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Rényi entropy

In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions.

The Rényi entropy is important in ecology and statistics as index of diversity. The Rényi entropy is also important in quantum information, where it can be used as a measure of entanglement. In the Heisenberg XY spin chain model, the Rényi entropy as a function of $α$ can be calculated explicitly because it is an automorphic function with respect to a particular subgroup of the modular group. In theoretical computer science, the min-entropy is used in the context of randomness extractors.

Definition
The Rényi entropy of order $$\alpha$$, where $$0 < \alpha < \infin$$ and $$\alpha \neq 1 $$, is defined as
 * $$\Eta_\alpha(X) = \frac{1}{1-\alpha}\log\Bigg(\sum_{i=1}^n p_i^\alpha\Bigg) .$$

It is further defined at $$\alpha = 0, 1, \infin$$ as
 * $$\Eta_\alpha(X) = \lim_{\gamma \to \alpha} \Eta_\gamma(X) .$$

Here, $$X$$ is a discrete random variable with possible outcomes in the set $$\mathcal{A} = \{x_1,x_2,...,x_n\}$$ and corresponding probabilities $$p_i \doteq \Pr(X=x_i)$$ for $$i=1,\dots,n$$. The resulting unit of information is determined by the base of the logarithm, e.g. shannon for base 2, or nat for base e. If the probabilities are $$p_i=1/n$$ for all $$i=1,\dots,n$$, then all the Rényi entropies of the distribution are equal: $$\Eta_\alpha(X)=\log n$$. In general, for all discrete random variables $$X$$, $$\Eta_\alpha(X)$$ is a non-increasing function in $$\alpha$$.

Applications often exploit the following relation between the Rényi entropy and the α-norm of the vector of probabilities:
 * $$\Eta_\alpha(X)=\frac{\alpha}{1-\alpha} \log \left(\|P\|_\alpha\right)$$.

Here, the discrete probability distribution $$P=(p_1,\dots,p_n)$$ is interpreted as a vector in $$\R^n$$ with $$p_i\geq 0$$ and $\sum_{i=1}^{n} p_i =1$.

The Rényi entropy for any $$\alpha \geq 0 $$ is Schur concave. Proven by the Schur-Ostrowski criterion.

Special cases
As $$\alpha$$ approaches zero, the Rényi entropy increasingly weighs all events with nonzero probability more equally, regardless of their probabilities. In the limit for $$\alpha \to 0$$, the Rényi entropy is just the logarithm of the size of the support of  $X$. The limit for $$\alpha \to 1$$ is the Shannon entropy. As $$\alpha$$ approaches infinity, the Rényi entropy is increasingly determined by the events of highest probability.

Hartley or max-entropy
Provided the probabilities are nonzero, $$\Eta_0$$ is the logarithm of the cardinality of the alphabet ($$\mathcal{A}$$) of $$X$$, sometimes called the Hartley entropy of $$X $$,
 * $$\Eta_0 (X) = \log n = \log |\mathcal{A}|\,$$

Shannon entropy
The limiting value of $$\Eta_\alpha$$ as $$\alpha \to 1$$ is the Shannon entropy:
 * $$\Eta_1 (X) \equiv \lim_{\alpha \to 1} \Eta_{\alpha} (X) = - \sum_{i=1}^n p_i \log p_i $$

Collision entropy
Collision entropy, sometimes just called "Rényi entropy", refers to the case $$\alpha = 2$$,
 * $$\Eta_2 (X) = - \log \sum_{i=1}^n p_i^2 = - \log P(X = Y) ,$$

where $p_{1}$ and $P = (p_{1}, 1 − p_{1})$ are independent and identically distributed. The collision entropy is related to the index of coincidence.

Min-entropy
In the limit as $$\alpha \rightarrow \infty $$, the Rényi entropy $$\Eta_\alpha$$ converges to the min-entropy $$\Eta_\infty$$:
 * $$\Eta_\infty(X) \doteq \min_i (-\log p_i) = -(\max_i \log p_i) = -\log \max_i p_i\,.$$

Equivalently, the min-entropy $$\Eta_\infty(X)$$ is the largest real number $b$ such that all events occur with probability at most $$2^{-b}$$.

The name min-entropy stems from the fact that it is the smallest entropy measure in the family of Rényi entropies. In this sense, it is the strongest way to measure the information content of a discrete random variable. In particular, the min-entropy is never larger than the Shannon entropy.

The min-entropy has important applications for randomness extractors in theoretical computer science: Extractors are able to extract randomness from random sources that have a large min-entropy; merely having a large Shannon entropy does not suffice for this task.

Inequalities for different orders α
That $$\Eta_\alpha$$ is non-increasing in $$\alpha$$ for any given distribution of probabilities $$p_i$$, which can be proven by differentiation, as
 * $$-\frac{d \Eta_\alpha}{d\alpha}

= \frac{1}{(1-\alpha)^2} \sum_{i=1}^n z_i \log(z_i / p_i) = \frac{1}{(1-\alpha)^2} D_{KL}(z\| p)$$ which is proportional to Kullback–Leibler divergence (which is always non-negative), where $$z_i = p_i^\alpha / \sum_{j=1}^n p_j^\alpha$$. In particular, it is strictly positive except when the distribution is uniform.

At the $$\alpha \to 1$$ limit, we have $$-\frac{d \Eta_\alpha}{d\alpha} \to \frac 12 \sum_i p_i (\ln p_i + H(p))^2 $$.

In particular cases inequalities can be proven also by Jensen's inequality:
 * $$\log n=\Eta_0\geq \Eta_1 \geq \Eta_2 \geq \Eta_\infty .$$

For values of $$\alpha>1$$, inequalities in the other direction also hold. In particular, we have
 * $$ \Eta_2 \le 2 \Eta_\infty .$$

On the other hand, the Shannon entropy $$\Eta_1$$ can be arbitrarily high for a random variable $$X$$ that has a given min-entropy. An example of this is given by the sequence of random variables $$X_n \sim \{0, \ldots, n\}$$ for $$n \geq 1$$ such that $$P(X_n = 0) = 1/2$$ and $$P(X_n = x) = 1/(2n)$$ since $$\Eta_\infty(X_n) = \log 2$$ but $$\Eta_1(X_n) = (\log 2 + \log 2n)/2$$.

Rényi divergence
As well as the absolute Rényi entropies, Rényi also defined a spectrum of divergence measures generalising the Kullback–Leibler divergence.

The Rényi divergence of order $Η$ or alpha-divergence of a distribution $Η$ from a distribution $Η$ is defined to be
 * $$D_\alpha (P \| Q) = \frac{1}{\alpha-1}\log\Bigg(\sum_{i=1}^n \frac{p_i^\alpha}{q_i^{\alpha-1}}\Bigg) = \frac{1}{\alpha-1}\log \mathbb E_{i \sim p}[(p_i/q_i)^{\alpha - 1}] \, $$

when $Η$ and $X$. We can define the Rényi divergence for the special values $Y$ by taking a limit, and in particular the limit $α$ gives the Kullback–Leibler divergence.

Some special cases:
 * $$D_0(P \| Q) = - \log Q(\{i : p_i > 0\})$$ : minus the log probability under $P$ that $Q$;
 * $$D_{1/2}(P \| Q) = -2 \log \sum_{i=1}^n \sqrt{p_i q_i} $$ : minus twice the logarithm of the Bhattacharyya coefficient;
 * $$D_1(P \| Q) = \sum_{i=1}^n p_i \log \frac{p_i}{q_i} $$ : the Kullback–Leibler divergence;
 * $$D_2(P \| Q) = \log \Big\langle \frac{p_i}{q_i} \Big\rangle $$ : the log of the expected ratio of the probabilities;
 * $$D_\infty(P \| Q) = \log \sup_i \frac{p_i}{q_i} $$ : the log of the maximum ratio of the probabilities.

The Rényi divergence is indeed a divergence, meaning simply that $$D_\alpha (P \| Q)$$ is greater than or equal to zero, and zero only when $0 < α < ∞$. For any fixed distributions $α ≠ 1$ and $α = 0, 1, ∞$, the Rényi divergence is nondecreasing as a function of its order $α → 1$, and it is continuous on the set of $Q$ for which it is finite, or for the sake of brevity, the information of order $p_{i} > 0$ obtained if the distribution $P = Q$ is replaced by the distribution $P$.

Financial interpretation
A pair of probability distributions can be viewed as a game of chance in which one of the distributions defines official odds and the other contains the actual probabilities. Knowledge of the actual probabilities allows a player to profit from the game. The expected profit rate is connected to the Rényi divergence as follows
 * $${\rm ExpectedRate} = \frac{1}{R}\, D_1(b\|m) + \frac{R-1}{R}\, D_{1/R}(b\|m) \,,$$

where $$m$$ is the distribution defining the official odds (i.e. the "market") for the game, $$b$$ is the investor-believed distribution and $$R$$ is the investor's risk aversion (the Arrow–Pratt relative risk aversion).

If the true distribution is $$p$$ (not necessarily coinciding with the investor's belief $$b$$), the long-term realized rate converges to the true expectation which has a similar mathematical structure
 * $${\rm RealizedRate} = \frac{1}{R}\,\Big( D_1(p\|m) - D_1(p\|b) \Big) + \frac{R-1}{R}\, D_{1/R}(b\|m) \,.$$

Properties specific to α = 1
The value $Q$, which gives the Shannon entropy and the Kullback–Leibler divergence, is the only value at which the chain rule of conditional probability holds exactly:
 * $$\Eta(A,X) = \Eta(A) + \mathbb{E}_{a \sim A} \big[ \Eta(X| A=a) \big]$$

for the absolute entropies, and
 * $$D_\mathrm{KL}(p(x|a)p(a)\|m(x,a)) = D_\mathrm{KL}(p(a)\|m(a)) + \mathbb{E}_{p(a)}\{D_\mathrm{KL}(p(x|a)\|m(x|a))\},$$

for the relative entropies.

The latter in particular means that if we seek a distribution $α$ which minimizes the divergence from some underlying prior measure $α$, and we acquire new information which only affects the distribution of $α$, then the distribution of $P$ remains $Q$, unchanged.

The other Rényi divergences satisfy the criteria of being positive and continuous, being invariant under 1-to-1 co-ordinate transformations, and of combining additively when $α = 1$ and $p(x, a)$ are independent, so that if $m(x, a)$, then
 * $$\Eta_\alpha(A,X) = \Eta_\alpha(A) + \Eta_\alpha(X)\;$$

and
 * $$D_\alpha(P(A)P(X)\|Q(A)Q(X)) = D_\alpha(P(A)\|Q(A)) + D_\alpha(P(X)\|Q(X)).$$

The stronger properties of the $a$ quantities allow the definition of conditional information and mutual information from communication theory.

Exponential families
The Rényi entropies and divergences for an exponential family admit simple expressions

\Eta_\alpha(p_F(x;\theta)) = \frac{1}{1-\alpha} \left(F(\alpha\theta)-\alpha F(\theta)+\log E_p[e^{(\alpha-1)k(x)}]\right) $$ and

D_\alpha(p:q) = \frac{J_{F,\alpha}(\theta:\theta')}{1-\alpha} $$ where

J_{F,\alpha}(\theta:\theta')= \alpha F(\theta)+(1-\alpha) F(\theta')- F(\alpha\theta+(1-\alpha)\theta') $$ is a Jensen difference divergence.

Physical meaning
The Rényi entropy in quantum physics is not considered to be an observable, due to its nonlinear dependence on the density matrix. (This nonlinear dependence applies even in the special case of the Shannon entropy.) It can, however, be given an operational meaning through the two-time measurements (also known as full counting statistics) of energy transfers.

The limit of the quantum mechanical Rényi entropy as $$\alpha\to 1$$ is the von Neumann entropy.

title: Rényi entropy


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title: User talk:Chyel


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Wikipedia:Articles for deletion/Sachiel

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was keep. ugen 64 21:00, 26 Apr 2005 (UTC)

Sachiel
I'm not sure if this is true. I'm pretty sure it's not. Kyle543 03:57, Apr 13, 2005 (UTC)
 * Delete unless somebody can explain what sort of cruft it is. RickK 04:48, Apr 13, 2005 (UTC)
 * It's Neon Genesis Evangelion cruft. Redirect to Angel (Neon Genesis Evangelion). —Korath (Talk) 05:00, Apr 13, 2005 (UTC)
 * Keep Smerdis of Tlön's rewrite. (I'm going to remove the original content, though, in favor of a disambig line, since the information was already at Angel (Neon Genesis Evangelion).) —Korath (Talk) 21:16, Apr 14, 2005 (UTC)
 * Agree to redirect to Angel (Neon Genesis Evangelion). Or else delete - nonencyclopedic Srcastic 05:09, Apr 13, 2005 (UTC)
 * Redirect. Meelar (talk) 05:11, Apr 13, 2005 (UTC)
 * Delete, not notable, cruft. Megan1967 08:22, 13 Apr 2005 (UTC)
 * I can live with a redirect. Mgm|(talk) 10:09, Apr 13, 2005 (UTC)
 * Keep, rewrite I wouldn't consider myself highly religious or anything, but I think it's pretty sad when so many people assume that a certain angel is just something from Evangelion! Evangelion borrowed the names of numerous biblical angels for its monsters.  Sachiel is a "real" angel, at least in Christian lore, and also the pseudo-Christian new-age angel mysticism that seems to be going around these days.  Try a Google search for "sachiel +angel -evangelion" and you'll see what I mean: hundreds of hits, very few are EVA-related. Andrew Lenahan - St ar bli nd  13:13, Apr 13, 2005 (UTC)
 * If and when someone rewrites it, he can do so over the redirect. However, the content that's currently here is all about the anime, so should be redirected to the appropriate page so it doesn't fork. —Korath (Talk) 14:27, Apr 13, 2005 (UTC)
 * Comment - I found a bit of information on the web about the archangel Sachiel and have added it to the article. There may be more in Davidson's Dictionary of Angels, which I can check later.  Not wholly sure we want separate articles on all the qabalistic angels of the weeks and planets (they get demons as well) but this data is no doubt as worthy as other (fictional) characters. -- Smerdis of Tlön 20:38, 14 Apr 2005 (UTC)
 * Keep the rewritten article. — Xezbeth 05:23, Apr 15, 2005 (UTC)

 * This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.

title: Wikipedia:Articles for deletion/Sachiel


text:
Talk:Michael Novak

The Rumsfeld Quote
I'd venture to guess that Novak taught Rumsfeld no such thing. I think that's a joke. —Preceding unsigned comment added by 65.30.19.26 (talk) 03:08, 7 September 2007 (UTC)

Templeton Prize edit
I've edited the entry to mention the Templeton Prize. Winning the "Nobel prize for religion" is no small thing! I didn't put in anything about the numerous other awards he has received.

I also added a link to his website and removed some outdated links, one of which had a false and hostile POV description. Chris Chittleborough 07:48, 12 September 2005 (UTC)

I have added the following link to give a more balanced view on Novak
 * International Relations Center profile detailing Novak's corporate and political involvement — Preceding unsigned comment added by 216.80.111.15 (talk) 11:45, December 20, 2006
 * That's an out-and-out attack on Novak, full of silly mistakes. WP:EL forbids links like that. CWC 11:43, 3 June 2007 (UTC)

Strange quotations
Even if I contributed a little.... I should say that this page is a real mess! Full of strange quotations instead of clear definitions or simple "voices": it's actually dreadful. Henry Cassini 21:21, 10 January 2007 (UTC)

There's an awful lot of quotes in here with no discussion. Why are these important quotes? I've read many other philosophers' pages and never seen so many long quotes before. Also, there are a lot of loaded words in here, like "his greatest accomplishment," and a bunch in the section on Harvard. Vandymorgan 14:40, 19 December 2006 (UTC)

I've tried to clean up the overall structure of the entry by adding a new subsection bringing the chronological account of his life up to his present position, and then by changing the subheading "Quotes" to read "Controversial Claims." The quotes do seem to have been selected to appear controversial.131.212.34.6 23:44, 2 June 2007 (UTC)Thomas J. Farrell, University of Minnesota Duluth.

 * Thanks for that, Prof Farrell. (Please consider registering a username here. It's only one extra password to remember, and we can use all the good editors we can get.)
 * I agree that the quotations are out of place, and I plan to delete some. I see no reason to quote from a novel (The Tiber Was Silver) here, and the last quote (from A Free Society Reader) seems far too theological for this general encyclopedia. The quote from The Experience of Nothingness needs a lot more context to be useful to 99% of our readers.
 * What do other contributors think? Which quotes should stay and which should go? Cheers, CWC 11:43, 3 June 2007 (UTC)

I do not understand the comment "seems far too theological for this general encyclopedia." Do theological quotes violate some Wikipedia Rule? --Gclausen 07:18, 13 July 2007 (UTC)

 * Err, that was just my polite way of saying full of weird jargon (if "jargon" is the right word). But I've kept that quote for the time being, while deleting the other two I mentioned. CWC 17:56, 13 July 2007 (UTC)

Seminarian
Later in the article, there is mention of Novak having been a seminarian. That should be mentioned in the beginning, under Early Life. When (and for which Diocese) was he a seminarian? --Melchior2006 (talk) 14:35, 7 May 2011 (UTC)

NYT obituary
https://www.nytimes.com/2017/02/19/us/michael-novak-dead-catholic-scholar.html Michael Novak, Catholic Scholar Who Championed Capitalism, Dies at 83 By WILLIAM GRIMES New York Times FEB. 19, 2017 --Nbauman (talk) 20:08, 19 February 2017 (UTC)

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External links modified (January 2018)
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Update bibliography
"A Theology for a Radical Politics" is identified in the article but is not included in the bibliography. 172.58.219.253 (talk) 18:41, 11 May 2021 (UTC)

Update institutions
Mr. Novak's teaching at the University of Notre Dame is described in the article but is absent from the list that should include it. 172.58.219.253 (talk) 18:44, 11 May 2021 (UTC)

Update bibliography
Confession of a Catholic published by Harper & Row, San Francisco, in 1983, two years prior to your listed 1985 publisher date. 68.189.42.93 (talk) 00:26, 16 September 2023 (UTC)

title: Talk:Michael Novak


text:
File:AVFamicom.jpg

The AV Family Computer, a redesigned model of Japan's Family Computer (a.k.a. the Nintendo Entertainment System.

title: File:AVFamicom.jpg


text:
Restriction point

The restriction point (R), also known as the Start or G1/S checkpoint, is a cell cycle checkpoint in the G1 phase of the animal cell cycle at which the cell becomes "committed" to the cell cycle, and after which extracellular signals are no longer required to stimulate proliferation. The defining biochemical feature of the restriction point is the activation of G1/S- and S-phase cyclin-CDK complexes, which in turn phosphorylate proteins that initiate DNA replication, centrosome duplication, and other early cell cycle events. It is one of three main cell cycle checkpoints, the other two being the G2-M DNA damage checkpoint and the spindle checkpoint.

History
Originally, Howard Martin Temin showed that chicken cells reach a point at which they are committed to replicate their DNA and are not dependent on extracellular signals. About 20 years later, in 1973, Arthur Pardee demonstrated that a single restriction point exists in G1. Previously, G1 had been defined simply as the time between mitosis and S phase. No molecular or morphological place-markers for a cell's position in G1 were known. Pardee used a double-block method in which he shifted cells from one cell cycle block (such as critical amino acid withdrawal or serum withdrawal) to another and compared each block's efficiency at preventing progression to S phase. He found that both blocks in all cases examined were equally efficient at blocking S phase progression, indicating that they must all act at the same point in G1, which he termed the "restriction point", or R-point.

In 1985, Zetterberg and Larsson discovered that, in all stages of the cell cycle, serum deprivation results in inhibition of protein synthesis. Only in postmitotic cells (i.e. cells in early G1) did serum withdrawal force cells into quiescence (G0). In fact, Zetterberg found that virtually all of the variability in cell cycle length can be accounted for in the time it takes the cell to move from the restriction point to S phase.

Extracellular signals
Except for early embryonic development, most cells in multicellular organisms persist in a quiescent state known as G0, where proliferation does not occur, and cells are typically terminally differentiated; other specialized cells continue to divide into adulthood. For both of these groups of cells, a decision has been made to either exit the cell cycle and become quiescent (G0), or to reenter G1.

A cell's decision to enter, or reenter, the cell cycle is made before S-phase in G1 at what is known as the restriction point, and is determined by the combination of promotional and inhibitory extracellular signals that are received and processed. Before the R-point, a cell requires these extracellular stimulants to begin progressing through the first three sub-phases of G1 (competence, entry G1a, progression G1b). After the R-point has been passed in G1b, however, extracellular signals are no longer required, and the cell is irreversibly committed to preparing for DNA duplication. Further progression is regulated by intracellular mechanisms. Removal of stimulants before the cell reaches the R-point may result in the cell's reversion to quiescence. Under these conditions, cells are actually set back in the cell cycle, and will require additional time (about 8 hours more than the withdrawal time in culture) after passing the restriction point to enter S phase.

 Mitogen Signaling

Growth factors (e.g., PDGF, FGF, and EGF) regulate entry of cells into the cell cycle and progression to the restriction point. After passing this switch-like “point of no return,” cell cycle completion is no longer dependent on the presence of mitogens. Sustained mitogen signaling promotes cell cycle entry largely through regulation of the G1 cyclins (cyclin D1-3) and their assembly with Cdk4/6, which may be mediated in parallel through both MAPK and PI3K pathways.

MAPK Signaling Cascade

The binding of extracellular growth factors to their receptor tyrosine kinases (RTK) triggers a conformational change and promotes dimerization and autophosphorylation of tyrosine residues on the cytoplasmic tail of the RTKs. These phosphorylated tyrosine residues facilitate the docking of proteins containing an SH2-domain (e.g., Grb2), which can subsequently recruit other signaling proteins to the plasma membrane and trigger signaling kinase cascades. RTK-associated Grb2 binds Sos, which is a guanine nucleotide exchange factor that converts membrane-bound Ras to its active form (Ras-GDP $$\longrightarrow$$ Ras-GTP). Active Ras activates the MAP kinase cascade, binding and activating Raf, which phosphorylates and activates MEK, which phosphorylates and activates ERK (also known as MAPK, see also MAPK/ERK pathway).

Active ERK then translocates into the nucleus where it activates multiple targets, such as the transcription factor serum-response factor (SRF), resulting in expression of immediate early genes—notably the transcription factors Fos and Myc. Fos/Jun dimers comprise the transcription factor complex AP-1 and activate delayed response genes, including the major G1 cyclin, cyclin D1. Myc also regulates expression of a wide variety of pro-proliferative and pro-growth genes, including some induction of cyclin D2 and Cdk4. Additionally, sustained ERK activity seems to be important for phosphorylation and nuclear localization of CDK2, further supporting progression through the restriction point.

PI3K Pathway Signaling

p85, another SH2-domain-containing protein, binds activated RTKs and recruits PI3K (phosphoinositide-3-kinase), phosphorylating the phospholipid PIP2 to PIP3, leading to recruitment of Akt (via its PH-domain). In addition to other pro-growth and pro-survival functions, Akt inhibits glycogen synthase kinase-3β (GSK3β), thereby preventing GSK3β -mediated phosphorylation and subsequent degradation of cyclin D1 (see figure ). Akt further regulates G1/S components by mTOR-mediated promotion of cyclin D1 translation, phosphorylation of the Cdk inhibitors p27kip1 (preventing its nuclear import) and p21Cip1 (decreasing stability), and inactivating phosphorylation of the transcription factor FOXO4 (which regulates p27 expression). Together, this stabilization of cyclin D1 and destabilization of Cdk inhibitors favors G1 and G1/S-Cdk activity.

Anti-mitogen Signaling

Anti-mitogens like the cytokine TGF-β inhibit progression through the restriction point, causing a G1 arrest. TGF-β signaling activates Smads, which complex with E2F4/5 to repress Myc expression and also associate with Miz1 to activate expression of the Cdk inhibitor p15INK4b to block cyclin D-Cdk complex formation and activity. Cells arrested with TGF-β also accumulate p21 and p27.

Mechanism
Overview

As described above, signals from extracellular growth factors are transduced in a typical manner. Growth factor binds to receptors on the cell surface, and a variety of phosphorylation cascades result in Ca2+ uptake and protein phosphorylation. Phosphoprotein levels are counterbalanced by phosphatases. Ultimately, transcriptional activation of certain target genes occurs. Extracellular signaling must be maintained, and the cell must also have access to sufficient nutrient supplies to support rapid protein synthesis. Accumulation of cyclin D's are essential.

Cyclin D-bound Cdks 4 and 6 are activated by Cdk-activating kinase and drive the cell towards the restriction point. Cyclin D, however has a high turnover rate (t1/2<25 min). It is because of this quick turnover rate that the cell is extremely sensitive to mitogenic signaling levels, which not only stimulate cyclin D production, but also help to stabilize cyclin D within the cell. In this way, cyclin D acts as a mitogenic signal sensor. Cdk inhibitors (CKI), such as the Ink4 proteins and p21, help to prevent improper cyclin-cdk activity.

Active cyclin D-cdk complexes phosphorylate retinoblastoma protein (pRb) in the nucleus. Unphosphorylated Rb acts as an inhibitor of G1 by preventing E2F-mediated transcription. Once phosphorylated, E2F activates the transcription of cyclins E and A. Active cyclin E-cdk begins to accumulate and completes pRb phosphorylation, as shown in the figure.

Cdk inhibitors and regulation of Cyclin D/Cdk complex activity

p27 and p21 are stoichiometric inhibitors of G1/S- and S-cyclin-Cdk complexes. While p21 levels increase during cell-cycle entry, p27 is generally inactivated as cells progress to late G1. High cell density, mitogen starvation, and TGF-β result in accumulation of p27 and cell cycle arrest. Similarly, DNA damage and other stressors increase p21 levels, while mitogen-stimulated ERK2 and Akt activity leads to inactivating phosphorylation of p21.

Early work on p27 overexpression suggested that it can associate with and inhibit cyclin D-Cdk4/6 complexes and cyclin E/A-Cdk2 complexes in vitro and in select cell types. However, kinetic studies by LaBaer et al. (1997) found that titrating in p21 and p27 promotes assembly of the cyclin d-Cdk complex, increasing overall activity and nuclear localization of the complex. Subsequent studies elucidated that p27 may be required for cyclin D-Cdk complex formation, as p27-/-, p21-/- MEFs showed a decrease in cyclin D-Cdk4 complexation that could be rescued with p27 re-expression.

Work by James et al. (2008) further suggests that phosphorylation of tyrosine residues on p27 can switch p27 between an inhibitory and non-inhibitory state while bound to cyclin D-Cdk4/6, offering a model for how p27 is capable of regulating both cyclin-Cdk complex assembly and activity. Association of p27 with cyclin D-Cdk4/6 may further promote cell cycle progression by limiting the pool of p27 available for inactivating cyclin E-Cdk2 complexes. Increasing cyclin E-Cdk2 activity in late G1 (and cyclin A-Cdk2 in early S) leads to p21/p27 phosphorylation that promotes their nuclear export, ubiquitination, and degradation.

Dynamics
A paper published by the Lingchong You and Joe Nevins groups at Duke University in 2008 demonstrated that the a bistable hysteric E2F switch underlies the restriction point. E2F promotes its own activation, and also promotes the inhibition of its own inhibitor (pRb), forming two feedback loops (among others) that are important in establishing bistable systems. The authors of this study used a destabilized GFP-system under the control of the E2F promoter as a readout of E2F activity. Serum-starved cells were stimulated with varying serum concentrations, and the GFP readout was recorded at a single-cell level. They found that the GFP reporter was either on or off, indicating that E2F was either completely activated or deactivated at all of the different serum levels analyzed. Further experiments, in which they analyzed the history-dependence of the E2F system confirmed that it operates as a hysteretic bistable switch.

In cancer
Cancer can be seen as a disruption of normal restriction point function, as cells continually and inappropriately reenter the cell cycle, and do not enter G0. Mutations at many steps in the pathway towards the restriction point can result in cancerous growth of cells. Some of the genes most commonly mutated in cancer include Cdks and CKIs; overactive Cdks or underactive CKIs lower the stringency of the restriction point, allowing more cells to bypass senescence.

The restriction point is an important consideration in the development of new drug therapies. Under normal physiological conditions, all cell proliferation is regulated by the restriction point. This can be exploited and used as a way to protect non-cancerous cells from chemotherapy treatments. Chemotherapy drugs typically attack cells that are proliferating rapidly. By using drugs that inhibit completion of the restriction point, such as growth factor receptor inhibitors, normal cells are prevented from proliferating, and are thus protected from chemotherapy treatments.

title: Restriction point


text:
Dan (son of Jacob)

According to the Book of Genesis, Dan (דָּן, Dān, "judgment" or "he judged") was the first of the two sons of Jacob and Bilhah (Jacob's fifth son). His mother, Bilhah, was Rachel's handmaid, who becomes one of Jacob's concubines (Book of Genesis, ). In the Biblical account, he is the founder of the Israelite Tribe of Dan. He was the father of Hushim, according to Gen 46:23. Samson was a descendant of Dan.

Name
The text of the Torah explains that the name of Dan derives from dananni, meaning "he has judged me", in reference to Rachel's belief that she had gained a child as the result of a judgment from God.

Biblical references
Owing to the Book of Judges, in the account of Micah's Idol, describing the Tribe of Dan as having used ephod and teraphim in worship, and Samson (a member of the Tribe of Dan) being described as failing to adhere to the rules of a Nazarite, classical rabbinical writers concluded that Dan was very much a black sheep. In the Book of Jeremiah, the north of Canaan is associated with darkness and evil, and so rabbinical sources treated Dan as the archetype of wickedness.

In the apocryphal Testaments of the Patriarchs, Dan is portrayed as having hated Joseph, and having been the one that invented the idea of deceiving Jacob by the smearing of Joseph's coat with the blood of a kid. In the apocryphal Prayer of Asenath, Dan is portrayed as plotting with the Egyptian crown prince, against Joseph and Asenath. In the Blessing of Jacob, Dan is described as a serpent, which seems to have been interpreted as connecting Dan to Belial, a connection made, for example, in the apocryphal Testament of Dan.

Early Christian writers, such as Irenaeus and Hippolytus, even believed that the Antichrist would come from the Tribe of Dan.

John the Apostle omits the Tribe of Dan when mentioning the twelve tribes of the sons of Israel, in regard to the 144,000 sealed Israelites. Instead of Dan, the tribe of Joseph appears twice (being also represented by Manasseh).

title: Dan (son of Jacob)


text:
San Juan Romero

"San Juan Romero" is a short story by the Brazilian writer Rita Maria Felix da Silva. It is also the name of the fictional Mexican village the story features, and it was the first story to feature the recurring character "Sir James Winterwood". In the tale, Winterwood arrives in San Juan Romero after his adventures throughout North America. Soon he learns about the terrible curse that haunted the village, concerning a nasty secret involving the people of that land, originally a group of miners. Since this tale deals with the evil in the human heart, it has been termed a "metaphysical western". The writer Romeu Martins classified this short story as a work in the genre Weird Western. Another curious feature of this story is a mention of one member of the literary version of the Whitehill family.

Readers of the story have varyingly placed the village either near the Mexican frontier with the United States or farther south towards Central America.

title: San Juan Romero


text:
Norah Stoner

Norah Jane Stoner (April 20, 1945) is a former politician in Ontario, Canada. She was a Liberal member of the Legislative Assembly of Ontario from 1987 to 1990.

Background
Stoner worked as a commercial artist before entering political life.

Politics
Stoner was a member of the Pickering Council from 1977 to 1983, and of the Durham Regional Council from 1983 to 1987.

She was elected to the Ontario legislature in the 1987 provincial election, defeating incumbent Progressive Conservative George Ashe by almost 6,000 votes in the riding of Durham West. She served as a backbench supporter of David Peterson's government, and was appointed as parliamentary assistant to the Minister of Colleges and Universities in 1989.

The Liberals were defeated by the NDP in the 1990 provincial election, and Stoner lost her seat to NDP candidate Jim Wiseman by just under 2,000 votes.

Later life
Stoner returned to working as a painter, and operates the Norah Stoner Studio in Toronto.

title: Norah Stoner


text:
NC17 (album)

NC17 (stylized in all lowercase) is the debut album by Treble Charger released on July 4, 1994. It was re-released by Sonic Unyon in 1997. "Red" from this album was also re-recorded for Maybe It's Me. The album is named after the band's original name, before they changed it due to copyright issues with an American band having the same name.

Treble Charger also recorded a demo tape named NC17, with a number of tracks found on the album, but also included was a song named "Barcelona Chair". The Artwork features the Smokin' Worm of Smokin' Worm records.

Track listing
All songs written by Treble Charger.

 * 1) "10th Grade Love" – 4:04
 * 2) "In Your Way" – 3:37
 * 3) "Trinity Bellwoods" – 4:31
 * 4) "Dress" – 3:28
 * 5) "Cubicle" – 4:41
 * 6) "Popcorn Chicken" – 1:37
 * 7) "Red" – 5:10
 * 8) "Soaker" – 3:54
 * 9) "Deception Made Simple" – 4:18
 * 10) "Pilot Light" – 4:44
 * 11) "Hint" – 19:00

Credits

 * Treble Charger - producer, artwork
 * Greig Nori   - guitar, vocals
 * Bill Priddle - guitar, vocals
 * Rosie Martin - bass guitar, backing vocals
 * Morris Palter    - drums, percussion
 * Joao Carvalho     - mastering
 * Chris Jackson     - artwork
 * Rob Sanzo         - producer, engineer

title: NC17 (album)


text:
Talk:Grandmother hypothesis

Comment
Here's an interesting bit:

 * Both pregnancy and childbirth are extremely detrimental to the health and longevity of women. Pregnancy increases a woman’s caloric intake requirements

I'd like to note that there's some dispute over just how much your energy intake affects your longevity. Aubrey de Grey recently wrote a paper that casts doubt on the notion that eating fewer Calories will significantly prolong you. At the very least, the article should explain the link between calories and ageing, for those who are unfamiliar with the notion. —RadRafe 04:00, 13 Apr 2005 (UTC)

What about the fact that most societies were patrilineal? The women would go live in another society away from their mothers (the grandmothers).

 * *coughcough* Paternal grandparents *coughcough* 209.234.66.97 15:42, 18 May 2006 (UTC)

 * cough cough indeed. This is completely anecdotal but my paternal grandmother was WAY more involved with me & my sisters than maternal grandmother... Tova2014 (talk) 03:30, 30 January 2024 (UTC)

In addition to lacking proper citation, I have to question the general knowledge of the author who believes "topographical dangers such as falls from a height" would be a significant danger to the direct ancestral hominids, who, in addition to retaining a degree of aboreal aptitude, spent the majority of their existence on savannah plains and forest edges. Perhaps a reference to more likely socialy constructed effects of menopause should be offered as an explanation for "[the] high level of variability in menopausal symptoms across populations[.]"

Wrong way round
From the article:

"The grandmother hypothesis is meant to explain why menopause, rare in mammal species, arose in human evolution"

In actuality, the Grandmother Hypothesis purports to explain why menopause had been maintained, not why it arose. Mid-life infertility occurs because female animals run out of oocytes. It happens among any number of species. The question is, why, when human lifespans increased and other aspects of senescence began to occur later in life, did reproductive senescence not keep pace? —Preceding unsigned comment added by 198.60.1.105 (talk) 19:51, 15 September 2008 (UTC)

 * well said! Tova2014 (talk) 03:29, 30 January 2024 (UTC)

Non-human species
I've come across an interesting BBC article here - "Whales and humans linked by 'helpful grandmothers' ". I don't feel sufficiently expert on the topic to incorporate this into the article, which seems to deal essentially with the human species, but others may wish to do so. Ghmyrtle (talk) 07:34, 3 July 2010 (UTC)

 * very interesting! I'm somewhat skeptical of the "grandmother hypothesis" since menopause occurs both in mothers AND non-mothers. I'm not a scientist but it seems to me this (anthropological) theory is a bit over-reaching. Tova2014 (talk) 03:28, 30 January 2024 (UTC)

updating chimpanzee research
I tried to insert references to two articles I found online, both mentioning the "grandmother hypothesis" and adding seemingly relevant research on chimpanzee menopause. Unfortunately the footnotes are a bit garbled. I hope someone will look at my edits and help with the formatting. Many thanks! Tova2014 (talk) 03:25, 30 January 2024 (UTC)

title: Talk:Grandmother hypothesis


text:
Frank Harary

Frank Harary (March 11, 1921 – January 4, 2005) was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle (and each edge of the graph had to be either blue or red). Because of the theorem on friends and strangers, one team or the other would have to win.

Biography
Frank Harary was born in New York City, the oldest child to a family of Jewish immigrants from Syria and Russia. He earned his bachelor's and master's degrees from Brooklyn College in 1941 and 1945 respectively and his Ph.D., with supervisor Alfred L. Foster, from University of California, Berkeley in 1948.

Prior to his teaching career he became a research assistant in the Institute of Social Research at the University of Michigan.

Harary's first publication, "Atomic Boolean-like rings with finite radical", went through much effort to be put into the Duke Mathematical Journal in 1950. This article was first submitted to the American Mathematical Society in November 1948, then sent to the Duke Mathematical Journal where it was revised three times before it was finally published two years after its initial submission. Harary began his teaching career at the University of Michigan in 1953 where he was first an assistant professor, then in 1959 associate professor and in 1964 was appointed as a professor of mathematics, a position he held until 1986.

From 1987 he was Professor (and Distinguished Professor Emeritus) in the Computer Science Department at New Mexico State University in Las Cruces. He was one of the founders of the Journal of Combinatorial Theory and the Journal of Graph Theory.

In 1949 Harary published On the algebraic structure of knots. Shortly after this publication in 1953 Harary published his first book (jointly with George Uhlenbeck) On the number of Husimi trees. It was following this text that he began to build up a worldwide reputation for his work in graph theory. In 1965 his first book Structural models: An introduction to the theory of directed graphs was published, and for the rest of his life his interest would be in the field of graph theory.

While beginning his work in graph theory around 1965, Harary began buying property in Ann Arbor, and subdividing the houses he bought into apartments. This led to criticism for poor maintenance, "scores of building code violations", and six condemnations of buildings he owned. In a 1969 newspaper article, Harary was quoted as stating "We just wanted these properties for the land value ... we wanted to move the tenants out", while his wife Jayne stated "We've wanted to help poor blacks find better housing, but we've taken the rap again and again." Harary and his wife Jayne had six children together, Miriam, Natalie, Judith, Thomas, Joel and Chaya.

From 1973 to 2007 Harary jointly wrote five more books, each in the field of graph theory. In the time before his death, Harary traveled the world researching and publishing over 800 papers (with some 300 different co-authors), in mathematical journals and other scientific publications, more than any mathematician other than Paul Erdos. Harary recorded that he lectured in 166 different cities around the United States and some 274 cities in over 80 different countries. Harary was particularly proud that he had given lectures in cities around the world beginning with every letter of the alphabet, even including "X" when he traveled to Xanten, Germany. Harary also played a curious role in the award-winning film Good Will Hunting. The film displayed formulas he had published on the enumeration of trees, which were supposed to be fiendishly difficult.

It was in 1986 at the age of 65 that Harary retired from his professorship at the University of Michigan. Harary did not take his retirement lightly however; following his retirement Harary was appointed as a Distinguished Professor of Computer Sciences at New Mexico State University in Las Cruces. He held this position until his death in 2005. The same year as his retirement Harary was made an honorary fellow of the National Academy of Sciences of India; he also served as an editor for about 20 different journals focusing primarily on graph theory and combinatorial theory. It was following his retirement that Harary was elected as an honorary lifetime member of the Calcutta Mathematical Society and of the South African Mathematical Society.

He died at Memorial Medical Center in Las Cruces, New Mexico. At the time of his death in Las Cruces other members of the department of Computer Science felt the loss for the great mind that once worked beside them. The head of the department of Computer Science at the time of Harary's death Desh Ranjan had this to say, "Dr. Harary was a true scholar with a genuine love for graph theory which was an endless source of new discoveries, beauty, curiosity, surprises and joy for him till the very end of his life."

Mathematics
Harary's work in graph theory was diverse. Some topics of great interest to him were:

 * Graph enumeration, that is, counting graphs of a specified kind. He coauthored a book on the subject (Harary and Palmer 1973). The main difficulty is that two graphs that are isomorphic should not be counted twice; thus, one has to apply Pólya's theory of counting under group action.  Harary was an expert in this.
 * Signed graphs. Harary invented this branch of graph theory,  which grew out of a problem of theoretical social psychology investigated by the psychologist Dorwin Cartwright and Harary.
 * Applications of graph theory in numerous areas, especially to social science such as balance theory, opinion dynamics, and the theory of tournaments. Harary was co-author of John Wiley's first e-book, Graph Theory and Geography.

Among over 700 scholarly articles Harary wrote, two were co-authored with Paul Erdős, giving Harary an Erdős number of 1. He lectured extensively and kept alphabetical lists of the cities where he spoke.

Harary's most famous classic book Graph Theory was published in 1969 and offered a practical introduction to the field of graph theory. It is evident that Harary's focus in this book and amongst his other publications was towards the varied and diverse application of graph theory to other fields of mathematics, physics and many others. Taken from the preface of Graph Theory, Harary notes ...

"...there are applications of graph theory to some areas of physics, chemistry, communication science, computer technology, electrical and civil engineering, architecture, operational research, genetics, psychology, sociology, economics, anthropology, and linguistics."

Harary quickly began promoting inquiry based learning through his texts, apparent by his reference to the tradition of the Moore method. Harary made many unique contributions to graph theory as he explored more and more different fields of study and successfully attempted to relate them to graph theory. Harary's classic book Graph Theory begins by providing the reader with much of the requisite knowledge of basic graphs and then dives right into proving the diversity of content that is held within graph theory. Some of the other mathematical fields that Harary directly relates to graph theory in his book begin to appear around chapter 13, these topics include linear algebra, and abstract algebra.

Harary also made an influential contribution in the theory of social learning used in sociology and behavioral economics, deriving a criterion for consensus in John R. P. French's model of social power. This anticipated by several decades, albeit in a special case, the widely used DeGroot learning model.

Tree square root
One motivation for the study of graph theory is its application to sociograms described by Jacob L. Moreno. For instance the adjacency matrix of a sociogram was used by Leon Festinger. Festinger identified the graph theory clique with the social clique and examined the diagonal of the cube of a groups’ adjacency matrix to detect cliques. Harary joined with Ian Ross to improve on Festinger's clique detection.

The admission of powers of an adjacency matrix led Harary and Ross to note that a complete graph can be obtained from the square of an adjacency matrix of a tree. Relying on their study of clique detection, they described a class of graphs for which the adjacency matrix is the square of the adjacency matrix of a tree.

 * If a graph G is the square of a tree, then it has a unique tree square root
 * Some vocabulary necessary to understand this proof and the methods used here are provided in Harary's The Square of a Tree: (Cliqual, unicliqual, multicliqual, cocliqual, neighborhood, neighborly, cut point, block)
 * How to determine if some graph G is the square of a tree.
 * Iff a graph G is complete or satisfies the following 5 properties then G = T2
 * (i) Every point of G is neighborly and G is connected.
 * (ii) If two cliques meet at only one point b, then there is a third clique with which they share b and exactly one other point.
 * (iii) There is a 1-1 correspondence between the cliques and the multicliqual points b of G such that clique C(b) corresponding to b contains exactly as many multicliqual points as the number of cliques which include b.
 * (iv) No two cliques intersect in more than two points.
 * (v) The number of pairs of cliques that meet in two points is one less than the number of cliques.

 * Algorithm for finding the tree square root of a graph G.
 * Step 1: Find all the cliques of G.
 * Step 2: Let the cliques of G be C1,...,Cn, and consider a collection of multicliqual points b1,...,bn corresponding to these cliques in accordance with condition iii.  The elements of this collection are the nonendpoints of T.  Find all of the pairwise intersections of the n cliques and form the graph S by joining the points bi and bj by a line if and only if the corresponding cliques Ci and Cj intersect in two points.  S is then a tree by condition v.
 * Step 3: For each clique Ci of G, let ni be the number of unicliqual points. To the tree S obtained in step 2, attach ni endpoints to bi, obtaining the tree T which we sought.

Once we have the tree in question we can create an adjacency matrix for the tree T and check that it is indeed the tree which we sought. Squaring the adjacency matrix of T should yield an adjacency matrix for a graph which is isomorphic to the graph G which we started with. Probably the simplest way to observe this theorem in action is to observe the case which Harary mentions in The Square of a Tree. Specifically the example in question describes the tree corresponding the graph of K5

"Consider the tree consisting of one point joined with all the others. When the tree is squared, the result is the complete graph.  We wish to illustrate... T2$$=$$K5"

Upon squaring the adjacency matrix of the previously mentioned tree, we can observe that the theorem does in fact hold true. We can also observe that this pattern of setting up a tree where "one point joined with all the others" will always indeed yield the correct tree for all complete graphs.

title: Frank Harary


text:
Category:Manila

Manila is the capital city of the Philippines and is located in Metro Manila, the National Capital Region.

Some articles which are listed under Category:Metro Manila may also relate to Manila. The City of Manila is the central local government unit of Metro Manila which occupies less than 10% of the Metro's land area and contains only 14% of the Metro's population.

title: Category:Manila


text: User talk:68.94.227.42

title: User talk:68.94.227.42


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User:Athrash

- Athrash | {Talk)  04:05, 13 Apr 2005 (UTC)

εν αφχη ην ο λογος

 *  My favorite destination: MANILA, Philippines — skyline NEW and OLD

title: User:Athrash


text: User talk:68.123.248.236

title: User talk:68.123.248.236


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Bill Ballinger

William George Ballinger (born December 17, 1945) is a former politician in Ontario, Canada. He was a Liberal member of the Legislative Assembly of Ontario from 1987 to 1990 who represented the GTA riding of Durham—York.

Background
Ballinger was educated at the University of Waterloo and Toronto Teacher's College. He owns and operates Artforms, in Uxbridge, Ont.

Politics
He served as mayor, councillor and regional councillor in Uxbridge, Ontario.

He was elected to the Ontario legislature in the 1987 provincial election, defeating Progressive Conservative incumbent Ross Stevenson by 482 votes. He served as parliamentary assistant to the Minister of Municipal Affairs from 1988 to 1989.

The Liberals were defeated by the Ontario New Democratic Party in the 1990 provincial election, and Ballinger lost his seat to NDP candidate Larry O'Connor by 1,230 votes.

title: Bill Ballinger


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Brad Radke

Brad William Radke (born October 27, 1972) is an American former professional baseball pitcher who played his entire 12-season career with the Minnesota Twins of Major League Baseball (MLB). Radke won 148 career games and was one of the most consistent pitchers in the Twins organization during the late 1990s.

Biography
Radke was born in Eau Claire, Wisconsin and graduated from Jesuit High School of Tampa where he set a single-season school record with a 0.31 earned run average. He also played for the school's basketball team. He accepted a scholarship to play college baseball at South Florida.

Minnesota Twins
Radke was not considered a top prospect before being drafted in the 8th round of the 1991 amateur draft by the Twins. Once he was in the majors though, he was valued highly and the Twins were offered a large amount of talent for him, but they never gave him up.

In his debut season (1995), he finished 11–14 with a 5.32 ERA. In 1997, he finished an excellent season with a 20–10 record and a 3.87 ERA in 239 innings. During the year, he won 12 consecutive games in 12 consecutive starts, becoming only the third player since 1950 (along with Bob Gibson and Pat Dobson) to accomplish the feat. He finished third in American League Cy Young Award voting.

From 1998 to 2001, Radke averaged 12 wins a year and 32 starts each season. He pitched over 210 innings a season for the Twins.

In 2002, for the first time in his big league career, he failed to pitch in 30 games and fell one win short from finishing with 10 wins for the eight straight season. His ERA was 4.72, the first time since Radke's rookie season in 1995 that he had recorded an ERA above 4.50.

In 2003 and 2004, Radke came back to form, notching 14 and 11 wins respectively.

He was known for being one of the best control pitchers of the modern era, walking an average of only 41 batters a year, in an average of 34 games a year. He was, however, also known for giving up home runs, yielding as many as 40 in a single season, and he was often plagued by first-inning troubles. This had the effect of making his ERA totals sometimes seem deceptively high, as his first-inning ERA was sometimes more than a full run higher than his ERA's for the rest of the game. His susceptibility to home runs was lampooned in a commercial for Sega Sports' World Series Baseball II in 1995, and featured Radke watching as home runs sailed out of the park.

Radke had hinted that he might retire following the 2006 season, citing a torn labrum (through which he had been pitching the 2006 season). A stress fracture in his shoulder suffered in late August sidelined him as of September 2. On September 12, he threw catch from a distance of 110 ft (slightly less than twice the distance from the pitcher's mound to home plate) without pain, an important step in the way to his return for the last week or two of the season and the Twins' playoff drive, and even more important with Francisco Liriano's season appearing to be over with the reappearance of pain in his left elbow on September 13. On September 28, Radke returned to action, pitching five innings and surrendering one unearned run, earning no decision in a 2-1 Twins victory over the Kansas City Royals. It was Radke's last regular season start. He finished the season with a 12-9 record in 28 starts. In his last major league appearance, he pitched in the third game of the division series against the Oakland Athletics, giving up four runs on two two-run home runs in four innings. He officially announced his retirement from baseball on December 19, 2006. At the time of his retirement, Radke ranked second in franchise history in starts (377), third in wins (148), third in innings pitched (2,451) and third in strikeouts (1,467).

On July 11, 2009, Radke was inducted into the Minnesota Twins Hall of Fame. On April 12, 2010, Radke was selected to raise one of the Twins pennant flags in left field at Target Field.

Batting
Being in the AL, interleague play forced him to bat 29 times. He had 3 hits, a .103 batting average. He had no walks, but 5 sacrifice hits.

Postseason
Radke made his first of back-to-back-to-back postseason appearances in 2002. His postseason totals are very solid with an overall 3.19 ERA in 31 innings pitched.

His best postseason series was his first, against Oakland. He started two games out of the five, winning both with a 1.54 ERA. Radke only gave up one run in the deciding game of the series before the 5–1 Twins lead was almost squandered in the ninth inning, when Eddie Guardado gave up three runs. But the Twins won 5–4 and advanced to the 2002 American League Championship Series. He would go on to lose the only game he pitched against the Angels, but shut them out for the first six innings of that game. In the end, the Twins lost the game 7–1 and the series 4–1.

He was 2–3 overall in the postseason.

Personal life
In 2002, Radke and his wife, Heather, announced the formation of a charity, the Brad and Heather Radke Family Foundation, which would support the Hennepin County Medical Center.

Radke's son, Kasey, pitched for the University of Tampa and his son, Ryan, played basketball for Radke's alma mater, Jesuit High School.

In 2011, Radke sold his Greenwood, Minnesota home for $2.4 million (equivalent to $ million in ).

Highlights

 * All-Star (1998)
 * Led league in strikeout-to-walk ratio (5.27-to-1, 2001)
 * 7th in the league in strikeouts (174, 1997)
 * 2nd in the league in complete games (six, 2001, tied with Mark Mulder, behind only Steve Sparks)
 * Finished 3rd in Cy Young Award balloting in 1997, behind Roger Clemens and Randy Johnson.
 * Ranks #18 in strikeout to walk ratio All-time SO/BB leaderboard from BaseballReference.com
 * Ranks #32 in lowest walks per nine innings pitched ratio (1.681) All-time lowest BB/9IP leaderboard from BaseballReference.com

title: Brad Radke


text: User talk:70.146.113.77

title: User talk:70.146.113.77


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Auguste Herbin

Auguste Herbin (29 April 1882 – 31 January 1960) was a French painter of modern art. He is best known for his Cubist and abstract paintings consisting of colorful geometric figures. He co-founded the groups Abstraction-Création and Salon des Réalités Nouvelles which promoted non-figurative abstract art.

Early life
Herbin was born in Quiévy, Nord. His father was a craftsman. Herbin studied drawing at the École des Beaux-Arts de Lille, from 1899 to 1901, when he settled in Paris.

Career
The initial influence of Impressionism and Post-Impressionism visible in paintings that he sent to the Salon des Indépendants in 1906 gradually gave way to an involvement with Fauvism, and he exhibited at the Salon d'Automne in 1907. He started to experiment with Cubism after his move in 1909 to the Bateau-Lavoir studios, where he met Pablo Picasso, Georges Braque, Otto Freundlich and Juan Gris; he was also encouraged by his friendship with the art collector and critic Wilhelm Uhde. His work was exhibited in the same room as that of Jean Metzinger, Albert Gleizes and Fernand Léger in the Salon des Indépendants of 1910.

In 1914, at the outbreak of World War I, he was exempted from military service because of his short stature and was committed to work in an airplane factory near Paris.

After producing his first abstract paintings in 1917, Herbin came to the attention of Léonce Rosenberg who, after World War I, made him part of the group centred on his Galerie de l'Effort Moderne and exhibited his work there on several occasions in March 1918 and 1921. Herbin's radical reliefs of simple geometric forms in painted wood, such as Colored Wood Relief (1921; Paris, Musée National d'Art Moderne), challenged not only the status of the easel painting but also traditional figure–ground relationships. The incomprehension that greeted these reliefs and related furniture designs, even from those critics most favorably disposed towards Cubism, was such that until 1926 or 1927 he followed Rosenberg's advice to return to a representational style and produced paintings in the New Objectivity style.

Herbin himself later disowned his landscapes, still lifes and genre scenes of this period, such as Bowls Players (1923; Paris, Musée National d'Art Moderne), in which the objects were depicted as schematized volumes. Under the influence of surrealism, he became increasingly critical of the rational forms employed by De Stijl. After 1927, Herbin becomes interested by microphotographs of crystals and plants and completely abandons figurative painting.

In the 1930s, he co-founded the group Abstraction-Création in Paris and served as publisher and author for the journal ''Abstraction-Création. Art non figurativ''. In the second issue of the journal he wrote against the rising Fascism and oppression of all kinds. As a member of the Communist Association des Écrivains et Artistes Révolutionnaires he signed a statement against the political indifference of artists. Critical of Stalinism, he left the Communist party in the 1940s.

Beginning in 1942, Herbin developed a language of form and color, his "alphabet plastique". Increasingly, his paintings consist only of colorful arrangements of triangles, circles and rectangles. In 1946 he was one of the founders of the Salon des Réalités Nouvelles, a successor of Abstraction-Création. He later served as the group's vice-president.

Late life and death
After 1953, Herbin was paralyzed on the right side, forcing him to paint with the left hand. He died in Paris on 31 January 1960. One painting remained unfinished—the motif of the painting was constructed on the word Fin.

During the 2000s, an important series of original Herbin's signed rugs have been realised by Didier Marien from the Boccara Gallery with the agreement of the rights holders. Those rugs exhibited in France, but also in Moscow, London and New York played a key role in the worldwide rediscovery of Herbin's artistic creations.

Public collections
Among the public collections holding works by Auguste Herbin are:
 * Museum de Fundatie, Zwolle, The Netherlands
 * Kröller-Müller Museum, Otterlo, The Netherlands
 * National Galleries of Scotland
 * Matisse Museum, Le Cateau-Cambrésis, France
 * KUNSTEN Museum of Modern Art Aalborg, Denmark
 * Museum of Modern Art, Ceret, France

title: Auguste Herbin


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Maurice Hilleman

Maurice Ralph Hilleman (August 30, 1919 – April 11, 2005) was a leading American microbiologist who specialized in vaccinology and developed over 40 vaccines, an unparalleled record of productivity. According to one estimate, his vaccines save nearly eight million lives each year. He has been described as one of the most influential vaccinologists ever. He has been called the "father of modern vaccines". Robert Gallo called Hilleman "the most successful vaccinologist in history". He has been noted by some researchers as having saved more lives than any other scientist in the 20th century.

Of the 14 vaccines routinely recommended in American vaccine schedules, Hilleman and his team developed eight: those for measles, mumps, hepatitis A, hepatitis B, chickenpox, Neisseria meningitidis, Streptococcus pneumoniae and Haemophilus influenzae bacteria. During the "1957-1958 Asian flu pandemic", his vaccine is believed to have saved hundreds of thousands of lives. He also played a key role in developing the vaccine for the "1968-1969 Hong Kong flu pandemic". He also played a role in the discovery of antigenic shift and drift, the cold-producing adenoviruses, the hepatitis viruses, and the potentially cancer-causing virus SV40.

Early life and education
Hilleman was born on a farm near the high plains town of Miles City, Montana. His parents were Anna (Uelsmann) and Gustav Hillemann, and he was their eighth child. His twin sister died when he was born, and his mother died two days later. He was raised in the nearby household of his uncle, Bob Hilleman, and worked in his youth on the family farm. He credited much of his success to his work with chickens as a boy; since the 1930s, fertile chicken eggs had often been used to grow viruses for vaccines.

His family belonged to the Lutheran Church–Missouri Synod. When he was in the eighth grade, he discovered Charles Darwin, and was caught reading On the Origin of Species in church. Later in life, he rejected religion. Due to lack of funds, he almost failed to attend college. His eldest brother interceded, and Hilleman graduated first in his class in 1941 from Montana State University with family help and scholarships. He won a fellowship to the University of Chicago and received his doctoral degree in microbiology in 1944. His doctoral thesis was on chlamydia infections, which were then thought to be caused by a virus. Hilleman showed that these infections were actually caused by a species of bacterium, Chlamydia trachomatis, that grows only inside of cells.

Career
After joining E.R. Squibb & Sons (now Bristol-Myers Squibb), Hilleman developed a vaccine against Japanese B encephalitis, a disease that threatened American troops in the Pacific Ocean theater of World War II. As chief of the Department of Respiratory Diseases at Army Medical Center (now the Walter Reed Army Institute of Research) from 1948 to 1957, Hilleman discovered the genetic changes that occur when the influenza virus mutates, known as antigenic shift and Antigenic drift, which he theorized would mean that a yearly influenza vaccination would be necessary.

In 1957, Hilleman joined Merck & Co. (Kenilworth, New Jersey), as head of its new virus and cell biology research department in West Point, Pennsylvania. It was at Merck that Hilleman developed most of the forty experimental and licensed animal and human vaccines for which he is credited, working both at the laboratory bench as well as providing scientific leadership.

Hilleman served on many national and international advisory boards and committees, academic, governmental and private, including the National Institutes of Health's Office of AIDS Research Program Evaluation and the Advisory Committee on Immunization Practices of the National Immunization Program.

Asian flu pandemic
Hilleman was among the first to recognize that a 1957 outbreak of influenza in Hong Kong could become a huge pandemic. Working on a hunch, after nine 14-hour days he and a colleague determined that it was a new strain of flu that could kill millions. Forty million doses of vaccines were prepared and distributed. Although 69,000 Americans died, the pandemic could have resulted in many more deaths in the United States. Hilleman was awarded the Distinguished Service Medal from the American military for his work. His vaccine is believed to have saved hundreds of thousands of lives.

In 1968, during the Hong Kong flu pandemic, Hilleman and his team also played a key role in developing a vaccine, and nine million doses became available in 4 months.

SV40
Hilleman was one of the vaccine pioneers to warn about the possibility that simian viruses might contaminate vaccines. The best-known of these viruses is SV40, a viral contaminant of the polio vaccine, whose discovery led to the recall of Salk's vaccine in 1961 and its replacement with Albert Sabin's oral vaccine. The contamination occurred in both vaccines at very low levels, but because the oral vaccine was ingested rather than injected, it did not result in any harm.

Mumps vaccine
In 1963, his daughter Jeryl Lynn came down with the mumps. He cultivated material from her, and used it as the basis of a mumps vaccine. The Jeryl Lynn strain of the mumps vaccine is still used. The strain is used in the trivalent (measles, mumps and rubella) MMR vaccine that he also developed, the first approved vaccine to incorporate multiple live virus strains. Like many other vaccines and medications of that time period, the vaccine was tested in children with intellectual disabilities who lived in group homes; this was because, given the poor hygiene and cramped quarters of their accommodations, they were at much higher risk of infectious disease.

Hepatitis B vaccine
He and his group invented a vaccine for hepatitis B by treating blood serum with pepsin, urea and formaldehyde. This was licensed in 1981, but withdrawn in 1986 in the United States and replaced by a vaccine that was produced in yeast. The latter vaccine is still in use. By 2003, 150 countries were using it and the incidence of the disease in the United States in young people had decreased by 95%. Hilleman considered his work on this vaccine to be his single greatest achievement. Liver transplant pioneer Thomas Starzl said "...controlling the hepatitis B virus scourge ranks as one of the most outstanding contributions to human health of the twentieth century...Maurice removed one of the most important obstacles to the field of organ transplantation".

Later work and life
In his later life, Hilleman advised the World Health Organization. He retired as senior vice president of the Merck Research Labs in 1984 at its mandatory retirement age of 65. He then directed the newly created Merck Institute for Vaccinology where he worked for the next twenty years until his death in 2005.

At the time of his death in Philadelphia on April 11, 2005, at the age of 85, Hilleman was Adjunct Professor of Pediatrics at the University of Pennsylvania in Philadelphia.

Method and personality
Hilleman was a forceful man yet at the same time, modest in his claims. None of his vaccines or discoveries are named after him. He ran his laboratory like a military unit, and he was the one in command. For a time, he kept a row of "shrunken heads" (actually fakes made by one of his children) in his office as trophies representing each of his fired employees. He used profanity and tirades freely to drive his arguments home, and once, famously, refused to attend a mandatory "charm school" course intended to make Merck middle managers more civil. His subordinates were fiercely loyal to him.

Awards and honors
Hilleman was an elected member of the National Academy of Sciences, the Institute of Medicine, the American Academy of Arts and Sciences, and the American Philosophical Society. In 1988, President Ronald Reagan presented him with the National Medal of Science, the nation's highest scientific honor. He received the Prince Mahidol Award from the King of Thailand for the advancement of public health, as well as a special lifetime achievement award from the World Health Organization, the Mary Woodard Lasker Award for Public Service and the Sabin Gold Medal and Lifetime Achievement Awards. In 1975, Hilleman received the Golden Plate Award of the American Academy of Achievement.

Legacy
In March 2005, the University of Pennsylvania School of Medicine's Department of Pediatrics and The Children's Hospital of Philadelphia, in collaboration with The Merck Company Foundation, announced the creation of The Maurice R. Hilleman Chair in Vaccinology.

Robert Gallo, co-discoverer of HIV (the virus that causes AIDS), said in 2005: "If I had to name a person who has done more for the benefit of human health, with less recognition than anyone else, it would be Maurice Hilleman. Maurice should be recognized as the most successful vaccinologist in history."

In 2005, Anthony Fauci, director of the US National Institute of Allergy and Infectious Diseases, said that Hilleman's contributions were "the best kept secret among the lay public. If you look at the whole field of vaccinology, nobody was more influential." In addition, Fauci said that "Hilleman is one of the true giants of science, medicine and public health in the 20th century. One can say without hyperbole that Maurice has changed the world."

In 2007, Paul Offit published a biography of Hilleman, entitled Vaccinated: One Man's Quest to Defeat the World's Deadliest Diseases.

In 2007, Anthony S. Fauci wrote in a biographical memoir of Hilleman: "Maurice was perhaps the single most influential public health figure of the twentieth century, if one considers the millions of lives saved and the countless people who were spared suffering because of his work. Over the course of his career, Maurice and his colleagues developed more than forty vaccines. Of the fourteen vaccines currently recommended in the United States, Maurice developed eight."In 2008, Merck named its Maurice R. Hilleman Center for Vaccine Manufacturing, in Durham, North Carolina, in memory of Hilleman.

In 2009, the American Society of Microbiology (ASM) established the Maurice Hilleman/Merck Award in Vaccinology to honor major contributions to pathogenesis, vaccine discovery, vaccine development, and/or control of vaccine-preventable diseases. The annual award was presented from 2008 to 2018. The first laureate was Stanley Plotkin. Subsequent awardees were Samuel L. Katz (2010),  Albert Z. Kapikian (2011), Myron Levine (2012),  Emil Gotschlich and R. Gwin Follis-Chevron (2013), Dan M. Granoff (2014), Peter Palese (2016) and Stephen Whitehead (2018)

In 2016, a documentary film titled Hilleman: A Perilous Quest to Save the World's Children, chronicling Hilleman's life and career, was released by Medical History Pictures, Inc.

In 2016, Montana State University dedicated a series of scholarships in memory of its alumnus Hilleman, called the Hilleman Scholars Program, for incoming students who "commit to work at their education beyond ordinary expectations and help future scholars that come after them".

title: Maurice Hilleman


text:
User talk:Therighteous

Hello. Thanks for vandalizing my user page and making blatant POV edits to Oliver North. You'll probably be blocked for it, but enjoy it while you can. T IMBO  ( T A L K )  04:10, 13 Apr 2005 (UTC)

Please stop vandalizing Wikipedia, or you will be banned from editing. Last warning. CDC  (talk)  04:24, 13 Apr 2005 (UTC)

title: User talk:Therighteous


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Small-signal model

Small-signal modeling is a common analysis technique in electronics engineering used to approximate the behavior of electronic circuits containing nonlinear devices with linear equations. It is applicable to electronic circuits in which the AC signals (i.e., the time-varying currents and voltages in the circuit) are small relative to the DC bias currents and voltages. A small-signal model is an AC equivalent circuit in which the nonlinear circuit elements are replaced by linear elements whose values are given by the first-order (linear) approximation of their characteristic curve near the bias point.

Overview
Many of the electrical components used in simple electric circuits, such as resistors, inductors, and capacitors are linear. Circuits made with these components, called linear circuits, are governed by linear differential equations, and can be solved easily with powerful mathematical frequency domain methods such as the Laplace transform.

In contrast, many of the components that make up electronic circuits, such as diodes, transistors, integrated circuits, and vacuum tubes are nonlinear; that is the current through them is not proportional to the voltage, and the output of two-port devices like transistors is not proportional to their input. The relationship between current and voltage in them is given by a curved line on a graph, their characteristic curve (I-V curve). In general these circuits don't have simple mathematical solutions. To calculate the current and voltage in them generally requires either graphical methods or simulation on computers using electronic circuit simulation programs like SPICE.

However in some electronic circuits such as radio receivers, telecommunications, sensors, instrumentation and signal processing circuits, the AC signals are "small" compared to the DC voltages and currents in the circuit. In these, perturbation theory can be used to derive an approximate AC equivalent circuit which is linear, allowing the AC behavior of the circuit to be calculated easily. In these circuits a steady DC current or voltage from the power supply, called a bias, is applied to each nonlinear component such as a transistor and vacuum tube to set its operating point, and the time-varying AC current or voltage which represents the signal to be processed is added to it. The point on the graph of the characteristic curve representing the bias current and voltage is called the quiescent point (Q point). In the above circuits the AC signal is small compared to the bias, representing a small perturbation of the DC voltage or current in the circuit about the Q point. If the characteristic curve of the device is sufficiently flat over the region occupied by the signal, using a Taylor series expansion the nonlinear function can be approximated near the bias point by its first order partial derivative (this is equivalent to approximating the characteristic curve by a straight line tangent to it at the bias point). These partial derivatives represent the incremental capacitance, resistance, inductance and gain seen by the signal, and can be used to create a linear equivalent circuit giving the response of the real circuit to a small AC signal. This is called the "small-signal model".

The small signal model is dependent on the DC bias currents and voltages in the circuit (the Q point). Changing the bias moves the operating point up or down on the curves, thus changing the equivalent small-signal AC resistance, gain, etc. seen by the signal.

Any nonlinear component whose characteristics are given by a continuous, single-valued, smooth (differentiable) curve can be approximated by a linear small-signal model. Small-signal models exist for electron tubes, diodes, field-effect transistors (FET) and bipolar transistors, notably the hybrid-pi model and various two-port networks. Manufacturers often list the small-signal characteristics of such components at "typical" bias values on their data sheets.

Variable notation

 * DC quantities (also known as bias), constant values with respect to time, are denoted by uppercase letters with uppercase subscripts. For example, the DC input bias voltage of a transistor would be denoted $$V_\mathrm{IN}$$.  For example, one might say that $$V_\mathrm{IN} = 5$$.
 * Small-signal quantities, which have zero average value, are denoted using lowercase letters with lowercase subscripts. Small signals typically used for modeling are sinusoidal, or "AC", signals. For example, the input signal of a transistor would be denoted as $$v_\mathrm{in}$$. For example, one might say that $$v_\mathrm{in}(t) = 0.2\cos (2\pi t)$$.
 * Total quantities, combining both small-signal and large-signal quantities, are denoted using lower case letters and uppercase subscripts. For example, the total input voltage to the aforementioned transistor would be denoted as $$v_\mathrm{IN}(t)$$.  The small-signal model of the total signal is then the sum of the DC component and the small-signal component of the total signal, or in algebraic notation, $$v_\mathrm{IN}(t)=V_\mathrm{IN}+v_\mathrm{in}(t)$$.  For example, $$v_\mathrm{IN}(t)=5 + 0.2\cos (2\pi t)$$

PN junction diodes
The (large-signal) Shockley equation for a diode can be linearized about the bias point or quiescent point (sometimes called Q-point) to find the small-signal conductance, capacitance and resistance of the diode. This procedure is described in more detail under diode modelling, which provides an example of the linearization procedure followed in small-signal models of semiconductor devices.

Differences between small signal and large signal
A large signal is any signal having enough magnitude to reveal a circuit's nonlinear behavior. The signal may be a DC signal or an AC signal or indeed, any signal. How large a signal needs to be (in magnitude) before it is considered a large signal depends on the circuit and context in which the signal is being used. In some highly nonlinear circuits practically all signals need to be considered as large signals.

A small signal is part of a model of a large signal. To avoid confusion, note that there is such a thing as a small signal (a part of a model) and a small-signal model (a model of a large signal).

A small signal model consists of a small signal (having zero average value, for example a sinusoid, but any AC signal could be used) superimposed on a bias signal (or superimposed on a DC constant signal) such that the sum of the small signal plus the bias signal gives the total signal which is exactly equal to the original (large) signal to be modeled. This resolution of a signal into two components allows the technique of superposition to be used to simplify further analysis. (If superposition applies in the context.)

In analysis of the small signal's contribution to the circuit, the nonlinear components, which would be the DC components, are analyzed separately taking into account nonlinearity.

title: Small-signal model


text:
Wikipedia:Articles for deletion/Export-oriented

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was keep. ugen 64 21:01, 26 Apr 2005 (UTC)

Export-oriented

 * Delete. Dicdef/adjective... I can't see it ever being encyclopedic... concept is better covered in other economics-related articles. Feco 04:11, 13 Apr 2005 (UTC)
 * Move to wiktionary if this is actually a specific term used in international commerce and then delete. Just delete if not.  Postdlf 04:23, 13 Apr 2005 (UTC)
 * I have made a rewrite. Unless there is something to merge this with, I suggest keep and expand. Sjakkalle 13:04, 13 Apr 2005 (UTC)
 * Keep and expand, although I'm not sure there's not somewhere this could be merged. Also might need a disambiguation for export-oriented growth (the development strategy). Meelar (talk) 18:56, Apr 13, 2005 (UTC)

 * This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


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Solarsoft

Solarsoft is a collaborative software development system created at Lockheed-Martin to support solar data analysis and spacecraft operation activities. It is widely recognized in the solar physics community as having revolutionized solar data analysis starting in the early 1990s. Solarsoft is in active development and use by research groups on all seven continents.

Solarsoft is a store-and-forward system that makes use of rsync, csh and other UNIX tools to distribute the software to a wide variety of platforms. Solarsoft predates CVS and most other collaborative development systems; hence, it does not provide direct support for many features that today would be considered necessary, such as software versioning. The use of Solarsoft has grown to include calibration data and even complete catalog indices for some instruments, as well as the scientific software.

Most of the software in the Solarsoft tree pertains to either solar data analysis or specific space missions or observatories such as Yohkoh or SOHO. The vast majority is written in IDL, the most commonly used analysis platform in the solar physics community, though some C, ana, and PDL modules are also available.

title: Solarsoft


text:
Talk:Contour plowing

Vfd
On April 7, 2005, this article was nominated for deletion. The result was keep. See Votes for deletion/Contour plowing for a record of the discussion. —Korath (Talk) 04:11, Apr 13, 2005 (UTC)

Suggested merge
Contour bunding is a similar concept, but acheived in a slightly different way. Someone else might like to merge the two articles. I am just going to add merge templates to alert readers to the existence of the two related articles. JonH (talk) 12:21, 3 May 2009 (UTC)

 * Done. Wongm (talk) 11:45, 22 July 2009 (UTC)

External links modified
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title: Talk:Contour plowing


text: User talk:68.62.169.14

title: User talk:68.62.169.14