text:
\section{Introduction}
The face numbers of simplicial $d$-polytopes are characterized by the celebrated $g$-theorem, conjectured by McMullen~\cite{McMullen:NumberFaces-71} and proved by Stanley~\cite{Stanley:NumberFacesSimplicialPolytope-80} and Billera-Lee~\cite{BilleraLee:SufficiencyMcMullensConditions-1981}. In contrast, the $f$-vector, and the finer flag $f$-vector, of general $d$-polytopes of dimension $d \geq 4$ are not well understood, despite considerable effort, see e.g. Gr\"{u}nbaum's book~\cite[Ch.10]{Grunbaum:ConvexPolytopes-03}; likewise for regular and strongly regular CW spheres. Are there ``qualitative" differences between these sets of vectors? In this note we suggest geometric measures to make this question precise. The computational complexity aspect is also considered.
For other measures of complexity in dimension $4$, like \emph{fatness}, see e.g. Ziegler's ICM paper~\cite{Ziegler-ICM}, and e.g. \cite{Ziegler-semigroup, Sjoberg-Ziegler:semi.alg} for general $d$.
\subsection{Geometric complexity}
Let $\mathcal{F}$ be a family of graded posets of rank $d+1$ with a minimum and a maximum. For instance denote by $\mathcal{F}=\mathcal{P}^d$ (resp. $\mathcal{P}^d_s$) the face lattices of all (resp. simplicial) $d$-polytopes. Let $f(\mathcal{F})$ be the set of $f$-vectors of elements in $\mathcal{F}$, counting the number of elements in each rank $i$, denoted $f_i$, for $1\leq i\leq d$. (Note the shift of index by $1$ with respect to the dimension convention.)

For a subset $T$ of $\mathbb{R}^d$ and $t\in T$ let $\overline{\Conv(T)}$ (resp. $\overline{\Cone_t(T)}$) be the minimal closed convex set (resp. cone with apex $t$) containing $T$. Let $\sigma^d$ denote the $d$-simplex.

The following are geometric consequences of the $g$-theorem.
\begin{theorem}\label{obs:simp.density}
(1) \emph{Convex hull}: $C_d:=\overline{\Conv(f(\mathcal{P}^d_s))}=\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d_s))}$ is a simplicial cone of dimension $\lfloor d/2 \rfloor$.

(2) \emph{Density of rays}: for any $\epsilon>0$ and any $x\in C_d$ there exists a simplicial polytope $P\in \mathcal{P}^d_s$ such that the angle between $x-f(\sigma^d)$ and $f(P)-f(\sigma^d)$ is less than $\epsilon$.

(3) \emph{Density of points}: for any $x\in C_d$ there exists a simplicial polytope $P\in \mathcal{P}^d_s$ such that in the $l_1$-norm $||x-f(P)||_1=O(||x||_1^{1-\frac{1}{\lfloor d/2\rfloor}})=o(||x||_1)$. (The $O(\cdot)$ estimate is tight; $d\ge 2$.)

(4) \emph{Boundary polytopes}: the only polytopes $P\in \mathcal{P}^d_s$ with $f(P)$ on the boundary of $C_d$ are the $k$-stacked polytopes for some $k\le \frac{d}{2} -1$; only the $1$-stacked polytopes have $f(P)$ on an extremal ray, all are on the same ray.
\end{theorem}

When $d\geq 4$, all analogous statements for $\mathcal{P}^d$ seem open.
Explicitly:

\begin{problem}\label{prob:polytope-density}
(1) \emph{Convex hull.} Is $\overline{\Conv(f(\mathcal{P}^d))}=\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$?

(1') \emph{Finite generation.}  Is $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$ finitely generated?

(2) \emph{Ray density.}
Are the rays from $f(\sigma^d)$ through $f(P)$ for all $P\in \mathcal{P}^d$ dense in $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$?

(3) \emph{Point density.} Is it true that for any $x\in \overline{\Conv(f(\mathcal{P}^d))}$ there exists $P\in \mathcal{P}^d$ such that $||x-f(P)||_1=o(||x||_1)$?

(4) \emph{Boundary.} For which polytopes $P\in \mathcal{P}^d$ does $f(P)$ lie on the boundary of
$\overline{\Conv(f(\mathcal{P}^d))}$? Of $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$?
\end{problem}

For $d=4$ Ziegler~\cite{Ziegler-semigroup} showed that
the limits of the rays spanned by $f(\mathcal{P}^d)$ in $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$ form a convex set; this is open for $d>4$.
Possibly all rays in $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$ are limit rays, which is equivalent to a YES answer to (1,3); and just to (1) if restricting to the extremal rays.

As for (1') for $d=4$, it is not known if the \emph{fatness} parameter
$\frac{f_1+f_2}{f_0+f_3}$ is bounded above by some constant $C$.
If not, then $\overline{\Cone_{f(\sigma^4)}(f(\mathcal{P}^4))}$ would be determined, with exactly 5 facets~\cite{Bayer-flag_dim_4, Eppstien-Kuperberg-Ziegler:fat}.
Ziegler~\cite{Ziegler-fatness} showed that if $C$ exists then $C\ge 9$.

Similar questions to those in Problem~\ref{prob:polytope-density} can be asked about the set of \emph{flag} $f$-vectors of $d$-polytopes and again are open for $d\ge 4$ (and known for $d\le 3$ by Steinitz~\cite{Steinitz1906}; there the flag $f$-vector is determined by the $f$-vector, see the $cd$-index below).

For $\mathcal{F}$ as above, let $\flag(\mathcal{F})$ be the set of flag $f$-vectors of elements in $\mathcal{F}$, counting the number of chains occupying each subset of ranks $S\subseteq [d]$ (called $S$-chains).
Billera and Ehrenborg~\cite{Billera-Ehrenborg:cdMonotonicity} proved that the simplex $\sigma^d$ minimizes all components of the flag $f$-vector among $d$-polytopes, so we choose it as the apex and consider the cone $\overline{\Cone_{\flag(\sigma^d)}(\flag(\mathcal{P}^d))}$ in the flag analog of Problem~\ref{prob:polytope-density}.

For the larger family of regular CW $(d-1)$-dimensional spheres the situation is better understood.
 Denote by $\mathcal{W}^d$ the family of face posets of regular CW $(d-1)$-spheres, and let $D^d\in \mathcal{W}^d$ be the dihedral $(d-1)$-sphere -- it has exactly two cells in each dimension up to $d-1$; then $D^d$ minimizes the number of $S$-chains for any $S\subseteq [d]$.
Combining a construction of Stanley~\cite{Stanley-cd} with the nonnegativity of the $cd$-index proved by Karu~\cite{Karu-cd}, gives the following known analog of Theorem~\ref{obs:simp.density}(1).

\begin{proposition}\label{obs:CW-density}
 $W_d:=\overline{\Conv(\flag(\mathcal{W}^d))}=\overline{\Cone_{\flag(D^d)}(\flag(\mathcal{W}^d))}$ is a simplicial cone of dimension $c_d-1$, for $c_d$ the $d$th Fibonacci number (e.g. $c_4=5$).
\end{proposition}

The dimension $c_d-1$ was found earlier by Bayer and Billera~\cite{Bayer-Billera:generalizedD-Srelations}, and holds also for the smaller cone $\overline{\Cone_{f(\sigma^d)}(\flag(\mathcal{P}^d))}$; see also~\cite{Kalai:NewBasis}.

The flag analogs of Theorem~\ref{obs:simp.density}(2--4) are open for  $\mathcal{W}^d$, to be
discussed in Sec.~\ref{subsec:cd}.

\subsection{Computational complexity}
Computational complexity gains importance in Enumerative Combinatorics in recent years, see Pak's ICM paper~\cite{Pak-ICM} for a recent survey.
Yet, this perspective is still largely missing in $f$-vector theory.

Fix $d$ and
consider the following decision problems: given a vector $v\in \mathbb{Z}^d_{\ge 0}$ (resp. $v\in \mathbb{Z}^{2^d}_{\ge 0}$), does $v=f(P)$ (resp. $v=\flag(P)$) for some $P\in \mathcal{F}$?

For $\mathcal{F}=\mathcal{P}^d$ this is decidable, by finding all combinatorial types of $d$-polytopes with $n$ vertices -- see Gr\"{u}nbaum's book~\cite[Sec.5.5]{Grunbaum:ConvexPolytopes-03} for a proof using Tarski's elimination of quantifiers theorem.
Using the existential theory of the reals, e.g.~\cite{Canny-exist_reals, Renegar-exist_reals_ICM}, gives an algorithm that runs in time double exponential in size of the encoding of $v$ (in binary, on a deterministic Turing machine).

For $\mathcal{F}=\mathcal{P}_s^d$ this is \emph{effectively} decidable,
namely:
For a vector $v=(v_1,\ldots, v_d)\in \mathbb{Z}^d_{\ge 0}$ denote $N(v):=\sum_{i=1}^{d}\lceil\lg_2(v_i)\rceil$, the number of bits in its encoding in binary. Then,
\begin{theorem}\label{obs:g-effective}
Deciding if $v\in f(\mathcal{P}^d_s)$ can be done in polynomial time in $N(v)$.
\end{theorem}

\begin{problem}\label{prob:decide-f}
Can deciding whether $v\in f(\mathcal{P}^d)$ be done in polynomial time in $N(v)$?
\end{problem}

Recognizing the cone $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$ may turn out undecidable:
\begin{problem}~\label{prob:cone-comput}
Fix $d\ge 4$. Is the following problem decidable?: given a hyperplane $H$ through $f(\sigma^d)$, does it support the cone $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d))}$, or contain an interior ray of it?
\end{problem}

As mentioned, for $d=4$, if fatness of $4$-polytopes is unbounded then the decision problem is easy.

The analogs of Problems~\ref{prob:decide-f} and~\ref{prob:cone-comput} for flag-$f$ vectors of $d$-polytopes are open; likewise for Problem~\ref{prob:decide-f} for regular CW $(d-1)$-spheres. Considering the larger family of Gorenstein* posets, their recognition is decidable and we obtain:
\begin{proposition}\label{obs:decideGorenstein*}
Deciding if $v$ is the flag $f$-vector of a Gorenstein* poset can be done in doubly exponential time in $N(v)$.
\end{proposition}

Is there an effective decision algorithm? In the case $d=4$ the flag $f$-vectors in $\mathcal{W}^4$ are characterized~\cite{Murai-Nevo:rank5cd}; yet it is not clear whether the numerical conditions given can be verified effectively; see Problem~\ref{prob:cd-hardness}.

\section{Preliminaries}
\subsection{$g$-numbers} For $P\in \mathcal{P}^d_s$ with the convention of the introduction, $f_i(P)$ denotes the number of rank $i$ (i.e. $(i-1)$-dimensional) faces of $P$. Define the numbers $h_i(P)$ ($i=0,1\ldots,d$)
by
$$x^d \sum_{i=0}^d h_i(P)(\frac{1}{x})^i =
(x-1)^d \sum_{i=0}^d f_{i}(P)(\frac{1}{x-1})^i.$$
Note that the \emph{$f$-vector} of $P$, $f(P)=(f_0,\ldots,f_{d})$, and its \emph{$h$-vector}
$h(P)=(h_0,h_1,\ldots,h_d)$, are obtained one from the other by applying an invertible linear transformation. Thus, the following theorem indeed characterizes the face numbers of simplicial polytopes.
\begin{theorem}[$g$-theorem~\cite{BilleraLee:SufficiencyMcMullensConditions-1981, Stanley:NumberFacesSimplicialPolytope-80}]\label{thm:g-thm}
An integer vector $h=(h_0,\ldots,h_d)$ is the $h$-vector of
a simplicial $d$-polytope iff the following two conditions hold:

(1) $h_i=h_{d-i}$ for every $0\leq i\leq \lfloor\frac{d}{2}\rfloor$, and

(2) $(h_0=1,h_1-h_0,\ldots,h_{\lfloor\frac{d}{2}\rfloor} - h_{\lfloor\frac{d}{2}\rfloor -1})$ is an M-sequence.
\end{theorem}

\subsection{Gorenstein* posets.}
 A poset $P$ with minimum $\hat{0}$ and maximum $\hat{1}$ is \emph{Gorenstein*} if the reduced order complex $\mathcal{O}(P)$, consisting of all chains in $P\setminus\{\hat{0},\hat{1}\}$, is a Gorenstein* simplicial complex. Namely, for any face $F\in \mathcal{O}(P)$ including the empty one, the link $\lk_{\mathcal{O}(P)}(F)$ has dimension $\dim(\mathcal{O}(P))-|F|$ and is homologous to a rational $(\dim(\mathcal{O}(P))-|F|)$-sphere.
For example, all regular CW spheres are Gorenstein*, thus also all polytope face lattices.

\subsection{$cd$-index.}
For fixed $d$ and $P\in \mathcal{W}^d$, or any Gorenstein* poset of rank $d+1$, we recall its $cd$-index, introduced by Fine.
For a word $w=w_1\cdots w_d$ over alphabet $\{\aaa, \bb\}$, let $S(w):=\{i:\ w_i=b\}$ and for a subset $S\subseteq [d]$ let $w(S)$ be the unique word $w$ over $\{\aaa, \bb\}$ with $d$ letters such that $S(w)=S$.
Define polynomials in non-commuting variables $\Gamma_P(\aaa,\bb):=\sum_{S\subseteq [d]}f_S(P)w(S)$ and $\Psi_P(\aaa,\bb):=\Gamma_P(\aaa - \bb, \bb)$.
It turns out that for $\cc=\aaa+\bb$ of degree $1$ and $\dd=\aaa\bb+\bb\aaa$ of degree $2$, $\Psi_P(\aaa,\bb)=\Phi_P(\cc, \dd)$; this uniquely defined polynomial $\Phi_P$ of homogenous degree $d$ in non-commuting variables $\cc$ and $\dd$ is called the $cd$-index of $P$.
Stanley~\cite{Stanley-cd} proved for $P\in \mathcal{P}^d$, and Karu~\cite{Karu-cd} for any Gorenstein* poset, that:
\begin{theorem}\label{thm:cd>=0}
For any Gorenstein* poset $P$, all coefficients of its $cd$-index $\Phi_P$ are nonnegative.
\end{theorem}
For $B_2$ the boolean lattice on two atoms, $Q_m$ the face poset of the $m$-gon,
and any $cd$-word $w=w_1\cdots w_k$, Stanley~\cite{Stanley-cd} considered the join poset $P_{w,m}=P_1*\ldots* P_k$ where $P_i=B_2$ if $w_i=\cc$ and $P_i=Q_m$ if $w_i=\dd$. It is a regular CW sphere as a join of such. As $\Phi_{P*Q}=\Phi_P\Phi_Q$ holds for any posets $P,Q$ admitting a $cd$-index, Stanley
concluded that when $m$ approaches infinity the coefficient vector of $\Phi_{P_{w,m}}$ approached the ray spanned by the $w$th coordinate.
This explains Proposition~\ref{obs:CW-density}.

\section{Proofs and Discussion}\label{sec:3}
\subsection{Consequences of the $g$-theorem.}
\begin{proof}[Proof of Theorem~\ref{obs:g-effective}]
Recall the $g$-theorem, Theorem~\ref{thm:g-thm}.
Denote $g_i=h_i-h_{i-1}$ for $0<i\le \lfloor d/2\rfloor$.
Checking whether $(1,g_1,\ldots,g_{\lfloor d/2\rfloor})$ is an M-sequence can be done in polynomial time in the size of the encoding of $g:=(g_1,\ldots, g_{\lfloor d/2\rfloor})$ in binary. Indeed, we recall the trivial algorithm one needs to run: (i) for each $i$ produce the $i$th Macaulay representation (see e.g. \cite{Stanley:CombinatoricsCommutativeAlgebra-96} for a definition) of $g_i$ in $\poly(\lg_2 g_i)$-time, (ii) then check if the Macaulay inequalities $g_i^{<i>}\ge g_{i+1}$ hold in $\poly(\max(\lg_2 g_i, \lg_2 g_{i+1})$-time. This verifies Theorem~\ref{obs:g-effective}.
\end{proof}

\begin{proof}[Proof of Theorem~\ref{obs:simp.density}]
The cone $\overline{\Cone_{f(\sigma^d)}(f(\mathcal{P}^d_s))}$ is affinely equivalent to the $g$-cone with apex the origin $\overline{\Cone_0(g(P):\ P\in \mathcal{P}^d_s)}$, which is simply the nonnegative orthant $A_{\lfloor d/2\rfloor}$ in $\mathbb{R}^{\lfloor d/2\rfloor}$. Thus we verify Theorem~\ref{obs:simp.density} by considering the analogous statements for $g$-vectors $g(P)$ and the cone $A_{\lfloor d/2\rfloor}$ rather than $f$-vectors $f(P)$ and the cone $C_d$.

The McMullen-Walkup polytopes~\cite{McMullenWalkup:GLBC-71} approach the extremal rays of $A_{\lfloor d/2\rfloor}$, verifying (1).

For (2), first recall the \emph{connected sum} construction (with respect to a given facet): for two  $d$-polytopes $P_1$ and $P_2$, after applying a projective transformation to one of them, they can be
glued along a common facet (namely, $(d-1)$-face) $\sigma$ to form a new convex $d$-polytope $P=P_1\#_{\sigma}P_2$. Combinatorially, the face lattices are related by
  $\partial P=(\partial P_1\cup_{\sigma}\partial P_2)\setminus \{\sigma\}$.
  Note that on the level of face lattices, the operations $\#_{\sigma}$ are associative and commutative, so we omit the order of summands and of operations from the language.

Now, take connected sum of an appropriate number of copies of appropriate  McMullen-Walkup polytopes  to show that any ray in $A_{\lfloor d/2\rfloor}$ is a limit of a sequence of distinct rays spanned by the $g(P)$ in $A_{\lfloor d/2\rfloor}$.
Indeed, the $g$-vectors sum up under connected sum: $g(P_1\#_{\sigma} P_2)=g(P_1)+ g(P_2)$.

More strongly, for (3) one requires the M-sequence inequalities in the $g$-theorem:
consider the vector $x(a)=(0,0,\ldots,0,a)$ in $A_{\lfloor d/2\rfloor}$ for $a>>1$ and the least $M$-sequence with respect to the reversed lexicographic order such that its $\lfloor d/2 \rfloor$th coordinate equals $a$, denoted
$M(a)$. The Macaulay inequalities show that $||x(a)-M(a)||_1=\Theta(a^{\frac{\lfloor d/2\rfloor -1}{\lfloor d/2\rfloor}})$ (for all $d\ge 2$).
Further, it follows that for any vector $x=(x_1,x_2,\ldots,x_{\lfloor d/2\rfloor})\in A_{\lfloor d/2\rfloor}$ there exists an $M$-sequence $M(x)$ with
$||x-M(x)||_1=O(||x||_1^{\frac{\lfloor d/2\rfloor -1}{\lfloor d/2\rfloor}})$, e.g. by repeating the above argument for the coordinate vectors $x_ie_i$ and summing up.
No better estimate is possible: if $M=(v_1,v_2\ldots,v_{\lfloor d/2\rfloor})\in A_{\lfloor d/2\rfloor}$ is an $M$-sequence with $||x(a)-M||_1=o(a^{1-\frac{1}{\lfloor d/2\rfloor}})$ then $v_{\lfloor d/2\rfloor -1}=o(a^{1-\frac{1}{\lfloor d/2\rfloor}})$ so by the Macaulay inequalities $v_{\lfloor d/2\rfloor}=o(a)$, and we get the contradiction $||M-x(a)||_1\ge |a-o(a)|=\Omega(||x(a)||_1)$.

For (4) consider the Macaulay conditions again. We see that the only $g$-vectors of simplicial $d$-polytopes $g(P)$ on the boundary of $A_{\lfloor d/2\rfloor}$ are those of the form $(a_1,\ldots,a_k,0,\ldots, 0)$ for positive $a_i$s, corresponding exactly to $(k-1)$-stacked polytopes by~\cite{McMullenWalkup:GLBC-71, Murai-Nevo:GLBC}.
The only $g(P)$ on an extremal ray are of the form $(a_1,0,\ldots, 0)$, corresponding to $1$-stacked polytopes by the
Lower Bound Theorem~\cite{Barnette:LBT-73, Kalai:LBT}. This completes the verification of Theorem~\ref{obs:simp.density}.
\end{proof}

\subsection{$cd$-index of regular CW spheres.}\label{subsec:cd}
For a flag analog of Theorem~\ref{obs:simp.density}(2--4) for $W_d$
we first linearly transform to the $cd$-nonnegative orthant $A_{c_d-1}$ in $\mathbb{R}^{c_d-1}$ and consider $cd$-indices rather than flag $f$-vectors.
As for (2),
 we lack the needed connected sum type constructions for complexes in $\mathcal{W}^d$. For example, is it possible to modify a poset $P\in \mathcal{W}^d$ to another poset $P'\in \mathcal{W}^d$ such that (i) $P'$ has a top dimensional cell whose boundary is dihedral (i.e.  isomorphic to $D^{d-1}$), and (ii) the coefficients are close, namely, for any $cd$-word $w$, $|[w]_{\Phi_{P'}}-[w]_{\Phi_P}|=o(\Phi_P(1,1))$?

 If Yes then ray density as asserted in (2) would follow, by taking connected sum over dihedral cells.

As for (4),
the inequality on the $cd$-index by Murai and Yanagawa~\cite[Thm.1.4]{Murai-Yanagawa} shows that the only extremal rays in $W_d$ realized by posets in $\mathcal{W}^d$ are those corresponding to $cd$-words with a single $\dd$.
For $d=4$, thanks to a complete characterization of the possible $cd$-indices~\cite{Murai-Nevo:rank5cd}, (4) is answered. In particular,
on the facet of $A_{c_4-1}$ with coordinate coefficient $[\cc\dd\cc]=0$ the points are sparse. They in fact lie in ``lower dimension", where the $\dd^2$ coordinate is uniquely determined by the coordinates $\cc^2\dd$ and $\dd\cc^2$ via the coefficient equation $[\dd^2]=[\cc^2\dd][\dd\cc^2]$.

Next we consider the  characterization in~\cite{Murai-Nevo:rank5cd} from the computational complexity point of view; the part relevant for a potential computational hardness result is:
\begin{theorem}[Murai-N.~\cite{Murai-Nevo:rank5cd}]
Let $\Phi$ be a $cd$-polynomial of homogenous degree $4$ with nonnegative integer coefficients satisfying $[\cc^4]=1$ and $[\cc\dd\cc]=1$. Then $\Phi=\Phi(P)$ for some Gorenstein* poset of rank $5$ (or even regular CW $3$-sphere) iff there exist nonnegative integers $x_1,x_2,x_3$ and $y_1,y_2,y_3$ such that
\begin{equation}\label{eq:cdc=1}
x_1+x_2+x_3=[\cc^2\dd],\  y_1+y_2+y_3=[\dd \cc^2],\  x_1y_1+x_2y_2+x_3y_3=[\cc^2\dd][\dd \cc^2]-[\dd^2].                                                                                \end{equation}
\end{theorem}
\begin{problem}\label{prob:cd-hardness}
Let $N=\lceil\lg_2 [\cc^2\dd]\rceil +\lceil\lg_2 [\dd\cc^2]\rceil +\lceil\lg_2 [\dd^2]\rceil$.
Can it be decided in $\poly(N)$-time whether the diophantine system Eq.~(\ref{eq:cdc=1}) has a solution?
\end{problem}
Deciding in $\exp(N)$-time is trivial. Recall that some binary diophantine quadratics are known to be NP-complete~\cite{Manders-Adleman:NPcompleteQuadrics}.
Next we consider arbitrary Gorenstein* posets.
\begin{proof}[Proof of Proposition~\ref{obs:decideGorenstein*}]
All Gorenstein* posets of fixed rank with given flag $f$-vector of binary bit complexity $N$ can be obtained in $\exp(\exp(N))$-time. Indeed, the total number of possible chains of faces is $\Pi_i f_{\{i\}}=\exp(O(N))$, and each potential poset
corresponds to a subset, so all together we have to consider $\exp(\exp(O(N)))$ number of posets $P$. For each
 $P$ we compute the cellular homology groups over say the field of rationals, for all intervals in $P$; they are $\exp(O(N))$ many. For each interval the computation is polynomial in the size of the interval, so takes $\poly(\exp(O(N)))$ time.
 Proposition~\ref{obs:decideGorenstein*} follows.
 \end{proof}
Possibly a decision can be made in $\poly(N)$-time.

\textbf{Acknowledgements.}
I thank the anonymous referees for helpful suggestions on the presentation.
\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


As business professionals, authors, and consultants, we work in a world in which our faith in our ideas and actions is tested time and time again. When we take a risk by suggesting a new idea and a path that we are convinced will help others grow, we know that we will be opening ourselves up to potential criticism and loss of control. After all, organizations, as we have learned, concentrate on critique and evaluation, not necessarily originality and expression. Even when innovation is considered necessary for organizational survival, private and public organizations often still value linear and well-defined actions and results above the artistic and creative expressions of their workforces. And the spotlight of creative success can be so intense that the members of the workforce don't want to deal with the attention.
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Venturing into an invisible creative space is a nonlinear, messy, unclear process, and it's seen by many organization leaders as an inefficient use of time that shows mixed results. Even when there is an earnest commitment to acquiring and generating fresh new ideas, organizations limit this approach in an effort to keep the ideation and cultivation of sparks tightly controlled. Too much ideation is seen as fluff and vaporware, not something of substance and form.
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"Confidence is like a blooming flower, comes from the ground never doubting its purpose, its existence, its journey." —Marie M.
"Confidence smells like an ocean breeze — coolly, calmly, charismatically persistent." —Peter P.
"Confidence means never denying that which you know from within." —Jim H.
"Spicy to the tongue, beautiful to the eye, gentle to the touch, aromatic to the nose — confidence is." —Lori J.
Oliver Wendell Holmes once said, "What lies behind us and what lies before us are tiny matters compared to what lies within us," suggesting that our real challenge lies within and is often the biggest barrier to making a leap and venturing into a more creative space. Throughout our work and life experiences we have identified several dynamics that influence whether or not we will make a leap and pursue cultivating our creative genius further.
To step into the unknown requires a great deal of confidence. The opposite of confidence is self-doubt. Self-doubt is the part of creative contemplation that says, What if people do not like what I have to suggest? Or, No one is likely to support my idea, or, worse, It's too far-fetched, so why bother even sharing it? Why should I expose myself? Self-doubt is more concerned with impossibility and figuring out ways to defeat our inspirations than encouraging possibility and risk taking. Self-doubt feeds our fear that if we fail we will be alone and exposed and vulnerable. As we said before, organizations value and reward proven and concrete results. Therefore, feeding our creative genius and letting our imagination wander and venture is often perceived as risky.
We learn very early in life that such things as equations, theories, and ideas need proof to be accepted. Consequently, we are concerned with fitting in, staying in a space of certainty and safety rather than venturing into darker, hidden spaces of our imagination and creative passion. We are split between producing clear, tangible, concrete results and pursuing, cultivating, and experimenting with the faint renderings that have been playing out in our minds. The state of our creative genius and whether we break out and venture into unknown territory depends on our willingness to take risks and accept failure as one of the possibilities.
When we asked Rick Dzavik, the former European innovation leader for a large consumer health-care company, if he ever had any doubts about his success and ability to obtain support for his innovation agenda, he smiled and said, "Every day. From the moment we began to conceive and shape a program for building a more innovative culture to actually implementing one, my team and I would frequently question our own actions and even went as far as not trusting our intuition on things because of past experiences. It took a long time to hit our stride, but eventually, as we gained traction, we improved our level of confidence." Of course, Dzavik and his team were hugely successful, even though they still had some doubts along the way. So keep in mind that when you're contemplating whether or not to venture into unknown places, things may feel beyond your reach, similar to Indiana Jones looking across the chasm. It may at first be daunting, but you won't know until you ultimately make the leap.
In work today the stakes are increasingly high. Because of increased competition, high-performance targets, and the vicissitude associated with corporate takeovers and layoffs, our desire and willingness to venture out is shaky at best. And in general, as John Lennon sang so eloquently, "Life is what happens to you while you're busy making other plans," causing you to react and shift your priorities. Without notice, your husband one day declares to you that he hates his job and quits, or your boss informs you that your services are no longer needed and you are out of a job. The emphasis on the bottom line and constant pressure to produce in most modern jobs often make the human psyche the ball in a ping-pong match between our desire to operate in artistic, self expressive ways and our need to conform to the realities of the corporate stage and associated spotlights of tried-and-true behaviors. We want to express ourselves and unleash our creative flow, but we easily give in to self-doubt and retreat into safe behaviors when we need to make a decision or commit to a course of action.
Have you ever had a spark of an idea but suppressed it as quickly as it came to you because of your lack of confidence? Our creative streams are often dammed by a combination of self-doubt and the unconscious, bland expectations of other people and our organizations. Work is perceived as a place of sweat and toil where little or no time is devoted to attracting or advancing energy to creative thought. As a result, we avoid taking the step to release that vital creative spirit we are born with, opting instead to keep it safe and hidden in the dark recesses of our minds.
The next time you have a spark and hesitate to share it with someone else, either at work or at home, imagine that they will not only not judge or criticize it, but instead fully embrace it and help you to realize the spark's full potential! Then go ahead and share it!


A large number of churches attend Spring Harvest as their annual gathering. Bringing a group of family and friends to Spring Harvest is incredibly rewarding, as friends and families gather to encounter God and spend quality time together.
If you've made a booking click below to download the spreadsheet.
Once it is completed please email or post it to the relevant resort as detailed at the bottom of the spreadsheet.
If you're bringing a group to Butlin's in Minehead or Skegness you can find out more information by downloading the Tips and Information sheet via the link below. We have created a number of resources to help make it as easy as possible. The first thing you'll need to do is spread the word and let people know about Spring Harvest. There are a number of promotional tools, including brochures and videos, that will help you to do that.
If you are coming as part of a group and are looking to claim the Group Discount of 16th person comes free, you can register your group via the link below. Once you've registered your group, individual bookings can be assigned to it in order to claim the discount.
Please note Harrogate accommodation is different to Minehead and Skegness. Harrogate is "non-residential" so there is an event ticket to access the programme, and accommodation is booked independently. Click here to find out more.


On Sunday, we went to see Wall-e, another great animation from Pixar. For those of you who haven't seen it already, I might be about to give away the plot, So stop reading now if you don't like spoilers.
Pixar have produced superb high quality digital animation in the past, and this film is up to their usual standard. This time however, the plot is a little darker and more foreboding than previous Pixar features. The world as we know it has been buried under mounds of garbage and Earth has become a giant rubbish dump. Humanity have fled the polluted planet and have degenerated into boneless piles of flab, transported around a gargantuan spaceship on hover-chairs, and ministered to by a vast army of automata. On earth all the remaining infrastructure has been crushed by mountains of refuse. The robotic machinery left with the task of the cleanup have broken down. All except for one tiny compactor robot, who continues tirelessly with the insurmountable and seemingly impossible task of sorting and stacking the garbage.
Pretty heavy stuff! Nevertheless, our celluloid hero, Wall-e, who owes a lot to Short Circuit (another hollywood robot), is such a cute endearing little chap, that we soon forget about the rather grim apocalyptic undertones in the plot. Wall-e meets up with EVE, who despite the spelling of her name is addressed as Eva, so I'm not really sure whether she should be called Eve or Eva. Whatever! Eva is a slim, curvaceous, high performance, high-tech machine who looks suspiciously similar to many products designed by Apple. And she's packing heat! Underneath her sleek white casing this gal has some pretty awesome firepower. You would be ill-advised to give her any back-chat. Yet another feisty strong female heroine.
The villain in this movie turns out to be a rogue mainframe (the "Auto-pilot) who I thought bore a striking resemblance to "Colossus", the villain in the novel of the same name by D. F. Jones, which was made into a movie in the early seventies. Since this is a kids' movie "Auto-pilot" is not nearly as murderous and sinister as D. F. Jones' Colossus. However, this latest movie from Pixar does nothing to enhance the reputation of mainframes, who often get to play the bad guy.
Needless to say Wall-e and Eva rekindle the spirit of humanity in the hearts of the humans and together they save the world, well at least in so far as it is possible to save the world after it has been destroyed. Still we are left with the impression that as long as there are humans left alive somewhere in the universe they will carry a vestige of "hope" in their hearts. Or at least we all hope so. In which case you can rest assured that it is quite ok to take your kids along to this movie.
As one would expect, things get rough for our heroes at some stage of the movie. Wall-e is damaged so severely that he seems totally FUBAR! Eva takes his wrecked frame back to his hide-out, a giant rubbish skip, where he has collected "useful" items from the rubbish as he sorted it. This includes Rubik cubes, "Zippo" cigarette lighters, old circuit boards, old iPods etc. It looks like a giant version of your average nerd garage, which offers lots of potential for product placement. Eva finds enough spare parts to repair Wall-e. As he "reboots", we hear a familiar sound. Our ten year old boy, leans over the armrest on my seat and whispers excitedly, "That's the same sound our computer makes!".
Indeed it is! It is the Mac Start-up Chime. A sound buried so deep in the innards of the OS, that it can only be suppressed with a special plugin. So it sounds as if Wall-e boots up under Mac OS X! Well, hardly surprising for a movie made by Pixar. Apple compatible systems seem very popular for space travel. After all, those nasty aliens in Independence Day were Apple compatible (huh?). And other robots have booted with popular operating systems. For example there was poor old Robo-Cop. He actually booted up with MS-DOS! (Yikes! It's amazing that he could do any multi-task operations). The Terminator however, despite his advanced micro-processor hardware seemed to be running a Mainframe Operating System (wouldn't you know it? Super Villain, Mainframe - it's all too obvious).
And you might be forgiven for thinking that all Hollywood mainframes run Microsoft Windows the way they so easily fall victim to viruses injected from Windows workstations.
Still if you can't suspend belief for ninety minutes in a cinema, what hope is there? Despair is our only hope! Just what we need to take our minds of the technical depression that will no doubt follow close on the heels of the technical recession we are currently experiencing.


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Read our special report "On Tech Unemployment and the Labor vs Capital Balance of Power" by Nikola Danaylov at https://lifeboat.com/ex/on.tech.unemployment
Capital needs labor to operate, to create a return on investment and, ultimately, to grow. Labor needs capital for wages. Each needs the other and none can do it alone. So labor needs capital as much as capital needs labor. And, while the labor vs capital balance of power has fluctuated closer to one or the other throughout history, classical economics claims that, given their mutual co-dependence, in the long run, we end up (more-or-less) in an equilibrium. This equilibrium is, at least in theory, an ideal win-win scenario where capital is happy that its return on investment is growing and labor is happy that its wages are rising…
Our Alexandra Bause, Ryan Bethencourt, Judith Campisi, Keith Comito, Aubrey de Grey, Brian M. Delaney, Peter Fedichev, Steven A. Garan, Vadim Gladyshev, Vera Gorbunova, Andrei Gudkov, Steve Hill, Steve Horvath, Brian Kennedy, Michael Kope, Tim Maupin, Elena Milova, Joshua Mitteldorf, Alexey Moskalev, Matthew O'Connor, Robert Shmookler Reis, Paul A. Spiegel, Michael Rose, and Natasha Vita-More will be speaking/participating.
Read "Cracking the Aging Code: The New Science of Growing Old — And What It Means for Staying Young" at https://amzn.to/2WxPRz1
Jill Tarter joins our Astrobiology/SETI Board. Jill is known for her work on the Search for ExtraTerrestrial Intelligence (SETI). She holds the Emeritus and Bernard M. Oliver Chair for SETI at the SETI Institute and is the former director of the Center for SETI Research and has been with SETI since 1984.
Jill's astronomical work is illustrated in Carl Sagan's novel Contact. In the film version of Contact, the protagonist Ellie Arroway is played by Jodie Foster. Jill conversed with the actress for months before and during filming, and Arroway was largely based on her work.
Learn more at https://lifeboat.com/ex/bios.jill.cornell.tarter
Lon Anderson joins our blog team with the post "US invests hundreds of millions to produce Covid-19 vaccines" at https://lifeboat.com/blog/2020/05/us-in...vaccines
Steve Harris joins our blog team with the post "Functional Role of Dietary Intervention to Improve the Outcome of COVID-19: A Hypothesis of Work" at https://lifeboat.com/blog/2020/05/funct...-of-work
Jeremy Mancuso joins our blog team with the post "Our weird behavior during the pandemic is messing with AI models" at https://lifeboat.com/blog/2020/05/our-w...i-models
"The 12 Longest Living Animals That Roam the Earth" by Shailesh Prasad at https://lifeboat.com/blog/2020/05/the-1...he-earth
"2D Nano Sandwich Is Deliciously Useful for Detecting Biomolecules" by Genevieve Klien at https://lifeboat.com/blog/2020/05/2d-na...olecules
"A Hidden Pandemic in our Mouths?" by Eithen Pasta at https://lifeboat.com/blog/2020/05/a-hid...r-mouths
"Animation: The James Webb Space Telescope is folded to fit into its rocket" by Alberto Lao at https://lifeboat.com/blog/2020/05/anima...s-rocket
"As Hospitals Lose Revenue, More Than A Million Health Care Workers Lose Jobs" by Brent Ellman at https://lifeboat.com/blog/2020/05/as-ho...ose-jobs
"Bat 'super immunity' may explain how bats carry coronaviruses" by Nicholi Avery at https://lifeboat.com/blog/2020/05/bat-s...aviruses
"Bitcoin Acceptance Skyrockets in Venezuela Amid Hyperinflation Crisis" by Fyodor Rouge at https://lifeboat.com/blog/2020/05/bitco...n-crisis
"Bizarre new species discovered… on Twitter" by Roderick Reilly at https://lifeboat.com/blog/2020/05/bizar...-twitter
"Blood Factors Reverse Epigenetic Age" by Montie Adkins at https://lifeboat.com/blog/2020/05/blood...etic-age
"Can Human Minds Be Reduced to Computer Programs?" by Paul Battista at https://lifeboat.com/blog/2020/05/can-h...programs
"Chinese Official Confirms That China Ordered Labs To Destroy Coronavirus Samples" by Omuterema Akhahenda at https://lifeboat.com/blog/2020/05/chine...-samples
"The doomsday bunker market is thriving amid the coronavirus pandemic" by Derick Lee at https://lifeboat.com/blog/2020/05/the-d...pandemic
"Efficient, 'green' quantum-dot solar cells exploit defects" by Quinn Sena at https://lifeboat.com/blog/2020/05/effic...-defects
"Facebook trains AI on 'hateful memes'" by Tracy R. Atkins at https://lifeboat.com/blog/2020/05/faceb...ul-memes
"FDA OKs 1st Stem Cell Human Trial for COVID-19" by Lon Anderson at https://lifeboat.com/blog/2020/05/fda-o...covid-19
"First Observation of a Pauli Quantum Crystal" by Genevieve Klien at https://lifeboat.com/blog/2020/05/first...-crystal
"Gov. Cuomo: 'Shocking' 66% of new COVID-19 hospitalizations in NY are people who had been staying home" by Lon Anderson at https://lifeboat.com/blog/2020/05/gov-c...ing-home
"How SpaceX's Crew Dragon Demo-2 mission will work in 13 steps" by Genevieve Klien at https://lifeboat.com/blog/2020/05/how-s...13-steps
"How X-Ray Images Of Ancient Microfossils Will Help Identify Life On Mars" by Bruce Dorminey at https://lifeboat.com/blog/2020/05/how-x...-on-mars
"Important! The largest study yet on COVID-19 fatality shows top risks" by Nicholi Avery at https://lifeboat.com/blog/2020/05/impor...op-risks
"In 1110, The Moon Vanished From The Sky. We Might Finally Know What Caused It" by Roderick Reilly at https://lifeboat.com/blog/2020/05/in-11...aused-it
"Is Elon Musk going to Move Tesla and SpaceX to Texas?" by Bill D'Zio at https://lifeboat.com/blog/2020/05/is-el...to-texas
"Israel's Argaman Technologies develops a cotton that kills germs and viruses on contact" by Omuterema Akhahenda at https://lifeboat.com/blog/2020/05/israe...-contact
"Lab-Grown Mini Kidneys Are Bringing Science Closer to Custom Organs" by Lola Heavey at https://lifeboat.com/blog/2020/05/lab-g...m-organs
"Life on Mars? Will we find it? Will we colonize the Red Planet?" by Lola Heavey at https://lifeboat.com/blog/2020/05/life-...d-planet
"Men have high levels of enzyme key to COVID-19 infection, study finds" by Nicholi Avery at https://lifeboat.com/blog/2020/05/men-h...dy-finds
"Mind-controlled prostheses that 'feel' for real" by Saúl Morales Rodriguéz at https://lifeboat.com/blog/2020/05/mind-...for-real
"Moderna's coronavirus vaccine just showed signs of success in a preliminary study, raising early hopes in the fight against the pandemic" by Quinn Sena at https://lifeboat.com/blog/2020/05/moder...pandemic
"Nanotechnology: Life-Changing Innovation or Just Too Good to Be True?" by Brent Ellman at https://lifeboat.com/blog/2020/05/nanot...-be-true
"NASA's Curiosity Mars Rover Snaps Its Highest-Resolution Panorama Yet" by Alberto Lao at https://lifeboat.com/blog/2020/05/nasas...rama-yet
"Out Of This World! Tom Cruise Plots Movie To Shoot In Space With Elon Musk's SpaceX" by TJ Wass at https://lifeboat.com/blog/2020/05/out-o...s-spacex
"Reversing age: dual species measurement of epigenetic age with a single clock" by John Davies at https://lifeboat.com/blog/2020/05/rever...le-clock
"SARS antibodies can block COVID-19 infection: study" by Quinn Sena at https://lifeboat.com/blog/2020/05/sars-...on-study
"Scientists are making human-monkey hybrids in China" by Omuterema Akhahenda at https://lifeboat.com/blog/2020/05/scien...in-china
"Scientists engineered mice that are 4 percent human" by Brent Ellman at https://lifeboat.com/blog/author/brent-ellman
"Scientists Found A Way to Disable a Gene Responsible For Obesity: Worry About Getting Too Fat No More?" by Tracy R. Atkins at https://lifeboat.com/blog/2020/05/scien...-no-more
"Sony unveils first built-in AI image sensors" by Saúl Morales Rodriguéz at https://lifeboat.com/blog/2020/05/sony-...-sensors
"Sorrento finds a coronavirus antibody that blocks viral infection 100% in preclinical lab experiments" by Jeremy Mancuso at https://lifeboat.com/blog/2020/05/sorre...eriments
"SpaceX animation show how new 'Starship' will transport people to Mars" by Alberto Lao at https://lifeboat.com/blog/2020/05/space...-to-mars
"SPICA: an infrared telescope to look back into the early universe" by Roderick Reilly at https://lifeboat.com/blog/2020/05/spica...universe
"Star Wars and Space — May the 4th be with you" by Bill D'Zio at https://lifeboat.com/blog/2020/05/star-...with-you
"These drones will plant 40,000 trees in a month. By 2028, they'll have planted 1 billion" by Shailesh Prasad at https://lifeboat.com/blog/2020/05/these...-billion
"This Young Rat Plasma Just Reversed Aging 54% in Old Rats, Say Scientists" by John Davies at https://lifeboat.com/blog/2020/05/this-...ientists
"Transhumanism — The Future Of Mankind" by Michael Dodd at https://lifeboat.com/blog/2020/05/trans...-mankind
"Two Studies Just Revealed How Twisted Graphene Gets Even Weirder at a 'Magic Angle'" by Saúl Morales Rodriguéz at https://lifeboat.com/blog/2020/05/two-s...ic-angle
"Universities last in line as Europe eases coronavirus lockdown" by Steve Nichols at https://lifeboat.com/blog/2020/05/unive...lockdown
"Virologist hospitalized with coronavirus believes he got it through his eyes" by Lon Anderson at https://lifeboat.com/blog/2020/05/virol...his-eyes
"What If We Could Build an Alderson Disk?" by Shailesh Prasad at https://lifeboat.com/blog/2020/05/what-...son-disk
"What is China's cryptocurrency alternative sovereign digital currency?" by Derick Lee at https://lifeboat.com/blog/2020/05/what-...currency
"Yes, COVID-toe. A bizarre post-coronavirus symptom causes purple fingers, toes … maybe even ears" by Fyodor Rouge at https://lifeboat.com/blog/2020/05/yes-c...ven-ears
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redpajama_set_name: RedPajamaCommonCrawl


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In First Person
Support us Yesh Din site A66881BC-5DE1-4834-9D6C-FCA2EC46DA72 Created with sketchtool.
A Body of Testimonies
Settler violence impacts the daily routine of Palestinians in the occupied Palestinian territory. In first person brings the testimonies of Palestinians in their own words as documented by Yesh Din since 2005, describing the violence and ongoing harm to their person, property and land by Israeli settlers in the West Bank. In first person also illustrates Israeli authorities' inadequate investigation of incidents and treatment of perpetrators when the victims of offences are Palestinian.
Read More 6CECF2D1-356B-4344-A3FF-2AB5F9A57E45 Created with sketchtool.
Uprooting of 370 olive saplings
Date of the incident
Incident site
Type of offense
Damage to property
Investigation file closed: offender unknown
KK, 55, Jit
My grandfather owned a 335 dunam plot. It's called Qa'adat Halaweh. The plot is registered in my father's name. The land is about 200 meters north of the village of Jit. It borders the road going up to the settlement of Kedumim.
Four months ago, in January, the organization Rabbis for Human Rights donated about 400 olive saplings. They joined us and we planted the saplings on the plot together.
Two months later, in March, at 8 am we went to the field to plow, escorted by volunteers from Rabbis for Human Rights, we were about ten people, relatives and volunteers. While we worked, a yellow car with Israeli plates drove up the road towards Kedumim, stopped by us for a few moments and then drove on. I think the car belonged to DV, head of Kedumim council. I know her and I've seen her driving such a car.
About five minutes later, two settlement security vehicles stopped on the road by us, one was white and one was blue, I recognized them. Security vehicles patrol the road, driving off and returning and appearing from time to time.
About ten minutes later, two military hummer vehicles arrived. About ten soldiers got out, two looked like high-ranking officers. One of these officers turned to me and asked me in Arabic: "Who owns this land?" I said I own the land. The officer told me, this is a closed military zone for Israelis. The volunteers who came with us left.
Five of us were left, myself and my family with the tractor. We continued to plow. The cars drove off and three soldiers stayed to guard us. The settlement security vehicles continued to patrol, appearing and disappearing about every 15 minutes. We worked until 4 pm and then we went home.
Two months later, on May 6, 2007 in the afternoon, I went to my land to plow. I brought water so I could water the saplings. I was astounded to discover that all 370 saplings had been uprooted. Some of the saplings were taken away. There were bits of broken branches and the remains of dry saplings. Judging from the dryness of the saplings there, it looked like they had been uprooted a month or two earlier.
While I was standing there stunned, taking in the sight of it, a settlement security vehicle pulled up. That same white vehicle that was patrolling last time. The car stopped on the road. We didn't say anything to each other, I left while the vehicle stayed where it had stopped.
Two days later, on May 8, 2007, I went to Kedumim Police to file a complaint. The next day, after coordinating with the police, I waited on my land and at 5 pm a police vehicle and a military jeep arrived. There were two policemen in the police car, and an officer and a driver in the jeep. I showed them the damage, they photographed me in the field with the remains of the uprooted saplings. The policeman asked me what the distance was between the saplings, I said 4-7 meters.
Suddenly, settlers driving ATVs drove up. They drove down from the settlement Kedumim Illit and stopped about 300 meters from us. I was about to continue presenting the damage to the policemen, but once the settlers showed up, the policemen rushed to cut things short and leave. It seemed they were running away from the settlers.
Law Enforcement Authorities' decision upon conclusion of investigation
On October 1, 2007, the police informed Yesh Din that the investigation file was closed due to "offender unknown".
Yesh Din
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Click on an alumni listing from Georgetown, KY to find more information about the person.
The listing of alumni from Georgetown, KY includes graduates from 7 schools. To filter results, select a Georgetown, KY high school using the links to the right. The Georgetown alumni list on this page come from a variety of sources. Clicking one of your friends will give you locations that you can get back in touch with the fellow graduate. To view alumni that graduated in Georgetown around your class year, enter your graduation year in the search box at the top of the page. You may also be able to find friends close to your home town. We also have listings for graduates from Midway, KY, Lexington, KY, or Sadieville, KY.
Approximately 2,200 of residents in Georgetown (8%) are the normal age for attending high school (15-19). Also, around 1,000 Georgetown residents (4%) are the average age for high school seniors (18-19). Population stats are from the United States Census Bureau.


Android: GTD-style to-do manager Remember The Milk announced a major update to its Android app today, including an overhauled interface with new features and a free version of the app with basic features for all users. Remember The Milk 2.0 now allows you to edit multiple tasks at once, offers a dashboard that lets you skip quickly between items due today, tomorrow or later, and even a reminders bar so you're always aware of what's next.
The Remember The Milk Android app used to be free only if you had a $US25/year Pro account; now the app is free to all users, but only basic features are available to free users. Free users will be able to use the app, but they can only sync with RTM servers once every 24 hours, and they have to do it manually. Pro users get unlimited and automatic syncing, as well as home screen widgets, location-and-time-based reminders and more.
The update obviously benefits pro users the most, but offering a free version with basic features is a good way to get new users (or people who have tried RTM but gave up on it) to give it a shot. What do you think: is the update enough to make you take another look? Share your thoughts in the comments.
No... considering the reduced feature set there are far better free options for android users. Like Astrid for example.


The Ethiopian neighborhood in Gedera runs a few streets wide, and most residents came in the large waves of immigration in 1991 and afterwards. Prior to their arrival in Israel, many of the Ethiopians lived an agrarian lifestyle, working the land and growing their own food. When they were resettled in Israel, they were put in apartment buildings – cut off from that part of themselves. The community gardens help reestablish that bond. In this way, the gardens serve to strengthen the community – especially the elders, who tend to have the most trouble adapting to life in Israel.
There's another benefit too, says Yuvi Tashome, a Gar'in member, "The gardens are an opportunity for all the residents of a building to come together for a joint purpose. It is often the first time that they really meet and see who they are living with. They go through a long process of deciding together what it is that they want to see happening under their building. Through this process they develop skills, cooperate, and become a group that is influencing their own environment".
Community gardens are becoming increasingly popular in Israel. Gardens in Tel Aviv and Jerusalem neighborhoods are flourishing and new ones are springing up in many other cities around the country. The Yahel Social Change Program recently visited the "Earth's Promise" community garden in Be'er Sheva – an amazingly lush garden adjacent to an immigrant absorption center. In this garden, each family receives a small plot of land on which they can grow food for their own consumption. The plots are full of Ethiopian vegetables and herbs which the recent immigrants are unable to find in local stores. In this way, the gardens serve as a bridge between past and present.
Friends By Nature has plans to build a greenhouse and develop a three dunam (roughly an acre) parcel that was recently donated to them by the city in Gedera. The plan is to offer plots to committed families who will grow fresh vegetables and herbs – similar to the "Earth's Promise" garden. Future Yahel Social Change Program participants will have opportunities to work alongside community members in making that dream a reality.


Every woman desires picture perfect, glowing skin. Whether you are a student, homemaker, or a working professional, it is very important to have good skin.
one of the other many benefits of coconut oil is that it contributes to good dental health. this is so because it aids in the absorption of calcium in the body and Calcium is an important component of our teeth. It also works in stopping tooth decay.
The white sap from this common weed, also known as petty spurge, was described by Nicolas Culpeper's Complete Herbalist (1826) as "a good treatment for warts".
Don't try this at home, however, as its also an irritant.
Milkweed made its way from its native Europe to Australia, where biochemist Dr Jim Aylward had it in his garden.


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Home / Featured / 2013 General Assembly of the Orthodox Presbyterian Church Begins
2013 General Assembly of the Orthodox Presbyterian Church Begins
The OPC General Assembly is meeting at St. Mary's College in Moraga, California
Written by David Graves | Friday, June 7, 2013
There were three pastors nominated for moderator: Archibald Allison, Larry Westerveld, and Jeffrey Landis. After the nomination speeches, balloting was to take place though electronic voting devices but they did not work; paper ballots were provided for the delegates. Jeffrey Landis, pastor of Covenant Presbyterian Church in San Jose, Calif., was elected as moderator.
The 80th General Assembly of the Orthodox Presbyterian Church is meeting at St. Mary's College in Moraga, California, from June 5-11, 2013. This is the first OPC General Assembly in California in 23 years, and the first time it has been held in northern California.
Retiring Moderator Tony Curto convened the 80th General Assembly and preached the sermon for the opening worship service. The stated clerk, the Rev. George Cottenden, called the roll and declared a quorum was present with 139 commissioners.
It was reported that a shipment of supplies for the GA had been sent on a train that derailed earlier in the week; the Arrangements Committee announced that the supplies had arrived the morning the GA was to begin.
There were three pastors nominated for moderator: Archibald Allison (Presbytery of the Dakotas), Larry Westerveld (Presbytery of Philadelphia), and Jeffrey Landis (Presbytery of Northern California). After the nomination speeches, balloting was to take place though electronic voting devices but they did not work; paper ballots were provided for the delegates. Jeffrey Landis, pastor of Covenant Presbyterian Church in San Jose, Calif., was elected as moderator.
Pastor Landis has pastored Covenant since 1986. After graduating from Reformed Bible College with a BRE, he continued his education at Westminster Seminary in California earning both MAR and M-Div degrees. He has also completed his Doctor of Ministry degree at Reformed Theological Seminary. Landis and his wife Donna have two adult sons, Ben and Joel.
Before the GA recessed its first session, overtures, communications, complaints, and judicial appeals were officially presented to the assembly. The docket for the meeting was adopted.
Members of the assembly were elected to one of 13 Advisory Committees to consider and recommend action on matters during the course of the assembly. The various committees will meet Thursday morning to examine the business of the Church. Then the work of the Assembly will begin Thursday afternoon as the various committees bring their reports before the commissioners.
David Graves is pastor of Trinity Orthodox Presbyterian Church in Franklin, Penn.
The 222nd General Assembly Presbyterian Church…
Jim Wert Elected Moderator of the 43rd PCA General Assembly
James River Presbytery Overtures the PCA 45th GA to…
Western Carolina Presbytery Overtures the PCA 45th…


text:
Litozin is 'next generation' in joint care, says EuroPharma
By Jess Halliday
08-Sep-2005 - Last updated on 19-Jul-2008 at 18:04 GMT
Related tags: Osteoarthritis
EuroPharma is introducing an innovative joint care ingredient
derived from rose hip to the US market, claimed to be even more
effective than glucosamine. The arrival of Litozin is particularly
timely as osteoarthritis sufferers are seeking out natural relief
following the Vioxx safety scandal.
Available in Scandinavian countries for the past two years, Litozin was discovered and developed by small, family run Danish business Hyben Vital.
With five years of scientific research behind it and 13 studies completed to date, Litozin is making its debut on a US market that is hungry for safe and effective solutions.
EuroPharma founder and president Terry Lemerond told NutraIngredients-USA.com that the origins of the ingredient are home-spun. The grandfather suffered from arthritis and began eating rosehip jam, a traditional Scandinavian remedy, to alleviate the pain. He was so impressed by the effects that he started to grow the plant on his farm, and managed to identify the active galactolipid compound (GOPO).
GOPO content varies considerably between different species of rose hip, but Hyben Vital was able to develop a sub-species with the highest possible content.
Its patented drying process ensures that high levels of the compound remain in the finished product. EuroPharma says that conventional processing methods, including sun drying, destroy the GOPO, meaning that little or none of it remains in other commonly-available rose hip products.
Litozin is GRAS (generally recognized as safe) in the United States. "We are going to work with anyone who wants to put it in any kind of food, such as bread, bars or even powders," said Lemerond.
Lemerond takes the credit for introducing the hugely popular joint health ingredient glucosamine to the US market. He explained that glucosamine has a different mechanism of action to Litozin: it rebuilds cartilage but does not act as an anti-inflammatory.
Of the chemical, pharmacological and clinical studies involving Litozin completed to date, the most recent, published in the August 2005 issue of the Scandinavian Journal of Rheumatology, found it resulted in a significant reduction in pain on the WOMAC scale after three months.
Whereas glucosamine has been shown to be effective in 40 percent of study participants, Litozin boasts efficacy in 82 percent of cases, said Lemerond. What is more, in the Scandinavian Journal of Rheumatology study patients were allowed to take 'rescue medication' to reduce the pain after the first three weeks, if they felt the need.
With Litozin, use of rescue medication significantly declined, in some cases by 100 percent. This is particularly significant given the recent safety concerns over conventional pain relief medication such as Cox-2 inhibitor Vioxx.
Since Litozin is an anti-inflammatory, it could be useful for other inflammation-related conditions such as asthma, psoriasis and Crohn's disease. However its use in these areas has not yet been studied or patented.
Glucosamine sulphate was introduced to the US market in 1993, and estimates set the market value at around $800 million. Around half of the new joint health supplement products listed in Mintel's Global New Products Database in 2004 contain glucosamine - a far higher proportion than for any other ingredient.
Lemerond said that it will take a few years to get the word out about Litozin, but he expects that it will be "quite explosive" in time, becoming a $100 to $150 million product in the next two to three years.
In Sweden, where glucosamine is available on prescription and is therefore free to users, 50-60,000 units of Litozin are sold each month, according to Lemerond. He said this means that users are choosing to use a product they have to pay for over the free one, as it is so effective.
The first entry into the market will take place this month, through internet and mail order marketer Swanson Health Products.
Lemerond said that he is currently in negotiations to introduce it through additional distribution channels.
Related topics: Botanicals, Bone & joint health
DSM brings natural joint health ingredient to North America
EuroPharma to enhance product efficacy with enteric coating
First LitoZin-containing product reaches retail
New ingredients and research boost natural joint health
Give joint health consumers what they want
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AprèsFlex® 5-Day Joint Support is one of the world's best-selling joint health ingredients – with studies that demonstrate efficacy starting at 5 days...
By GeneChem Inc. Sialyllactose: Proven novel ingredient for osteoarthritis
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text:
Dr Sarah Nouwen
University Lecturer in Law
Fellow of the Lauterpacht Centre
Fellow, Pembroke College
Email: smhn3@cam.ac.uk
http://www.law.cam.ac.uk/people/academic/smh-nouwen/40
http://www.lcil.cam.ac.uk/people/sarah-nouwen
Complementarity in the Line of Fire: The Catalysing Effect of the International Criminal Court in Uganda and Sudan (Cambridge University Press)
Select Proceedings of the European Society of International Law, 2010, Volume 3 (Ed) (Hart)
"Legal Equality on Trial: Sovereigns and Individuals before the International Criminal Court" 43 Netherlands Yearbook of International Law 2012
"Doing Justice to the Political: The International Criminal Court in Uganda and Sudan" (2010) European Journal of International Law 941-965
"The Responsibility to Protect in Practice: Efforts to Promote Human Rights in Darfur" (2007) 24(65) Merkourios Utrecht Journal of International and European Law 58-70
"Sudan's Divided (and Divisive?) Peace Agreements" (2006) 19 Hague Yearbook of International Law 113-134
"The Special Court for Sierra Leone and the Immunity of Taylor: The Arrest Warrant Case Continued" 18(3) Leiden Journal of International Law 645-669
"The International Criminal Court: A Peacebuilder in Africa?" (Ed) in Devon Curtis and Gwinyayi A. Dzinesa (Ed), Peacebuilding, Power and Politics in Africa (Ohio University Pres), pp. 171-192
"The ICC and Complementarity Post Juba: Between International Imposition and Domestic Diversity" in O.J. Francis and P. Wrange (Ed), The International Criminal Court and the Juba Peace Process or Global Governance and Local Friction (Fountain Press)
"Complementarity in Uganda: Domestic Diversity or International Imposition?" in C. Stahn and M.E. Zeidy (Ed), The International Criminal Court and Complementarity: From Theory to Practice (Cambridge University Press)
Filed under: Conflict and Peace Building People


text:
Budníček pruhohlavý (Phylloscopus inornatus) je malým druhem pěvce z čeledi budníčkovitých (Phylloscopidae).

Popis
Od podobných, u nás hnízdících druhů budníčků se liší výraznými žlutavými křídelními páskami, žlutavými lemy ramenních letek a výrazným nadočním proužkem.

Rozšíření
Do Evropy se zatoulává ze sibiřské tajgy, nejčastěji na podzim. Do roku 2014 bylo na českém území zaznamenáno celkem 20 pozorování nebo odchytů.

Reference

Související články
 Seznam ptáků Česka

Externí odkazy

Budníčci

redpajama_set_name: RedPajamaWikipedia


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redpajama_set_name: RedPajamaGithub


text:
Tschoch () ist ein Dorf (Aul) im Rajon Gunib der nordkaukasischen Republik Dagestan in der Russischen Föderation. Es hat  Einwohner (Stand ).

Zur Dorfgemeinschaft von Tschoch zählen ferner das Dorf Kommuna mit gut 700 Einwohnern und das fast vollständig verlassene Dorf Gamsutl, wo es keine ständige Wohnbevölkerung mehr gibt.

Die Bewohner von Tschoch sind in der Mehrzahl Awaren.

Kultur
In Tschoch gibt es eine Poststelle, eine Bibliothek mit etlichen Tausend Bänden sowie ein Kulturzentrum mit Lese- und Kinosaal. Im Kulturzentrum finden Dorfanlässe, Ehrungen, Veteranentreffen und Schulanlässe statt.
In sowjetischer Zeit wurden mehrmals wöchentlich Filme vorgeführt; der Kinobetrieb ist jedoch seit dem Jahr 1996 eingestellt worden, da der Kinoapparat defekt ist.

Architektur
Wie in vielen dagestanischen Aulen wurde früher die Architektur durch die Flachdächer der Wohnhäuser geprägt, die mit gepresster Erde bedeckt waren. Mehrmals jährlich wurde spezielle, lehmige Erde herbeigeschafft und mit schweren Steintrommeln gewalzt, sodass das Dach wasserundurchlässig wurde. Mittlerweile haben jedoch die meisten Häuser Blechdächer; die eigentümlichen Steintrommeln werden zum Teil als Bauelemente in neuen Häusern verwendet oder ins Fundament eingebaut.

Verkehr
Tschoch wird von Kleinbussen (auf Russisch Marschrutki) aus der Republikshauptstadt Machatschkala und nach Lewaschi im gleichnamigen Rajon bedient. Hauptsächlich sind die Dorfbewohner jedoch auf ihren Privattransport angewiesen. Tschoch liegt an der Straße nach Sogratl, wo sich ein Memorial des awarischen Dichters Rassul Gamsatow befindet.

Einzelnachweise

Weblinks

Ort in Dagestan


text:
Tag: Tim Allen Contact Details
Tim Allen Contact Details, Phone Number, Social Profiles, Email ID, Website
Tim Allen (born June 13, 1953), known professionally as Tim Allen, is an American actor and comedian. He is known for playing Tim "The Toolman" Taylor on the ABC sitcom…
Rose Byrne Contact Details, Phone Number, Social Profiles, Email ID, Website January 21, 2021
US to join WHO-led vaccine project for poor nations: Fauci January 21, 2021
Oti Mabuse reveals pandemic meant she didn't see sister Motsi for almost a year January 21, 2021


Pursuant to Executive Order 17 (2014) and §§ 2.2-4007.1 and 2.2-4017 of the Code of Virginia, the Cemetery Board is conducting a periodic review and small business impact review of VAC citation: 18 VAC 47--20, title of regulation: Cemetery Board Rules and Regulations.
Comments may be submitted online to the Virginia Regulatory Town Hall at http://www.townhall.virginia.gov/L/Forums.cfm. Comments may also be sent to Name: Christine Martine, Title: Executive Director, Address: DPOR, 9960 Mayland Drive, Suite 400, City: Richmond, State: Virginia, Zip: 23233, Telephone: (804)367-8552, FAX: (866)826-8863, email address: cemetery@dpor.virginia.gov.


text:
Web Design Greenville SC
How to Know If You Have the Entrepreneur Gene (If it Even Exists)
June 30, 2018 Pappy Van Winkle
Is entrepreneurship caused by nature or nurture? Not that it makes much difference once the bug bites.
Scientists have been studying the potential role genes plays in a person's aptitude for entrepreneurship. I'd certainly be interested in their conclusions given my own background and career.
Both my father and grandfather owned small businesses, which makes me a third-generation entrepreneur. Does that mean I have the entrepreneur gene? I didn't really think so — until recently.
Until about six years ago, I had absolutely no intention of following in the footsteps of my father and grandfather. The risky life of the entrepreneur did not appeal to me. I liked everything to be predictable and safe. I earned my MBA from the prestigious University of Chicago Booth School of Business and joined established, brand-name companies — Texas Instruments, McKinsey & Company, Greylock IL.
I never made risky career moves.
By my mid-thirties, I was on a comfortable career track as an investor for a top VC firm making judgments about entrepreneurs and deciding which startup deserved to get funding. But something gradually changed. I felt myself increasingly drawn to the challenge of launching and building my own company. The death of my grandmother convinced me that life is short. I recognized the time had come to take bigger risks.
Did I make that decision because I have a genetic predisposition to entrepreneurship? I don't know, but five years into my new life as a startup founder I have a clearer sense of the traits required to be an entrepreneur.
Related: Passion Is What Unlocks Your Hustler's Work Ethic
A whole lotta passion and grit.
For an entrepreneur, starting and building a business is an obsession, not just a job. It consumes you. That's how it's been for me.
I was passionate about my previous jobs, of course. But it's different when you're building something from scratch — when it's your "baby." I've had to constantly visualize a different reality. That's another important trait of an entrepreneur: being a dreamer.
Another is grit. Things will go wrong even if you have the most carefully-crafted plans. Things were the hardest in the beginning. Investors told us no. Engineers and executives declined to join us. Potential partners were uninterested in speaking with us. Today isn't easy, just different types of challenges. Everyday is a new day in the trenches. What keeps us entrepreneurs going is passion for what we love.
You often hear about bankers and investors on Wall Street who make a ton of money but who hate their job. You definitely would not survive as an entrepreneur with that attitude. You have to wake up every morning prepared for the next setback…or the next success.
Related: It's Never Too Late to Pursue Your Passion
2. A little bit crazy.
There's really something inherently irrational about quitting a solid job to start a company. The odds are stacked up against you. Many businesses go under, most entrepreneurs fail. You're confronted by these facts when you launch your career as an entrepreneur.
You've got to be a bit crazy to want to become an entrepreneur. I sometimes wake up in the middle of the night thinking obsessively about an issue involving my company. Some nights I can't sleep.
The potential to hit it big financially is one incentive for starting a company, but it is not always what moves one to become an entrepreneur. It certainly wasn't what led me to start a business. I took a significant pay cut when I gave up my career as a VC investor to start my own company. For me and many entrepreneurs I know, launching a business is more than just about the monetary upside. It's about making an impact, leaving a mark, doing something bold — no matter how crazy it might seem.
Related: 25 Quotes About Making Money and Keeping Perspective
3. Laser focus on the future … and the next day.
How I viewed and approached the future changed when I became an entrepreneur. Like many overachievers, I used to meticulously plan the next years in my career. I knew where I wanted to be professionally in two, five and even 10 years. But when I started building a company, the medium-term plans somehow became less important.
Now I am mainly thinking about our long-term goals and focusing on the very next day. I wrestle with the same day-to-day concerns as many small business owners: Do we have enough funds to cover operations for the next quarter? Are we spending too much or too little on marketing agency? Do we have enough staff to keep up with growth?
The middle sort of goes away.
In the past, you probably thought about becoming a manager next year or reaching some milestone in the next two years. As an entrepreneur your thinking becomes "I'm building this massive thing, but let me get through tomorrow."
Related: Multimillionaires Share 7 Steps to Structure Your Day for Success
4. Best and worst job in the world.
I was asked recently if I ever had doubts or regrets about becoming an entrepreneur. My answer: Yes, of course. They come at least once a month. It's like a rollercoaster ride. The highs thrill you in ways you've never experienced. The lows make you want to crawl under the sheets and cry.
As I always tell friends and colleagues: This is the job I've loved the most, and it's the job I've hated the most. But I would do it all over again.
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Rafael Nadal cruised into the Barcelona Open quarterfinals by defeating fellow Spaniard Guillermo Garcia-Lopez 6-1, 6-3 on Thursday.
The top-ranked Nadal converted on his second match point to clinch his 16th straight victory on clay and set up an encounter with Martin Klizan, who eliminated Novak Djokovic in the second round, reports AP.
"I came out with the conviction that I could play a lot better than I did yesterday (against Roberto Carballes Baena), and that's what happened," Nadal said.
Coming off his 11th Monte Carlo title, Nadal has won 11 of his 12 ATP Tour matches this season, with the only loss coming from an injury retirement in the Australian Open quarterfinals.
"I had more options in the second set but a player like Nadal doesn't give you many chances," the 69th-ranked Garcia-Lopez said.
Klizan, the 140th-ranked Slovak who defeated Nadal in Beijing in 2014, reached the last eight by ousting veteran Feliciano Lopez 6-1, 6-4.
Second-seeded Grigor Dimitrov of Bulgaria saved two match points to defeat Malek Jaziri of Tunisia 7-5, 3-6, 7-6 (8), while third-seeded Dominic Thiem of Austria got past Jozef Kovalik of Slovakia 7-6 (5), 6-2 for his 12th win in 15 clay-court matches this season.
David Goffin of Belgium made it to the quarterfinals by coming from behind to defeat Karen Khachanov of Russia 2-6, 7-6 (2), 6-0, and 19-year-old Stefanos Tsitsipas of Greece upset local Albert Ramos-Vinolas 6-4, 7-5.


Tommy Tucker lived in Eltham from 1902 and had become great friends of both Edith and Hubert Bland through his association with the local Labour Party. After Hubert's death Tommy helped Edith overcome financial problems and eventually their friendship led to marriage. They married in 1917 at St Peters Roman Catholic Church, Woolwich and in 1922 they looked for somewhere to live near the Kentish coast. They found two wooden bungalows at St Mary's Bay, Dymchurch, Kent which they converted into their last home together. Edith died here in May 1924 aged 66.
Tommy Tucker remained living in the bungalow for another eleven years establishing himself as a pillar of the local community.