with long warranties of 10 to 25 years. That warranty makes most owners feel better about their purchase, but what if you have a problem and you found out the warranty is void? Yes, this can happen and for a reason you might not think of: you neglected to get regular panel cleaning. Cleaning of your panels is so vital to continued efficiency, that many manufacturers stipulate that you must have proof of regular cleaning in order to make claims on your warranty.
How Often Should You Get Dallas Solar Panel Cleaning?
Your manufacturer may have specific requirements about the frequency of your cleaning but here are some guidelines: In an urban or suburban area like Dallas, panels should be cleaned about every 6-8 months.
Slant of Panels: If your panels are not steeply tilted then they are likely to need more frequent cleaning because debris won't naturally fall off.
High Energy Bills: The more expensive your electricity costs, the more worthwhile it is to get more frequent cleaning to improve output.
Amount of Dust/Dirty Blown onto Your Panels: This can vary throughout the year, but if you're able to see dust on your windows, it's likely they need to be cleaned.
Drought Times: While Houston definitely has its share of rain and humidity, there are times when there is less rain and your panels will be more likely to get dusty.
Aside from keeping your warranty valid, regular cleaning increases efficiency and reduces your electricity costs. Aurum helps you protect your investment with solar panel cleaning Dallas business and homeowners can rely on. Call us at 800-749-0532 to receive a no obligation quote.


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What Is Sickle Cell Disease?
Causes of Sickle Cell Disease
Inheritance of Sickle Cell Disease
Symptoms of Sickle Cell Disease
Vaso-Occlusive Crisis
Diagnosis of Sickle Cell Disease
Transcranial Doppler Ultrasound Screening
Prognosis of Sickle Cell Disease
Living with Sickle Cell Disease
Sickle Cell Care Plan
Sickle Cell Disease and Fatigue
Sickle Cell Disease and Pregnancy
Sickle Cell Disease and Schooling
Sickle Cell Disease and the Eyes
Sickle Cell Disease and Sleep
Pain Management Guidelines for Sickle Cell Disease
Sickle Cell Disease in Children
Adakveo (Crizanlizumab)
Endari
Oxbryta (Voxelotor)
Opioid Narcotics
Levorphanol
Stem Cell Transplant
Experimental Therapies
ACZ885 (Canakinumab)
Memantine
NKTT120
Olinciguat (IW-1701)
Rivipansel (GMI-1070)
Her Sickled Journey
European Initiative Targets Diagnosis, Treatment of Rare Diseases
by Larry Luxner
Click here to subscribe to the Sickle Cell Anemia News newsletter!
A new international consortium based in Paris, and funded largely by the 28-member European Union, intends to speed the diagnosis of rare diseases, while also accelerating the development of treatments for the 95% of such illnesses that currently don't have one.
The European Joint Programme on Rare Diseases (EJP RD), established in January 2019, operates on a five-year budget of €101 million (about $112 million), and involves at least 130 entities in 35 countries. This includes all EU member states except for Cyprus, as well as Canada and seven EU associated members: Armenia, Georgia, Israel, Norway, Serbia, Switzerland, and Turkey.
About 55% of the total budget comes from Horizon 2020 — the EU's €80 billion ($90 billion) research and innovation program — and the remaining 45% from member countries.
The executive committee of the European Joint Programme on Rare Diseases met recently in Brussels. (Photos courtesy of EJP RD)
"Patients with a rare disease often suffer unnecessarily and die prematurely. We need to do much more to develop effective treatments and improve diagnosis," Carlos Moedas, the EU's commissioner for research, science and innovation, said during a recent meeting of the International Rare Diseases Research Consortium in Brussels.
"This partnership shows how we can pool Horizon 2020 funding and resources from EU member states and beyond in order to save lives and protect people," he said.
The new program is overseen by Inserm, the French National Institute of Health and Medical Research, and brings together hospitals, patient advocacy groups, 11 universities, and 30 funding organizations ranging from the Austrian Science Fund and Italy's Ministry of Health, to the Swedish Research Council and the Slovak Academy of Sciences.
Patient organizations are represented in EJP RD through Paris-based Eurordis — an umbrella group composed of 862 rare disease patient groups in 70 countries — and through 24 European Reference Networks.
1,000 new therapies by 2027
Molecular biologist Daria Julkowska, PhD, coordinates the initiative. She said EJP RD was borne out of the realization that "we needed to create a real ecosystem for rare disease research in Europe" by boosting the capacity of existing research infrastructure.
Daria Julkowska, PhD
"For example, today we have patient registries, biobanks and genomics data that can be very valuable, but only if you have the possibility of connecting them together and exploiting them for research," she told BioNews Services, publisher of this website, in a phone interview from Paris.
"Our goal is that any patient with a rare disease should receive a diagnosis within a maximum of one year, or be integrated into the research pipeline," she said. "That's our objective, and we hope to achieve it by 2027."
A secondary goal, she said, is to develop 1,000 new therapies for rare diseases within the next eight years, specifically targeting those illnesses that don't have any treatments.
Julkowska completed her studies in Poland and France, and did post-doctorate work at the Pasteur Institute. Following additional training in research management, she joined E-Rare in 2010 as a program manager, then two years later took over coordination of that specialized EU program.
Among other things, she said, the EJP RD will offer grants for research projects of up to €50,000 (about $56,000) each for patient organizations.
Unlike the patient advocate groups represented by Eurordis, the EJP RD won't lobby governments to approve reimbursement for expensive new therapies like Spinraza (nusinersen), a Biogen therapy for spinal muscular atrophy whose U.S. retail price is $750,000 the first year and $375,000 for every year thereafter.
"Since our consortium mostly focuses on research, our primary capacity is not to dictate the rules of reimbursement for drugs. This is above our level," Julkowska said. "What we can definitely do through our actions is finance dedicated research that would demonstrate the burden of lack of treatment for patients to use as proof for discussions with policymakers."
Tagged EJP RD, European Reference Networks, European Union, EURORDIS, Horizon 2020, INSERM, rare diseases, research.
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Sickle Cell Disease News is strictly a news and information website about the disease. It does not provide medical advice, diagnosis or treatment. This content is not intended to be a substitute for professional medical advice, diagnosis, or treatment. Always seek the advice of your physician or other qualified health provider with any questions you may have regarding a medical condition. Never disregard professional medical advice or delay in seeking it because of something you have read on this website.


Drug Description : When ordering Galvus be sure to choose a reputable online pharmacy that you trust.
PharmaPassport.com is the first choice when searching for safe and affordable Vildagliptin.
The Galvus medication you purchase is manufactured by Novartis. Vildagliptin is the generic alternative to Galvus.


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We've been big proponents of the remote working movement for years now, and as we dig digger into the culture it encompasses, multiple sub-topics arise and warrant further discussion. One of the most challenging topics we've encountered is working remotely when around family and friends. Just because you're on vacation or traveling doesn't stop you from putting in time at your virtual office.
In recent years I've had my fair share of remote working adventures. New locations, various internet connectivity challenges, and a host of friends, family, or significant other experiences to go along with it. Some of those trips were quite a challenge and learning was paramount for the future, whereas others were a great success without a beat skipped.
Most recently I returned from a week with my family and significant other on the west coast. My remote work for the week ran very smoothly, which had me thinking what the difference maker might be. As I've thought further on the topic, I came up with a few highly suggested thoughts from these experiences. Let's dig in.
This topic comes first, and I can't stress enough how paramount this is to your success. Poor accommodations not only sour a travel stint, but they can also create tension between you and your team, as well as the group you're traveling with.
Always double (and triple) check that your accommodations have comfortable spaces for you and your travel companions. In other words, make sure you don't set up shop in a studio apartment with little privacy for a week. It might save you $50 a night in rent, but is that worth a week of headaches? I know the answer to that one: it isn't.
Make sure everyone has a bedroom and that there's more than one common area to loiter in. Most noise pollution happens in either the kitchen (dishes, cooking, coffee making, cleaning) or the living area (tv, music, laughter). If you're trying to work at the kitchen table or in front of the tv, for example, you'll have problems.
For optimal working while out of town, settle in to an alternate common area or find a space with an office you can use. If you decide to pinch pennies and don't establish yourself in a space with ample options, you'll have to hustle down to the local library or coffee shop where nothing will be in your control: sounds, expectations, internet speeds, hours, etc.
Equally as important as the space with which you work will be the speed with which you can communicate with your team and execute on the work you wish to accomplish.
In a recent Airbnb stay, I communicated with the host very early asking about internet speeds, going so far as to have them run a speed test in the rental with a link I provided in our chats. By getting a sense of what they see in the space, I know if it will work for my needs.
Is it old school AOL email checking speeds, or can I comfortably have video calls when they come up? Are their dead spots in the house where wifi drops off drastically? It's surprising that many great rentals still have lackluster internet in 2015.
That being said, internet can still be crummier than you might anticipate despite your best efforts. I always suggest letting key contacts or clients know you'll be away from your typical office for x-number of days before you commit to multiple video calls or web presentations while you're away.
Don't forget about backup communication, too. How's cell phone service on that beachfront house 15 minutes from town? Does it have a landline? In my most recent trip, cell service was nonexistent, and I didn't even think to ask the host about this. It wasn't listed as a concern, so why would it be one? Turns out asking is a rule of thumb.
Remember the "Big 3" here: internet, cell service, and other local options.
Family wants your time, period. Friends that don't need to work suddenly feel like work isn't a big deal ("Let's get a 2pm margarita; it's vacation!!") Your significant other probably wants to explore and have quality time. Makes sense. That pressure can settle in thick so it's important to lay out your "ground rules" before arriving.
I've found it's key to bring this up when you're planning the trip, not as you board the plane. Let's say you'll be staying Saturday to Saturday somewhere. The weekend is yours, of course. but come Monday, you'll be working roughly 7 to 3 on client stuff. Make that clear.
It's important to have a conversation about those expectations, too. Let your parents, friends, or partner ask a few clarifying questions. Of course you want to be there with them. Of course spending time with them is also a priority! But the flexibility of your job has given you this opportunity, so you need to nurture that culture in order to enjoy the non-work time as much as possible.
If you have a morning routine before work, too, make sure you practice it while traveling as well. Meditation, stretching, going for a walk, social media, coffee, etc. Don't forget this just because you're on the road. It'll make work that much smoother!
Note: adjusting your daily routine can be important when traveling with family. If everyone's sleeping in until 10am and it offers you half the day to work in peace, make it a point to get up early and front-load the days! You'll get more done and have less time away from your new surroundings.
This piggybacks the previous point, but should be noted. The biggest item I've noticed about mutual satisfaction on a remote experience with family is that you're clear with them on when you have them in mind, too. It's critical.
Perhaps you'll start work early and take a lunch with them each day. Maybe everyone rises by 7am, so you catch a morning walk and make breakfast before they head out for the day. Or if they're not finishing breakfast until 11am, completely casual, make late afternoon and dinner plans for each day. Everyone will have something to look forward to.
No matter the group you're with, or the timelines that surface, you can always make it work with your team if you communicate clearly, early and often, about those expectations. When they keep your needs in mind, and you keep their expectations in mind, too, things will work out.
As a part of a growing mobile workforce, we need to be able to jet set to a tropical island in a heartbeat if the opportunity presents itself (with great internet, of course). But what to bring? Throwing things together the night before a trip can rack the nerves.
Invest in a simple travel bag or kit for your supplies to stay tidy. Keep cords and chargers in one place. Throw in a couple spare batteries if you'll be using wireless devices on longer trips. I'd even bring a small pouch full of remote essentials for any circumstance you might deal with: eye drops, headache medicine, nut butter packets, an energy bar or goo. And definitely make sure you've got a water bottle to bring along.
In addition to your on-the-go kit, you'll need something to protect things from people, to flights, to random accidents, and everything else that can come up. Find a backpack or carrying case that serves as "work" and keep everything else separate. Something sturdy, water resistant, and travel ready.
A quick tip for plane travel: carry-on your "work" and never, ever check it.
As you plan a trip, make sure travel arrangements happen appropriately. Read: not midday-Tuesday, returning midday-Monday the following week. This puts stress on you, your team, and everyone around you. With a few work days essentially "lost" to travel, productivity plummets and that feeling of pressure rises.
For longer travel, plan on making moves over the weekend. Flights might be a little more expensive, but stay away from booking 3 weeks out to avoid steep prices. For shorter stays, consider overlapping through a weekend so your weekday travel is limited to an evening flight, while a return flight can be made on a Sunday.
In addition to scheduling with your remote team in mind, always stay on top of communication if you are traveling on a work day. Pop on earlier in the day and clean out the inbox. Check in with your team or project lead. Provide a sense of your connectivity that day, and check in again once you're settled.
Being proactive goes a very long way in a position that offers workplace autonomy, so it's up to you to uphold that notion in return.
It goes without saying that working remotely can provide amazing opportunities that a typical "corporate" job cannot, but it comes with a higher level of personal responsibility. To you, to your team, and to the people you travel with.
After a handful of trips just this year, I've learned enough to know that keeping these thoughts in mind will turn a remote worker from amateur to pro. By establishing your needs and thoughts ahead of time, working remotely with those you love becomes not a burden, but a way to remain productive and connected while in a new place with those you care about. Take the the time to plan ahead so you can take the time to enjoy the trip.
Welcome to the big leagues, kid!
I'm curious: What have you learned along the way? What other tips or hacks can you share? We'd love to hear about them.
A five part series written for remote professionals who want to take their life and careers to a new level. This is Part Four in the series.
A five part series written for remote professionals who want to take their life and careers to a new level. This is Part Three in the series.


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Workplace spying 'offensive' to staff
Karen Sweeney
Advances in workplace technology are allowing employers to know how long workers are spending in the toilet in a level of surveillance that an economist has labelled "offensive".
It's no coincidence that technology benefits employers over employees, according to James Stanford, who told a parliamentary inquiry that innovation is solving the problems faced by those paying for it.
The Centre for Future Work has recommended limits be placed on how companies use electronic systems to monitor, survey and discipline workers, including CCTV, GPS tracking and computer monitoring.
"I think the use in an unregulated format of some of this electronic surveillance is … offensive to the dignity and privacy of workers," Dr Stanford, the centre's director, told a Senate inquiry into future employment on Wednesday.
While Dr Stanford has some concerns about technological advancement he doesn't think mass unemployment as a result is likely, but admits technology is partly to blame for under-use of workers.
While official figures put unemployment at 5.5 per cent, he says the true rate of under-utilisation is around 15 per cent.
"Our research suggests that less than half of the Australian labour force today fills what we once considered a standard job, a permanent full-time job with entitlements that they can count on to support themselves and their families," he said.
Significant groups of workers will be "displaced and harmed" by the way technology is implemented, he predicted.
But artificial intelligence expert Toby Walsh told the Sydney hearing there would always be a preference for the human touch in some professions, including doctors, psychologists and sales people.
"And there will be lots of people-focused jobs where it's emotional intelligence that's very important," Prof Walsh said.
The inquiry also heard the hospitality sector is struggling to find skilled workers, blaming negative perceptions around workplace-based training compared to university education.
A survey of final year school students last year found only a third saw vocational education and training (VET) and university as equal, Restaurant and Catering Australia policy manager James Coward told the committee.
"So when they're not actually viewing these things on a level footing it creates this idea hospitality sector work is only a temporary or a transitional kind of work, which is a very damaging perception for hospitality to have to contend with," he said.
Life is what happens to you while you're busy making other plans – J...
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Nested strakes make for lots of lines, hope they're right.
I had four solid hours of time to myself today to work on the soon to be boat and made good use of my time. After working out a decent system for laying out the planks/strakes last night I got straight to work marking out the last two planks on the first scarphed panel. I was able to layout the remaining two planks in roughly an hour and forty five minutes which, compared to last nights three hour session, seemed like light speed. I spot checked a number of marks to make sure they were right and I'm fairly comfortable that I got all the measurements correct (cross fingers).
As I was finishing up I was thinking about how long it's going to take to get all of these planks cut when it occurred to me that after I cut these planks out I could use them as a pattern for the next scarphed panel. I suppose this revelation should have been obvious, but it wasn't to me. Then I thought, why not just cut both panels at once, then I get two of each plank matched exactly.
That brought me to the next question which was "how am I going to cut these planks?" I hadn't really thought too much about it before because I was focusing on getting the layout correct, and I didn't really think that I would be at that point today, but here I was. I had unconsciously assumed that I would use my jigsaw, but I have never been happy with the speed or the lumpy cuts I always seem to get because even a millisecond's inattention is enough to change the direction of the saw. I always cut proud of the line, but cleanup is always a chore.
That got me thinking about using my Bosch 7-1/4" circular saw to do the cuts. When I built the shop last summer, I spent a huge amount of time with that saw and I got really comfortable with it. The cut line gauge is really accurate and it doesn't wander like a jigsaw and as long as the radius isn't too deep, it can follow a curve nicely. Oh, and it is Way faster than a jigsaw.
The blade was pretty dull from the shop build, so I ran up to Home Depot and got a Diablo 60 tooth thin kerf blade, mounted it, and got busy.
I lined up two of the scarphed panels so the edges matched up, screwed them together with a few wood screws and started cutting. It took just under an hour to cut all the planks out with a few breaks in between to let the dust settle and I'm really happy with how they turned out. No oops, crap, or whatever; it just worked and worked well. Every edge is smooth and about 1/16" proud of the line.
Nice smooth cut, just proud of line.
So, to make a long story short, I went from being overwhelmed with how much drudgery work I had to do, to having eight of the eleven planks cut out and nicely matched. I still have to mark out and do the same operation on plank number five and cut out a single keel strake, but I feel like I over the hump and may actually start making the wood look like a boat next week.
Can't even see that there are 8 planks; the benefits of stacked cuts.
Nice work!I keep lusting over those little 3 inch cordless circular saws, seems ideal for this task.
For tight radius work, one of those would be perfect. I have a 5" cordless circular saw, but the curves aren't steep enough on these planks to need a tighter radius. The 7-1/4" followed the curves very well (maybe even smoother than I could have done with the 5").


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Transport, Weather and Environmental Data Insights from Vaisala Partnership
We're very excited to be partnering with Vaisala, a global leader in weather, environmental, and industrial measurements, to drive sustainability in the travel industry.
VivaCity sensors, which use artificial intelligence and machine learning to capture anonymous traffic counts of different transport modes across a selected 'count line', will be paired with Vaisala's weather and environmental measurement products to enhance safety, efficiency, and decision making. These state of the art sensors will provide detailed insights into both street level and large scale weather and air quality changes across the West Midlands region.
The pandemic has shone a light on air quality and travel sustainability, with the contributions from different vehicles changing significantly. For example, data from Ricardo revealed that passenger car contribution decreased to 53% and LGVs and HGVs together contributed just under a third of the total NOx, during the lockdown periods in 2020.
Project with WM5G and Transport for West Midlands
VivaCity and Vaisala are currently working on a forward-looking project enabled by West Midlands 5G (WM5G) and Transport for West Midlands. Air quality and weather sensors are being installed across a number of sites alongside VivaCity Lab's traffic sensors, to provide researchers with the opportunity to explore the subtle differences in traffic flows as the weather changes.
The next stage of the £5.8 million Road Sensor Network Project will see around 350 sensors – provided by VivaCity and Vaisala – deployed across the seven constituent authorities of the West Midlands Combined Authority area, before its conclusion in March 2022. It is hoped that the findings will support other regions in developing similar networks to ease congestion hotspots and manage traffic flow more intuitively.
Mark Nicholson, CEO and Co-Founder at VivaCity, commented:
"The conversation around air quality, sustainability and the impact of travel has become essential, and it's great to be partnering with Vaisala to provide key and new data for local authorities and researchers. By providing these insights, decisions can be made about infrastructure and both immediate and longer term plans can be put in place to improve air quality."
Danny Johns, Business Development Manager, Weather and Environment, at Vaisala added:
"Using weather and air quality data together with VivaCity's traffic sensors provides valuable input to facilitate smoother traffic flows in the West Midlands region and demonstrates the power of the close collaboration between our two organisations. These various data sources help build a better understanding of the key relationship between the vehicles, the pollution they create, and the way that pollution either stays close to the ground or disperses depending on the prevailing weather conditions."
About Vaisala
Vaisala is a global leader in weather, environmental, and industrial measurements. Building on 85 years of experience, Vaisala provides observations for a better world, with space-proof technology even exploring Mars and beyond. They are a reliable partner for customers around the world, offering a comprehensive range of innovative observation and measurement products and services. Headquartered in Finland, Vaisala employs over 1,900 professionals worldwide and is listed on the Nasdaq Helsinki stock exchange.
Get in touch with the VivaCity team to find out more about our traffic management and data solution and ask for a free demo.
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Sign Up for Our Monthly Family Getaways Newsletter
Samantha Davis-FriedmanContributing Editor, Theme Parks
Hotel Review: Four Seasons Resort Orlando at Walt Disney World Resort
Families can watch a movie on the Starstruck Dive-In screen while swimming in the family pool.
Credit: 2018 Four Seasons Resort Orlando at Walt Disney World Resort
The range of hotel options at Walt Disney World Resort is designed to appeal to every type of traveler. But for clients looking for a luxury experience at the most magical place on earth, Florida's Four Seasons Orlando is the perfect choice.
The first and only property in central Florida to receive the AAA Five Diamond Award, the 443-room Four Seasons Resort Orlando combines the brand's signature luxury experiences with Disney's signature brand of magic to create a "best of both worlds" family vacation. As an added perk, Four Seasons Orlando guests have access to Walt Disney World Resort's Extra Magic Hours benefit, which means clients can enjoy even more time at the theme parks — and a private shuttle from the property to the theme parks makes transportation a breeze.
The resort's Splash Zone has a choreographed fountain that shoots water 30 feet into the air.
"It's two iconic brands in one seamless booking," said Kristin Miller, director of travel industry sales for Four Seasons Resort Orlando. "The benefit of our in-house Disney Planning Center allows agents to email or call for assistance with Disney Dining, ticketing or FastPass+ selections."
As expected, the resort's guestrooms are spacious and luxurious — or "fancy," as my teenage son described it — and our balcony provided a panoramic view that included Epcot and the Magic Kingdom. The property's on-site amenities also offer plenty to do if families need a break from theme park fun, including a Splash Zone with a choreographed fountain that shoots water 30 feet into the air; Drifters, an 11,008-square-foot not-so-lazy river that features two spray cannons, a 9-foot waterfall and a rapids section; and two 242-foot waterslides (guests must be 42 inches or taller to ride). Plus, every Saturday evening and select Thursdays, families can watch a movie on the Starstruck Dive-In screen while swimming in the family pool.
The lazy river features two spray cannons, a 9-foot waterfall and a rapids section.
In addition, The Hideout is a cool indoor spot for kids to get out of the Florida sun and play video games, pinball and billiards. The complimentary on-site Kids For All Seasons kids' camp is also available for children ages 4 to 12 from 10 a.m. to 6 p.m. daily. The program, housed in "The Mansion," offers indoor and outdoor activities that young guests can enjoy for a couple of hours or for the whole day. It even has its own interactive volcano. Evening programming is available for an additional fee.
The six dining options at the resort serve a variety of cuisines; standouts include PB&G, a poolside bar and grill; Ravello, an Italian restaurant with indoor-outdoor seating and an open kitchen; and Capa, a Spanish steakhouse that offers full entrees, tapas-style small plates and, most importantly, a spectacular rooftop view of the Magic Kingdom fireworks in the distance.
The resort offers spectacular views of the Magic Kingdom fireworks.
My teen is a foodie, so we ordered a variety of small plates that included Carne (beef carpaccio), Pulpo (grilled octopus) and Coliflor (cauliflower with caper and egg). But Capa also has two kids' menus for less-adventurous eaters: One offers standards such as chicken tenders and macaroni and cheese, but the other menu — for "young culinarians" — caters to more sophisticated palates with dishes like roasted chicken with truffle and white asparagus or seasonal fish with sunchoke and salsa verde.
One of the most popular activities on any Disney family vacation is a character dining experience, and at Four Seasons Orlando, the Good Morning Breakfast with Goofy and His Pals is a fun-filled way to start the day. The buffet breakfast features a huge selection of breakfast favorites (as well as a special kids' buffet), and a professional photographer is on hand to capture all the magical moments. Miller notes that guests can also arrange for a private meet-and-greet with any of their favorite Disney characters.
The Good Morning Breakfast with Goofy and His Pals is a fun-filled way to start the day.
"Four Seasons guests will surely enjoy more fun in the parks provided by the Extra Magic Hours," said Thomas Steinhauer, regional vice president and general manager of Four Seasons Orlando. "Plus, with the on-property diversions, guests will be ensured an unforgettable vacation."
Four Seasons Resort Orlando at Walt Disney World Resort
www.fourseasons.com
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