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Johann Puch

Johann Puch (Janez Puh, 27 June 1862 – 19 July 1914) was a Slovene inventor and mechanic who went on to become the founder of the Austrian Puch automobile plants, then one of the most significant vehicle producers in Europe.

Biography
Johann Puch was born on 27 June 1862 to Slovene peasants at house no. 79 in Sakušak near Ptuj (Pettau), part of Lower Styria, Slovenia. He was the son of the cottager Franz Puch and Agnes Ziserl Puch, and he was baptized Johann Puch the same day in Juršinci. The eldest son of nine children, he left his family home at the age of eight and at twelve apprenticed as a locksmith in Ptuj. Having finished his training in 1877, he moved to the Styrian capital Graz, where he did his military service and from 1885 worked for several employers. He concentrated on bicycle manufacturing and soon became a noted specialist. On 18 September 1889, he married Maria Anna Reinitzhuber at the cathedral in Graz.

In 1889 Puch travelled to a bicycle trade fair in Leipzig, where he concluded a contract with Thomas Humber's cycle company. The same year he founded his first workshop in Graz and started to distribute Styria safety bicycles. His enterprise quickly expanded and in 1891 he founded the Johann Puch & Comp. trading company with 34 employees, selling bicycles all over Austria-Hungary, as well as exporting to the United Kingdom and France. Racers on Styria bicycles were successful in long-distance road races, most notably Josef Fischer, winner of the first edition of Paris–Roubaix in 1896. At that time, Puch already employed more than 300 workers and sold about 6,000 bicycle per annum. His achievements but also discrepancies with his affiliates led to the founding of his own manufacturing company in 1899, called Johann Puch - Erste steiermärkische Fahrrad-Fabriks-Actien Gesellschaft (First Styrian Bicycle Stock Company) in Graz. The company started producing motorcycles in 1903 and automobiles in 1904. By 1912 Puch's factory employed 1,100 workers and manufactured 300 cars, 300 motorcycles and 16,000 bicycles per year. He retired in 1912 but remained honorary president of the company.

Up to 1914 Puch developed 21 different types of cars, and also lorries, buses, military and some other special vehicles, including sedan limousines for the imperial Habsburg family. He successfully obtained patents for more than 35 inventions and improvements. He died of a stroke while attending a horserace in Agram (Zagreb).

The Puch company manufactured vehicles for the Austro-Hungarian Army during World War I. Puch's motorcycles and cars were successful in races and rallies all over Europe and carried his name among vehicle producers. From 1934 the tradition was continued by the Steyr-Daimler-Puch company in Graz and Vienna.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Johann Puch


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Ecotype

In evolutionary ecology, an ecotype, sometimes called ecospecies, describes a genetically distinct geographic variety, population, or race within a species, which is genotypically adapted to specific environmental conditions.

Typically, though ecotypes exhibit phenotypic differences (such as in morphology or physiology) stemming from environmental heterogeneity, they are capable of interbreeding with other geographically adjacent ecotypes without loss of fertility or vigor.

Definition
An ecotype is a variant in which the phenotypic differences are too few or too subtle to warrant being classified as a subspecies. These different variants can occur in the same geographic region where distinct habitats such as meadow, forest, swamp, and sand dunes provide ecological niches. Where similar ecological conditions occur in widely separated places, it is possible for a similar ecotype to occur in the separated locations. An ecotype is different from a subspecies, which may exist across a number of different habitats. In animals, ecotypes owe their differing characteristics to the effects of a very local environment. Therefore, ecotypes have no taxonomic rank.

Terminology
Ecotypes are closely related to morphs. In the context of evolutionary biology, genetic polymorphism is the occurrence in the equilibrium of two or more distinctly different phenotypes within a population of a species, in other words, the occurrence of more than one form or morph. The frequency of these discontinuous forms (even that of the rarest) is too high to be explained by mutation. In order to be classified as such, morphs must occupy the same habitat at the same time and belong to a panmictic population (whose members can all potentially interbreed). Polymorphism is actively and steadily maintained in populations of species by natural selection (most famously sexual dimorphism in humans) in contrast to transient polymorphisms where conditions in a habitat change in such a way that a "form" is being replaced completely by another.

In fact, Begon, Townsend, and Harper assert that

There is not always clear distinction between local ecotypes and genetic polymorphisms.

The notions "form" and "ecotype" may appear to correspond to a static phenomenon, however; this is not always the case. Evolution occurs continuously both in time and space, so that two ecotypes or forms may qualify as distinct species in only a few generations. Begon, Townsend, and Harper use an illuminating analogy on this:

... the origin of a species, whether allopatric or sympatric, is a process, not an event. For the formation of a new species, like the boiling of an egg, there is some freedom to argue about when it is completed.

Thus ecotypes and morphs can be thought of as precursory steps of potential speciation.

Range and distribution
Experiments indicate that sometimes ecotypes manifest only when separated by great spatial distances (of the order of 1,000 km). This is due to hybridization whereby different but adjacent varieties of the same species (or generally of the same taxonomic rank) interbreed, thus overcoming local selection. However other studies reveal that the opposite may happen, i.e., ecotypes revealing at very small scales (of the order of 10 m), within populations, and despite hybridization.

In ecotypes, it is common for continuous, gradual geographic variation to impose analogous phenotypic and genetic variation. This situation is called cline. A well-known example of a cline is the skin color gradation in indigenous human populations worldwide, which is related to latitude and amounts of sunlight. But often the distribution of ecotypes is bimodal or multimodal. This means that ecotypes may display two or more distinct and discontinuous phenotypes even within the same population. Such phenomenon may lead to speciation and can occur if conditions in a local environment change dramatically through space or time.

Examples

 * Tundra reindeer and woodland reindeer are two ecotypes of reindeer. The first migrate (travelling 5,000 km) annually between the two environments in large numbers whereas the other (who are much fewer) remain in the forest for the summer. In North America, the species Rangifer tarandus (locally known as caribou), was subdivided into five subspecies by Banfield in 1961. Caribou are classified by ecotype depending on several behavioural factors – predominant habitat use (northern, tundra, mountain, forest, boreal forest, forest-dwelling), spacing (dispersed or aggregated) and migration (sedentary or migratory).  For example, the subspecies Rangifer tarandus caribou is further distinguished by a number of ecotypes, including boreal woodland caribou, mountain woodland caribou, and migratory woodland caribou (such as the migratory George River Caribou Herd in the Ungava region of Quebec).
 * Arabis fecunda, a herb endemic to some calcareous soils of Montana, United States, can be divided into two ecotypes. The one "low elevation" group lives near the ground in an arid, warm environment and has thus developed a significantly greater tolerance against drought than the "high elevation" group. The two ecotypes are separated by a horizontal distance of about 100 km.
 * It is commonly accepted that the Tucuxi dolphin has two ecotypes – the riverine ecotype found in some South American rivers and the pelagic ecotype found in the South Atlantic Ocean. In 2022, the common bottlenose dolphin (Tursiops truncatus), which had been considered to have two ecotypes in the western North Atlantic, was separated into two species by Costa et al. based on morphometric and genetic data, with the near-shore ecotype becoming Tursiops erebennus Cope, 1865, described in the nineteenth century from a specimen collected in the Delaware River.
 * The warbler finch and the Cocos Island finch are viewed as separate ecotypes.
 * The Scots pine (Pinus sylvestris) has 20 different ecotypes in an area from Scotland to Siberia, all capable of interbreeding.
 * Ecotype distinctions can be subtle and do not always require large distances; it has been observed that two populations of the same Helix snail species separated by only a few hundred kilometers prefer not to cross-mate, i.e., they reject one another as mates. This event probably occurs during the process of courtship, which may last for hours.

title: Ecotype


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Hadamard transform

The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on $2^{m}$ real numbers (or complex, or hypercomplex numbers, although the Hadamard matrices themselves are purely real).

The Hadamard transform can be regarded as being built out of size-2 discrete Fourier transforms (DFTs), and is in fact equivalent to a multidimensional DFT of size $2 × 2 × ⋯ × 2 × 2$. It decomposes an arbitrary input vector into a superposition of Walsh functions.

The transform is named for the French mathematician Jacques Hadamard, the German-American mathematician Hans Rademacher, and the American mathematician Joseph L. Walsh.

Definition
The Hadamard transform Hm is a 2m × 2m matrix, the Hadamard matrix (scaled by a normalization factor), that transforms 2m real numbers xn into 2m real numbers Xk. The Hadamard transform can be defined in two ways: recursively, or by using the binary (base-2) representation of the indices n and k.

Recursively, we define the 1 × 1 Hadamard transform H0 by the identity H0 = 1, and then define Hm for m > 0 by: $$H_m = \frac{1}{\sqrt2} \begin{pmatrix} H_{m-1} & H_{m-1} \\ H_{m-1} & -H_{m-1} \end{pmatrix}$$ where the 1/$\sqrt{2}$ is a normalization that is sometimes omitted.

For m > 1, we can also define Hm by: $$H_m = H_{1} \otimes H_{m-1}$$ where $$ \otimes $$ represents the Kronecker product. Thus, other than this normalization factor, the Hadamard matrices are made up entirely of 1 and −1.

Equivalently, we can define the Hadamard matrix by its (k, n)-th entry by writing $$\begin{align} k &= \sum^{m-1}_{i=0} {k_i 2^i} = k_{m-1} 2^{m-1} + k_{m-2} 2^{m-2} + \dots + k_1 2 + k_0 \\ n &= \sum^{m-1}_{i=0} {n_i 2^i} = n_{m-1} 2^{m-1} + n_{m-2} 2^{m-2} + \dots + n_1 2 + n_0 \end{align}$$

where the kj and nj are the bit elements (0 or 1) of k and n, respectively. Note that for the element in the top left corner, we define: $$k = n = 0$$. In this case, we have: $$ (H_m)_{k,n} = \frac{1}{2^{m/2}} (-1)^{\sum_j k_j n_j}$$

This is exactly the multidimensional $ 2 \times 2 \times \cdots \times 2 \times 2$ DFT, normalized to be unitary, if the inputs and outputs are regarded as multidimensional arrays indexed by the nj and kj, respectively.

Some examples of the Hadamard matrices follow. $$ \begin{align} H_0 & = +\begin{pmatrix}1\end{pmatrix}\\[5pt] H_1 & = \frac{1}{\sqrt2} \left(\begin{array}{rr}             1 &  1\\              1 & -1            \end{array}\right)\\[5pt] H_2 & = \frac{1}{2} \left(\begin{array}{rrrr}     1 &  1 &  1 &  1\\      1 & -1 &  1 & -1\\      1 &  1 & -1 & -1\\      1 & -1 & -1 &  1   \end{array}\right)\\[5pt] H_3 & = \frac{1}{2^{3/2}} \left(\begin{array}{rrrrrrrr}     1 &  1 &  1 &  1 &  1 &  1 &  1 &  1\\      1 & -1 &  1 & -1 &  1 & -1 &  1 & -1\\      1 &  1 & -1 & -1 &  1 &  1 & -1 & -1\\      1 & -1 & -1 &  1 &  1 & -1 & -1 &  1\\       1 &  1 &  1 &  1 & -1 & -1 & -1 & -1\\      1 & -1 &  1 & -1 & -1 &  1 & -1 &  1\\      1 &  1 & -1 & -1 & -1 & -1 &  1 &  1\\      1 & -1 & -1 &  1 & -1 &  1 &  1 & -1   \end{array}\right)\\[5pt] (H_n)_{i,j} & = \frac{1}{2^{n/2}} (-1)^{i \cdot j} \end{align} $$ where $$ i \cdot j $$ is the bitwise dot product of the binary representations of the numbers i and j. For example, if $ n \;\geq\; 2$, then $$ (H_n)_{3,2} \;=\; (-1)^{3 \cdot 2} \;=\; (-1)^{(1,1) \cdot (1,0)} \;=\; (-1)^{1+0} \;=\; (-1)^1 \;=\; -1$$agreeing with the above (ignoring the overall constant). Note that the first row, first column element of the matrix is denoted by $ (H_n)_{0,0} $.

H1 is precisely the size-2 DFT. It can also be regarded as the Fourier transform on the two-element additive group of Z/(2).

The rows of the Hadamard matrices are the Walsh functions.

Real
According to the above definition of matrix H, here we let H = H[m,n] $$H[m,n]=\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$$

In the Walsh transform, only 1 and −1 will appear in the matrix. The numbers 1 and −1 are real numbers so there is no need to perform a complex number calculation.

No multiplication is required
The DFT needs irrational multiplication, while the Hadamard transform does not. Even rational multiplication is not needed, since sign flips is all it takes.

Some properties are similar to those of the DFT
In the Walsh transform matrix, all entries in the first row (and column) are equal to 1. $$H[m,n] = \left(\begin{array}{rrrrrrrr} 1 &  1 &  1 &  1 &  1 &  1 &  1 &  1\\  1 &  1 &  1 &  1 & -1 & -1 & -1 & -1\\  1 &  1 & -1 & -1 & -1 & -1 &  1 &  1\\  1 &  1 & -1 & -1 &  1 &  1 & -1 & -1\\   1 & -1 & -1 &  1 &  1 & -1 & -1 &  1\\  1 & -1 & -1 &  1 & -1 &  1 &  1 & -1\\  1 & -1 &  1 & -1 & -1 &  1 & -1 &  1\\  1 & -1 &  1 & -1 &  1 & -1 &  1 & -1 \end{array}\right)$$

Discrete Fourier transform： $$e^{-j 2\pi mn/N}$$

In discrete Fourier transform, when m equal to zeros (mean first row), the result of DFT also is 1. At the second row, although it is different from the first row we can observe a characteristic of the matrix that the signal in the first raw matrix is low frequency and it will increase the frequency at second row, increase more frequency until the last row.

If we calculate zero crossing:

First row = 0 zero crossing Second row = 1 zero crossing Third row = 2 zero crossings ⋮ Eight row = 7 zero crossings

Relation to Fourier transform
The Hadamard transform is in fact equivalent to a multidimensional DFT of size $2 × 2 × ⋯ × 2 × 2$.

Another approach is to view the Hadamard transform as a Fourier transform on the Boolean group $$(\Z / 2\Z)^n$$. Using the Fourier transform on finite (abelian) groups, the Fourier transform of a function $$f \colon (\Z/2\Z)^n \to \Complex$$ is the function $$\widehat f$$ defined by $$\widehat{f}(\chi) = \sum_{a \in (\Z/2\Z)^n} f(a) \bar{\chi}(a)$$ where $$\chi$$ is a character of $$(\Z/2\Z)^n$$. Each character has the form $$\chi_r(a) = (-1)^{a \cdot r}$$ for some $$r \in (\Z/2\Z)^n$$, where the multiplication is the boolean dot product on bit strings, so we can identify the input to $$\widehat{f}$$ with $$r \in (\Z/2\Z)^n$$ (Pontryagin duality) and define $$\widehat f \colon (\Z/2\Z)^n \to \Complex$$ by $$\widehat{f}(r) = \sum_{a \in (\Z/2\Z)^n} f(a) (-1)^{r \cdot a}$$

This is the Hadamard transform of $$f$$, considering the input to $$f$$ and $$\widehat{f}$$ as boolean strings.

In terms of the above formulation where the Hadamard transform multiplies a vector of $$2^n$$ complex numbers $$v$$ on the left by the Hadamard matrix $$H_n$$ the equivalence is seen by taking $$f$$ to take as input the bit string corresponding to the index of an element of $$v$$, and having $$f$$ output the corresponding element of $$v$$.

Compare this to the usual discrete Fourier transform which when applied to a vector $$v$$ of $$2^n$$ complex numbers instead uses characters of the cyclic group $$\Z / 2^n \Z$$.

Computational complexity
In the classical domain, the Hadamard transform can be computed in $$n \log n$$ operations ($$n = 2^m$$), using the fast Hadamard transform algorithm.

In the quantum domain, the Hadamard transform can be computed in $$O(1)$$ time, as it is a quantum logic gate that can be parallelized.

Quantum computing applications
The Hadamard transform is used extensively in quantum computing. The 2 × 2 Hadamard transform $$H_1$$ is the quantum logic gate known as the Hadamard gate, and the application of a Hadamard gate to each qubit of an $n$-qubit register in parallel is equivalent to the Hadamard transform $H_n$.

Hadamard gate
In quantum computing, the Hadamard gate is a one-qubit rotation, mapping the qubit-basis states $$|0 \rangle $$ and $$|1 \rangle $$ to two superposition states with equal weight of the computational basis states $$|0 \rangle $$ and $$|1 \rangle $$. Usually the phases are chosen so that $$H=\frac{|0\rangle+|1\rangle}{\sqrt{2}}\langle0|+\frac{|0\rangle-|1\rangle}{\sqrt{2}}\langle1|$$

in Dirac notation. This corresponds to the transformation matrix $$H_1=\frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$$ in the $$|0 \rangle, |1 \rangle $$ basis, also known as the computational basis. The states $ \frac{\left|0\right\rangle + \left|1\right\rangle}{\sqrt{2}}$ and $\frac{\left|0\right\rangle - \left|1\right\rangle}{\sqrt{2}}$  are known as $$\left|\boldsymbol{+}\right\rangle$$ and $$\left|\boldsymbol{-}\right\rangle$$ respectively, and together constitute the polar basis in quantum computing.

Hadamard gate operations
$$\begin{align} H(|0\rangle) &= \frac{1}{\sqrt 2}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle =: |+\rangle\\ H(|1\rangle) &= \frac{1}{\sqrt 2}|0\rangle - \frac{1}{\sqrt{2}}|1\rangle =: |-\rangle\\ H(|+\rangle) &= H\left( \frac{1}{\sqrt 2}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle \right) = \frac{1}{2}\Big( |0\rangle + |1\rangle\Big) + \frac{1}{2}\Big(|0\rangle - |1\rangle\Big) = |0\rangle\\ H(|-\rangle) &= H\left( \frac{1}{\sqrt 2}|0\rangle - \frac{1}{\sqrt{2}}|1\rangle \right) = \frac{1}{2}\Big( |0\rangle + |1\rangle\Big) - \frac{1}{2}\Big(|0\rangle - |1\rangle\Big) = |1\rangle \end{align}$$

One application of the Hadamard gate to either a 0 or 1 qubit will produce a quantum state that, if observed, will be a 0 or 1 with equal probability (as seen in the first two operations). This is exactly like flipping a fair coin in the standard probabilistic model of computation. However, if the Hadamard gate is applied twice in succession (as is effectively being done in the last two operations), then the final state is always the same as the initial state.

Hadamard transform in quantum algorithms
Computing the quantum Hadamard transform is simply the application of a Hadamard gate to each qubit individually because of the tensor product structure of the Hadamard transform. This simple result means the quantum Hadamard transform requires $$\log_2 N $$ operations, compared to the classical case of $$N \log_2 N$$ operations.

For an $$n$$-qubit system, Hadamard gates acting on each of the $$n$$ qubits (each initialized to the $$|0\rangle$$) can be used to prepare uniform quantum superposition states when $$N$$ is of the form $$N = 2^n$$. In this case case with $$n$$ qubits, the combined Hadamard gate $$H_n$$ is expressed as the tensor product of $$n$$ Hadamard gates: $$H_n = \underbrace{H \otimes H \otimes \ldots \otimes H}_{n \text{ times}}$$

The resulting uniform quantum superposition state is then: $$ H_{n} |0\rangle^{\otimes n} = \frac{1}{\sqrt{2^n}} \sum_{j=0}^{2^n-1} |j\rangle$$ This generalizes the preparation of uniform quantum states using Hadamard gates for any $$N = 2^n$$.

Measurement of this uniform quantum state results in a random state between $$|0\rangle$$ and $

Many quantum algorithms use the Hadamard transform as an initial step, since as explained earlier, it maps n qubits initialized with $$|0 \rangle$$ to a superposition of all 2n orthogonal states in the $$ |0 \rangle, |1 \rangle $$ basis with equal weight. For example, this is used in the Deutsch–Jozsa algorithm, Simon's algorithm, the Bernstein–Vazirani algorithm, and in Grover's algorithm. Note that Shor's algorithm uses both an initial Hadamard transform, as well as the quantum Fourier transform, which are both types of Fourier transforms on finite groups; the first on $$(\Z / 2 \Z)^n$$ and the second on $$\Z /2^n \Z$$.

Preparation of uniform quantum superposition states in the general case, when $$N $$ ≠ $$2^n$$ is non-trivial and requires more work. An efficient and deterministic approach for preparing the superposition state

with a gate complexity and circuit depth of only $$ O(\log_2 N)$$ for all $$N$$ was recently presented. This approach requires only $$ n = \lceil \log_2 N \rceil$$ qubits. Importantly, neither ancilla qubits nor any quantum gates with multiple controls are needed in this approach for creating the uniform superposition state $$ |\Psi\rangle $$.

Molecular phylogenetics (evolutionary biology) applications
The Hadamard transform can be used to estimate phylogenetic trees from molecular data. Phylogenetics is the subfield of evolutionary biology focused on understanding the relationships among organisms. A Hadamard transform applied to a vector (or matrix) of site pattern frequencies obtained from a DNA multiple sequence alignment can be used to generate another vector that carries information about the tree topology. The invertible nature of the phylogenetic Hadamard transform also allows the calculation of site likelihoods from a tree topology vector, allowing one to use the Hadamard transform for maximum likelihood estimation of phylogenetic trees. However, the latter application is less useful than the transformation from the site pattern vector to the tree vector because there are other ways to calculate site likelihoods that are much more efficient. However, the invertible nature of the phylogenetic Hadamard transform does provide an elegant tool for mathematic phylogenetics.

The mechanics of the phylogenetic Hadamard transform involve the calculation of a vector $$\gamma(T)$$ that provides information about the topology and branch lengths for tree $$T$$ using the site pattern vector or matrix $$s(T)$$.

$$\gamma(T) = H^{-1}(\ln(Hs(T)))$$ where $$H$$ is the Hadamard matrix of the appropriate size. This equation can be rewritten as a series of three equations to simplify its interpretation:

$$\begin{align} r &= H s(T) \\ \rho &= \ln r \\ \gamma(T) &= H^{-1}\rho \end{align}$$

The invertible nature of this equation allows one to calculate an expected site pattern vector (or matrix) as follows:

$$s(T)=H^{-1}(\exp(H\gamma(T)))$$

We can use the Cavender–Farris–Neyman (CFN) two-state substitution model for DNA by encoding the nucleotides as binary characters (the purines A and G are encoded as R and the pyrimidines C and T are encoded as Y). This makes it possible to encode the multiple sequence alignment as the site pattern vector $$s(T)$$ that can be converted to a tree vector $$\gamma(T)$$, as shown in the following example:

The example shown in this table uses the simplified three equation scheme and it is for a four taxon tree that can be written as ((A,B),(C,D)); in newick format. The site patterns are written in the order ABCD. This particular tree has two long terminal branches (0.2 transversion substitutions per site), two short terminal branches (0.025 transversion substitutions per site), and a short internal branch (0.025 transversion substitutions per site); thus, it would be written as ((A:0.025,B:0.2):0.025,(C:0.025,D:0.2)); in newick format. This tree will exhibit long branch attraction if the data are analyzed using the maximum parsimony criterion (assuming the sequence analyzed is long enough for the observed site pattern frequencies to be close to the expected frequencies shown in the $$s(T)=H^{-1}\rho$$ column). The long branch attraction reflects the fact that the expected number of site patterns with index 6 -- which support the tree ((A,C),(B,D)); -- exceed the expected number of site patterns that support the true tree (index 4). Obviously, the invertible nature of the phylogenetic Hadamard transform means that the tree vector means that the tree vector $$\gamma(T)$$ corresponds to the correct tree. Parsimony analysis after the transformation is therefore statistically consistent, as would be a standard maximum likelihood analysis using the correct model (in this case the CFN model).

Note that the site pattern with 0 corresponds to the sites that have not changed (after encoding the nucleotides as purines or pyrimidines). The indices with asterisks (3, 5, and 6) are "parsimony-informative", and. the remaining indices represent site patterns where a single taxon differs from the other three taxa (so they are the equivalent of terminal branch lengths in a standard maximum likelihood phylogenetic tree).

If one wishes to use nucleotide data without recoding as R and Y (and ultimately as 0 and 1) it is possible to encode the site patterns as a matrix. If we consider a four-taxon tree there are a total of 256 site patterns (four nucleotides to the 4th power). However, symmetries of the Kimura three-parameter (or K81) model allow us to reduce the 256 possible site patterns for DNA to 64 patterns, making it possible to encode the nucleotide data for a four-taxon tree as an 8 × 8 matrix in a manner similar to the vector of 8 elements used above for transversion (RY) site patterns. This is accomplished by recoding the data using the Klein four-group:

As with RY data, site patterns are indexed relative to the base in the arbitrarily chosen first taxon with the bases in the subsequent taxa encoded relative to that first base. Thus, the first taxon receives the bit pair (0,0). Using those bit pairs one can produce two vectors similar to the RY vectors and then populate the matrix using those vectors. This can be illustrated using the example from Hendy et al. (1994), which is based on a multiple sequence alignment of four primate hemoglobin pseudogenes:

The much larger number of site patterns in column 0 reflects the fact that column 0 corresponds to transition differences, which accumulate more rapidly than transversion differences in virtually all comparisons of genomic regions (and definitely accumulate more rapidly in the hemoglobin pseudogenes used for this worked example ). If we consider the site pattern AAGG it would to binary pattern 0000 for the second element of the Klein group bit pair and 0011 for the first element. in this case binary pattern based on the first element first element corresponds to index 3 (so row 3 in column 0; indicated with a single asterisk in the table). The site patterns GGAA, CCTT, and TTCC would be encoded in the exact same way. The site pattern AACT would be encoded with binary pattern 0011 based on the second element and 0001 based on the first element; this yields index 1 for the first element and index 3 for the second. The index based on the second Klein group bit pair is multiplied by 8 to yield the column index (in this case it would be column 24) The cell that would include the count of AACT site patterns is indicated with two asterisks;  however,  the absence of a number in the example indicates that the sequence alignment include no AACT site patterns (likewise, CCAG, GGTC, and TTGA site patterns, which would be encoded in the same way, are absent).

Other applications
The Hadamard transform is also used in data encryption, as well as many signal processing and data compression algorithms, such as JPEG XR and MPEG-4 AVC. In video compression applications, it is usually used in the form of the sum of absolute transformed differences. It is also a crucial part of significant number of algorithms in quantum computing. The Hadamard transform is also applied in experimental techniques such as NMR, mass spectrometry and crystallography. It is additionally used in some versions of locality-sensitive hashing, to obtain pseudo-random matrix rotations.

title: Hadamard transform


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Karl Koch (botanist)

Karl Heinrich Emil Koch (6 June 1809 – 25 May 1879) was a German botanist. He is best known for his botanical explorations in the Caucasus region, including northeast Turkey. Most of his collections have today been lost. He is also known as the first professional horticultural officer in Germany.

Biography
He was born in Ettersburg near Weimar, Germany. He studied at the universities of Jena and Würzburg and taught, as privatdocent, at the University of Jena beginning 1834. He became an associate professor in 1836. He undertook a journey of research into southern Russia in 1836–38, and a second in 1843–44. The fruit of this second trip, in which he also visited Asia Minor, Great Armenia, the Caspian Sea, and the Caucasus Mountains, was his "Wanderungen im Oriente, während der Jahre 1843 und 1844" (1846).

After his second journey, he settled at the University of Berlin in 1847, where he was later appointed assistant professor. He was at the Berlin botanical gardens beginning in 1849. He became general secretary of the Berlin Horticultural Society (Verein zur Beförderung des Gartenbau, a Prussian state institution), in which capacity he published "Wochenschrift für Gartnerei und Pflanzenkunde" (1858–72). In 1859, he was appointed professor of the Agricultural High School in Berlin. He died in Berlin.

Writings
Besides the travel book already mentioned, Koch wrote "Reise durch Russland nach dem kaukasischen Isthmus" (Trip through Russia and the Caucasian isthmus, Stuttgart, 1842–43), "Fährtenabdrücke im bunten Sandstein" (with Ernst Erhard Schmid, 1841), "Hortus dendrologicus" (Berlin, 1853–54), "Dendrologie" (Erlangen, 1869–72), and other works.

title: Karl Koch (botanist)


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Talk:Finite group

Errr ... shouldn't this page have some content ...

Charles Matthews 14:46, 4 May 2004 (UTC)

OK ( three years later): The section on number of groups with a given set was incorrect, so I have replaced it. Messagetolove 01:22, 13 May 2007 (UTC)

A table of how many distinct groups for each order
There are textbooks and other references that present tables of how many distinct (non-isomorphic) groups exist for each order, for a reasonable range of integers such as n = 1, 2, 3, ... 30. Such a thing here would be a valuable example of concrete information, rather than abstrct wandering around (wondering around?) about the subject. Such a table should be provided here. For example with n = 8, there is the cyclic abelian group that can be illustated as the one that consists of the eight eighth=roots of -1. Also, there is the quaternion group (with n = 8, I emphasize) that is a non-abelian group. A non-abelian group cannot possibly be isomorphic to an abelian group, hence for n = 8, there are at least two distinct groups in existence. Upon further investigation, it is found that there are three abelian groups here, including two product groups plus two non-abelian groups, with order eight. 98.81.17.64 (talk) 22:32, 4 August 2010 (UTC)

 * You may be looking for the page list of small groups. It doesn't construct the enumeration like you describe (Wikipedia is not a textbook), but it does enumerate exhaustively all groups up to and including order 16.  Baccyak4H (Yak!) 14:19, 5 August 2010 (UTC)

 * I don't see any utility in listing the numbers of isomorphism classes of groups of small order, especially since the groups themselves have been listed elsewhere. Arcfrk (talk) 15:49, 5 August 2010 (UTC)

Another three years later
To echo the comments of Charles Matthews from 2004 and the follow-up in 2007, finite group theory is a well established subject. Focusing entirely on the number of finite groups of given order is misleading. Arcfrk (talk) 15:56, 5 August 2010 (UTC)

Request for Rewrite
This article is way too small, and doesn't talk at all about permutation groups, cyclic groups, etc. Instead it rants on about the the number of groups with n elements. The introduction is fine, but after that there is virtually no good information shown. Fraqtive42 (talk) 04:07, 14 September 2011 (UTC)

title: Talk:Finite group


text:
Linköping HC

Linköping Hockey Club, often known by its initials LHC, or colloquially among its fans as Cluben, is a Swedish professional ice hockey club from Linköping, founded in 1976. The home arena of the team is Saab Arena (formerly Cloetta Center) which accommodates 8,190 spectators.

Competing in the Swedish Hockey League (SHL; formerly Elitserien), the club is placed twelfth in the marathon standings for the top Swedish ice hockey league.

1942–1975: The club's roots
In 1942, a group of football players of BK Kenty founded the ice hockey club BK Robbi, who mostly played friendlies against other local clubs on Stångån during the winter. The board of Kenty had first been hesitant to establish a hockey department, but in 1945, the two clubs merged following lengthy discussions. Being heavily dependent on weather conditions, Kenty only played 30 games in five seasons during the second half of the 1940s. By the end of the 1950s, Kenty had established itself in Division 2, the domestic second tier. Meanwhile, the club was also granted a permanent home ground at Folkungavallen, close to the city centre. In 1969, Kenty merged with another local club, IK Terra. In the 1970s, Kenty suffered from internal differences, since part of the club's board wanted to financially prioritize football in favor of ice hockey.

1976–1998: Foundation of LHC and rise to Elitserien
Linköping HC was founded on 4 August 1976, as a spin-off from BK Kenty, and moved in to the newly-built indoor arena Stångebro Ishall.

1999–: Establishment in the top division
Linköping HC first played in the Swedish Hockey League (SHL; formerly Elitserien) in the 1999–2000 season, and has been in the top division since the 2001–02 season. They have reached the playoffs eight times. LHC reached the final for the first time in 2006–07, where they lost to Modo Hockey. In the 2007–08 season, Linköping HC advanced to the final again, this time against HV71; they lost and won the silver medal.

Season-by-season results
''This is a partial list of the last five seasons completed by Linköpings. For the full season-by-season history, see List of Linköping HC seasons.''

Current roster
Updated 15 March 2023

Scoring leaders
These are the top-ten point-scorers of Linköping HC since the 1975–76 season, in the top tier (Elitserien and SHL). Figures are updated after each completed regular season.

Note: Pos = Position; GP = Games played; G = Goals; A = Assists; Pts = Points; P/G = Points per game; = current Linköpings HC player

Appearance leaders
These are the top-ten players of Linköping HC with the most appearances since the 1975–76 season, in the top tier (Elitserien and SHL). Figures are updated after each completed regular season.

Note: Pos = Position; GP = Games played; G = Goals; A = Assists; Pts = Points; P/G = Points per game; = current Linköpings HC player

Other departments
Linköping's women's football team, Linköpings FC, is affiliated with and financially backed by Linköping HC. On 3 October 2008, the club announced that the elite men's and women's teams of local volleyball club Team Valla would also become affiliated with Linköping HC, under the name Linköpings Volleyboll Club.

title: Linköping HC


text:
Talk:Silbury Hill

West Dakota Prize
-

- A Winner of the September 2005 West Dakota Prize This entry, one of an unprecedented 52, has won the September 2005 West Dakota Prize, awarded for successfully employing the expression "legend states''" in a complete sentence. -

-

Base of the monument
"The base of the monument is 167 m (550 ft) in diameter and perfectly round"

Going by the pictures on here, the base of the monument certainly isn't 'perfectly round'. Perhaps this needs to be ammended. - Bill 11/05/07 (UK) 09.40am

Pyramid
Could you compare it to the Pyramids of Gizeh? Which is bigger?

 * Well, this one is small in comparsion. The hill is about 40 metres high, the largest pyramids are about three times taller. You can fit something like 15 "hills" inside a pyramid, (approx, the sides of the pyramids are much steeper than the hillsides so it is a little hard to estimate). // Solkoll 23:50, 3 Apr 2005 (UTC)

Template:Megalith
I've created a new template for megalithic sites, Template:Megalith, as used on Pikestones and Round Loaf. Some instructions on the template talk page, to show how to use it. Cheers! --PopUpPirate 13:29, 23 February 2007 (UTC)

2nd pic
These are NOT positive crop marks: they are two crop circles made in a field which has since been harvested. Positive crop marks are caused by underground features (ditches, walls etc); crop circles are caused above ground by drunken young farmers or Army types on secret night-time missions, or crazed hippies. Take your pick. 81.157.196.251 15:44, 12 March 2007 (UTC)

"Scientific theories"
Moses Cotsworth is given pride of place in this section, but his theory isn't referenced. I'm guessing this came from his 1904 book  	The Rational Almanac: tracing the evolution of modern almanacs from ancient ideas of time, and suggesting improvements ... 180 illustrations explaining the mystery of the Pyramids, etc  but this isn't a mainstream work. Cotsworth was a railway accounts clerk who sought to make his work easier by having the year "in all Nations" divided into months of equal length to avoid his having to work late balancing "the ever-changing differences between monthly totals for Income and Expenditure". Can anyone provide more, or perhaps we should expand the section so that it doesn't rely so heavily on Cotsworth? --Old Moonraker (talk) 05:44, 16 May 2009 (UTC)
 * Cotsworth removed. --Old Moonraker (talk) 13:10, 17 May 2009 (UTC)

Step?
In the section on scientific theories, there's suddenly mention of a step just below the summit which, as as an invisible editing note points out, hasn't been mentioned at all prior to this. As this step appears to be pretty integral to Devereux' theory (and possibly others), the article would definitely benefit greatly from information about this step being woven into the description of the hill: probably in paragraph two of the "Structure" section. I don't have any source material to attempt a description of the step or I'd add this info myself ~dom Kaos~ (talk) 21:17, 21 June 2009 (UTC)
 * Done or, at least started. --Old Moonraker (talk) 21:34, 24 June 2009 (UTC)
 * Good work - that now hangs together much better :-) ~dom Kaos~ (talk) 20:27, 25 June 2009 (UTC)

Crop circles!
There are many crop circles around Silbury hill and Avebury. You may see at least three here: http://www.wikimapia.org/#lat=51.416231&lon=-1.8545008&z=15&l=1&m=b

And there are many in database:

http://www.x-cosmos.it/cropcircles/

I think it worth mentioning.

--Varnav (talk) 10:35, 2 February 2010 (UTC)
 * The topic has a brief mention at "2nd pic" above: "caused... by drunken young farmers or Army types on secret night-time missions, or crazed hippies". What's the relevance, please? --Old Moonraker (talk) 10:47, 2 February 2010 (UTC)

 * Here is the better study: http://www.siue.edu/GEOGRAPHY/ONLINE/Northcote06.pdf But according to it the epicentre is actually Avebury, not Silbury Hill.

--Varnav (talk) 21:34, 2 February 2010 (UTC)
 * Followed the link (thanks) and skim-read, but couldn't find any mention of Silbury.--Old Moonraker (talk) 21:46, 2 February 2010 (UTC)
 * I also couldn't find any mention in that of Silbury, but the article has a lot to say about Avebury being the epicentre of English crop circles. Silbury, of course, is merely a hill within the parish of Avebury.
 * For me, these crop circles are mostly hocus pocus, but a very few of them do seem to raise difficult questions. Moonraker2 (talk) 00:32, 3 February 2010 (UTC)
 * Doesn't the pdf suggest mundane reasons for Avebury & crop circles? "these crop circles were influenced in their placement by intentional factors such as proximity to roads, population centres and cultural heritage areas, and not by postulated (and unsubstantiated) natural phenomena such as plasma vortices." Dougweller (talk) 12:32, 3 February 2010 (UTC)
 * Unfortunately no, it doesn't suggest mundane reasons. It contends that, as yet unknown natural causes are unlikely, but goes on to say "crop circles are a form of symbolic art or sign language, and as such, their purpose is to be "read" or appreciated by an audience. It is contended that this will be the case regardless of whether crop circles are "hoaxes" produced by individuals or are created by some other form of intelligence." That will be taken as positive by both sides of the debate. Richerman (talk) 13:27, 3 February 2010 (UTC)

 * It's not important in the article what makes crop circles - hoaxers or UFOs. But Avebury is the epicentre, not Silbury hill, so, we discuss the topic here —Preceding unsigned comment added by Varnav (talk • contribs) 10:41, 4 February 2010 (UTC)

2002 digging team leader
This recent WP:AGF edit removed "Fachtna McAvoy" as possible vandalism. It is however true (albeit possibly WP:COI, as McAvoy himself seems to have posted the entry) and verifiable from English Heritage's web page. I would restore the deletion, but would welcome views on subject's notability first. --Old Moonraker (talk) 00:25, 17 January 2011 (UTC)
 * These may help: and . That looks like enough. --Dougweller (talk) 06:28, 17 January 2011 (UTC)
 * I thought it was Jim Leary, but this blog suggests he replaced McAvoy early on - the recent EH book is of course by Leary and Field and doesn't mention McAvoy, although it does talk about other people on the project. Perhaps reading between the lines there was some falling out? It would be interesting to know, but at the moment, the weight of sourcing isn't particularly pointing to it not being Jim Leary. Jamesinderbyshire (talk) 10:34, 17 January 2011 (UTC)
 * I'm not sure when EH made her redundant - I found a page where she was appealing her redundancy when I searched, but can't recall dates. Dougweller (talk) 10:37, 17 January 2011 (UTC)
 * FMcA has posted an exhaustive and seemingly even-handed account (with a few interesting pictures) here. Gives the date of his removal from the project, June 2007, but doesn't help with the point at issue: whether or not to restore his name to the article. For me his prominent inclusion on the EH web page seems indicative. --Old Moonraker (talk) 12:00, 17 January 2011 (UTC)
 * Couple of general points on this. One is that at present, the article does not reflect the latest thinking in any depth - the Leary/Field book for example carries quite a number of scientifically plausible assertions that directly contradict previous widely held views and introduce new concepts and discoveries. So this needs writing up. Second point is that we should mention Leary as well in the article - he has the book and his name all over everything, along with Field. Against this backdrop there wouldn't be an objection to having User Fachtna McAvoy's edit in, but we should be wary as to what is said and the source you raise Old Moonraker, as there appear to be possible legal issues to do with a redundancy dispute in some of it. Jamesinderbyshire (talk) 12:38, 17 January 2011 (UTC)

Hi - just to say that there was a redundancy dispute (my claim for unfair dismissal against English Heritage) but legal proceedings were concluded in Dec 2010.Fachtna mcavoy (talk) 13:19, 17 January 2011 (UTC)
 * All done? OK, the consensus => restoring the edit, so I'll do that. Field has just published in British Archaeology a summary of the latest thinking; I looked at this quickly when it came out and didn't find anything greatly at odds with the WP piece. I'll look at it again in the light of the points (above) by User:Jamesinderbyshire, unless anybody beats me to it. --Old Moonraker (talk) 07:31, 19 January 2011 (UTC)
 * Well, we shouldn't have the widely discredited Dames under "Scientific Theories" for starters, but my reading of the Leary/Field book which finished a couple of months ago is that the Skanska/EH work did challenge quite a few old notions. I will try dropping some lines in on it in a bit and see what you think. Jamesinderbyshire (talk) 15:01, 19 January 2011 (UTC)
 * My apologies for removing content without noticing it was being discussed here. My reasoning was two fold, the reference clearly states there were many others involved.."Project was managed by Fachtna McAvoy between 2000 and 13th September 2007. From the 15th of June 2007 the archaeological work was directed by Jim Leary. Sarah May was the Project Manager between September 2007 and November 2008, and Brian Kerr was the Project Executive during this period. After November 2008 Jim Leary took over Project Management and Sarah May became the Project Executive. The Silbury Hill Conservation Project was under the overall project management of Rob Harding during the whole period and Amanda Chadburn was the Inspector for Ancient Monuments."
 * He has a clear conflict of interest, fair enough to add details but to just add his own name seems a bit unfair when "English Heritage" would suffice.  Teapot  george Talk  16:02, 19 January 2011 (UTC)

 * I am afraid that I do not see a 'conflict of interest' here. The reference is specifically to the archaeological fieldwork carried out at Silbury Hill in 2002. At this time, as throughout the project, Amanda Chadburn was the Inspector of Ancient Monuments and Rob Harding was the overall Project Manager.FachtnaFachtna mcavoy (talk) 17:35, 19 January 2011 (UTC)

 * I don't see a conflict of interest as such (other than for you personally in requesting the edit Fachtna) - the issue is one of balance, eg, how notable one leading name is compared to others. The Leary and Field book is one source of notability. I checked again more carefully and it does acknowledge McAvoy as excavation manager from 2000-7. It gives equal weight to a longish list of others though, including some whom Teapot does not list above. A bit tricky this one, as if we mention one, we should really give a list. It might be undue weight to list you specially Fachtna but if we do, we will need to list others. We also need to consider what is notable. I am not quite clear about the role of "excavation manager" within the scheme of things and perhaps others can comment on this. Is the "excavation manager" a scientific role or more like a project manager? If the latter, I would think it's not as notable to the public as scientists/instigators, lead academics, etc. Comments? Jamesinderbyshire (talk) 18:12, 19 January 2011 (UTC)
 * I think it is quite sufficient to say "As part of this remedial work English Heritage excavated two further small trenches" It does not need to mention specific people, especially those who are demanding to be mentioned. If Fachtna Mcavoy was notable enough to have his own article it might be worth considering but until then it would be more neutral to NOT include his name.  Teapot  george Talk  18:22, 19 January 2011 (UTC

Hello - I would like to point out that I am not 'demanding' anything and also that a properly neutral stance and consistent approach would see the replacement of 'Rob Harding' with 'English Heritage' - retaining the reference to the statement of roles and responsibilities provided on the English Heritage website.Fachtna mcavoy (talk) 00:21, 22 January 2011 (UTC)

 * Still not clear how important or otherwise the excavation manager is. If v. important, then notwithstanding that he's asking for the edit, it would be notable enough to NPOV'ley include. If of just moderate importance, I agree NOT. Jamesinderbyshire (talk) 19:04, 19 January 2011 (UTC)
 * It just looks like blatant self promotion to me with absolutely no merit.  Teapot  george Talk  19:32, 19 January 2011 (UTC)

It has of course been noted above (and I entirely agree) that the article needs to be updated in any case to include information contained in the book 'The Story of Silbury Hill' by David Field and Jim Leary which was published last year by English Heritage. For information the management/direction of the archaeological element of the Silbury Hill Conservation Project was only divided between a site/excavation manager (Jim Leary) and a Project Manager after I had been dismissed from and thereafter excluded from Silbury itself in June 2007.fachtnaFachtna mcavoy (talk) 20:41, 19 January 2011 (UTC)

I agree with Teapotgeorge, this is blatant self promotion and a clear conflict of interest. I don't believe that any consensus exists to keep the name in the article - which as currently written implies that this individual was the sole excavator. --Simple Boba.k.a. The Spaminator (Talk) 10:50, 20 January 2011 (UTC)

We have lost a link to useful material
This edit was rightly reverted, citing completely valid concerns over WP:COI. However parts of the external site, which do not deal with the personal circumstances of the contributor, contain useful material. Would it be in order if another, disinterested editor restored the more closely targeted link? Views? --Old Moonraker (talk) 12:57, 5 February 2011 (UTC)
 * I would advise not to add it, the major purpose of the sites content is another agenda entirely and Wikipedia should not really be involved in his personal disputes.  Teapot  george Talk  14:35, 5 February 2011 (UTC)
 * In the past when someone has posted a clear COI link I have deleted it, but left it in place if someone else other than the site owner subsequently posted it for good reason. However in this case I agree, no soapboxing however useful some of the content might seem to be. --Simple Boba.k.a. The Spaminator (Talk) 17:08, 5 February 2011 (UTC)
 * That's actually a very good site indeed and well worth linking to. We can simply link to the homepage or a different page from the one extolling Fachtna's virtues. Jamesinderbyshire (talk) 18:21, 5 February 2011 (UTC)
 * What is actually work linking to? All I see (from the "Home" link down) is a set of grievances that an employee has against his management and colleagues. It's your archetypal "i've been hard done by so I'm going to have my say" site. Under WP:ELNO it has absolutely no place on Wikipedia. --Simple Boba.k.a. The Spaminator (Talk) 18:31, 5 February 2011 (UTC)

Hello - the objectivity and neutrality of the contributors to wikipedia is very impressive but I think that the above comment is a little unfair. I am not 'trying to have my say' and do not do so on the website. The majority of the website content simply reproduces the documentation which I submitted to English Heritage setting out my concerns about the way I had been treated and the documentation in which English Heritage delivered its response.Fachtna mcavoy (talk) 23:08, 12 March 2011 (UTC)

 * Ah, sorry, I was thinking of another site - just checked it out and you are correct Simple Bob, it's a personal grievance site with lots of legal issues in it. I take the above comment back - correct not to link to it. Jamesinderbyshire (talk) 18:51, 5 February 2011 (UTC)
 * James, you have whetted our curiosity now—what was the "very good site indeed and well worth linking to"? --08:58, 6 February 2011 (UTC)
 * A recent re-shuffle of a couple of paragraphs, now reverted, helped me pick up James's thread. My last question was unnecessary, and my original question has been decisively answered. --Old Moonraker (talk) 06:19, 13 March 2011 (UTC)

An IP editor has added Leary & Field—thanks—but if the book is as significant as Jamesinderbyshire suggests should there be some changes to the article, referenced to their findings? --Old Moonraker (talk) 08:43, 22 January 2012 (UTC)

Nick Thomas
Professor Nicholas Thomas, Director of Cambridge University's Museum of Archaeology and Anthropology and professor of historical anthropology.. Dougweller (talk) 19:33, 5 January 2013 (UTC)
 * Ahem, thank you. Not that clear on his website. He must be a very modest chap. Would his site be seen as WP:SPS? Thanks. Martinevans123 (talk) 19:41, 5 January 2013 (UTC)
 * Or not? Would the real Prof Nick Thomas please stand up? Thanks. Martinevans123 (talk) 11:31, 6 January 2013 (UTC)

 * Wow, was I wrong and many apologies. I've removed this. See - this isn't significant enough a view for the article. Many many apologies, I should looked at the website more carefully - I know who Professor Thomas is and jumped to conclusions. Dougweller (talk) 11:35, 6 January 2013 (UTC)
 * No worries, I was a bit surprised by seeing Rudolf the Red-Nosed Archaeologist, I must admit. Martinevans123 (talk) 11:41, 6 January 2013 (UTC)
 * Note to (Not-Professor) Nick: I'm sure your suggestion is perfectly serious and looks perfectly reasonable to me. It's just that your website, as it's your own self-published research, counts as a WP:SPS or "self-published source" and thus is not considered as a WP:RS. So, sorry that your suggestion can't be added yet. Hope you understand. Martinevans123 (talk)

Height
The lede gives the height as 39.3m; the body gives it as 40m. These are from different sources, both apparently good and very close in time. Over to experts. Wikiain (talk) 00:19, 21 April 2018 (UTC)
 * 40m can be approximation of 39.3m, but what do you do with 30m which is the height in English Heritage site, which runs the place? אביהו (talk) 17:45, 23 July 2018 (UTC)

Size of Roman village
I have removed the comparison of the size of the Roman village to a multiple of football pitches as a football pitch is neither standardised or an internationally recognised unit of measurement. The Reuters article referenced doesn't give a size for the village. If anyone has a source for the size of the village in hectares or square metres, please add it. --Graham Phillips 110 (talk) 20:58, 26 January 2021 (UTC)

Menkaure
It's a real stretch equating Silbury with that pyramid. There is probably a Mesoamerican pyramid that is a better comparison. 99.229.34.174 (talk) 21:41, 4 October 2022 (UTC)

 * Silbury Hill is larger by volume than the pyramid of Menkaure, though Menkaure is taller. Menkaure was built around 2500 BC and Silbury Hill around 2400 BC. Ario1234 (talk) 23:56, 4 October 2022 (UTC)

title: Talk:Silbury Hill


text:
Marco Scutaro

Marcos Scutaro, better known as Marco Scutaro, (born October 30, 1975) is a Venezuelan former professional baseball infielder. He bats and throws right-handed. Scutaro made his major league debut with the New York Mets in 2002, and subsequently played for the Oakland Athletics, Toronto Blue Jays, Boston Red Sox, Colorado Rockies and San Francisco Giants. Scutaro was named the most valuable player of the 2012 National League Championship Series while with the Giants; he and the team then won the 2012 World Series over the Detroit Tigers.

Scutaro was one of the primary subjects of the 2005 documentary A Player to be Named Later.

Early life
Marcos Scutaro was born on October 30, 1975, in San Felipe, Venezuela. He is of Italian descent. He began playing baseball at age six.

Minor leagues
Scutaro originally signed with the Cleveland Indians as an amateur free agent on July 26, 1994. As a teenager, Scutaro considered Cleveland infielder and fellow Venezuelan Omar Vizquel his favorite player and would often watch Vizquel at spring training.

Scutaro was traded by the Indians to the Milwaukee Brewers on August 30, 2000, as the player to be named later in a trade that had sent Kane Davis, Paul Rigdon and Richie Sexson to the Brewers for Jason Bere, Bob Wickman and Steve Woodard on July 28. Scutaro was in the 2005 documentary film A Player To Be Named Later, which followed players from Indianapolis Indians, the Triple-A affiliate of the Milwaukee Brewers, for one season. He was waived at the start of the 2002 season by the Brewers, who needed to make room for Nelson Figueroa on its roster.

Scutaro was claimed off waivers by the New York Mets on April 5, 2002. He batted .319 with 22 doubles, seven home runs, 28 runs batted in and 48 runs scored in 97 games with the Triple-A Norfolk Tides in 2002. He was also selected to the International League squad for the Triple-A All-Star Game that summer.

New York Mets (2002–2003)
Scutaro's first promotion to the majors came on July 19 when the Mets recalled him from the Tides to replace the injured Joe McEwing. Scutaro introduced himself to Mets manager Bobby Valentine that afternoon while the latter was eating lunch at the hotel in Cincinnati where the team was staying. Valentine reciprocated the greeting without knowing who Scutaro was. After completing his meal, Valentine inquired about why Scutaro was lingering. "I just got called up", Scutaro responded.

Oakland Athletics (2004–2007)
Scutaro was again selected off waivers, this time by the Oakland Athletics, on October 9, 2003.

Scutaro landed a starting second baseman position after Mark Ellis had a season-ending shoulder injury during 2004 spring training.

In 2004, Scutaro reached career highs in batting average (.273), runs batted in (43), runs (50), hits (124), doubles (32), at bats (455) and games played (137). He played multiple positions during his four seasons in Oakland, including second base, shortstop, third base, left field and right field.

Toronto Blue Jays (2008–2009)
On November 18, 2007, Scutaro was traded to the Toronto Blue Jays for minor league pitchers Kristian Bell and Graham Godfrey.

Scutaro was the Jays' third baseman for at least a month, after teammate Scott Rolen injured a finger, and then Scutaro returned to a starter's role after teammate David Eckstein injured his right hip flexor on May 6. Shortly after Eckstein's return, Eckstein and Blue Jays teammate Aaron Hill collided trying to catch a fly ball. Hill suffered from concussion-like symptoms, and Scutaro filled in at second base.

Scutaro was the starting shortstop for the Blue Jays in 2009, and had his best season to date, achieving career highs in almost every offensive category: 12 home runs, 60 runs batted in, 35 doubles, 235 total bases, 162 hits, 100 runs, 14 stolen bases, and 90 walks in 574 at-bats, all while playing slick defense all year.

Boston Red Sox (2010–2011)
On December 3, 2009, Scutaro agreed to a two-year, $11 million deal with the Boston Red Sox. The deal also included a third-year mutual option. On April 12, 2010, Scutaro recorded the first hit in Target Field history on a single up the middle in the first inning off Minnesota Twins starter Carl Pavano. Soon after, Scutaro was caught stealing second base, making him the first out recorded at the Twins' new ballpark.

In his first season with the team, Scutaro set a number of career highs, including games (150), at-bats (632), hits (174) and doubles (38) while suffering for much of the season with a right shoulder injury which forced him out of practice.

Colorado Rockies (2012)
On October 30, 2011, the Red Sox and Scutaro agreed to exercise their mutual contract option. Then, on January 21, 2012, Scutaro was traded to the Colorado Rockies for pitcher Clayton Mortensen.

San Francisco Giants (2012–2014)
On July 27, 2012, Scutaro was traded, along with cash considerations, to the San Francisco Giants for infielder Charlie Culberson. In a game against the St. Louis Cardinals at Busch Stadium on August 8, 2012, Scutaro drove in a career high seven runs, including a grand slam. He hit .306 for the regular season, including .362 as a Giant, helping the Giants win the National League West title. He was awarded the NLCS MVP after tying the NLCS record with 14 hits and also batting .500 (14-for-28) with six runs scored and four runs batted in during the seven game series against the Cardinals. On October 28, in the tenth inning of Game 4 of the 2012 World Series, Scutaro drove in Ryan Theriot for the winning run, as the Giants swept the Detroit Tigers.

After the 2012 season, Scutaro and the Giants agreed to a three-year, $20 million contract, which became official on December 7, 2012. In 2013, Scutaro was the starting second baseman, with Tony Abreu and Nick Noonan as his main backups. In 81 games in the first half, Scutaro hit .316/.367/.400 with two home runs, 22 runs batted in and 37 runs, and he was named to the 2013 All-Star Game. Scutaro played his last game of 2013 on September 15, and was officially shut down on September 24. He underwent surgery on September 27 that inserted a pin in his left pinkie correcting his mallet finger, an injury he suffered on June 11 against the Pirates when he was hit by Tony Watson. In 127 games in 2013, he hit .297/.357/.369 with two home runs, 31 runs batted in and 57 runs.

Scutaro started the 2014 season on the disabled list with back problems. He played in five games in July before his back issues forced him to return to the disabled list for the remainder of the season. On December 19, 2014, Scutaro underwent back surgery that some reports indicated could end his career. The Giants designated him for assignment on January 21, 2015, and he was removed from the 40-man roster. On January 28, 2015, Scutaro was released by the Giants. The Giants re-signed Scutaro to a major league contract on June 17 and placed him on the 60-day disabled list. He continued to rehabilitate his injury with the Giants, not with the intention of playing, but "in hopes of maintaining a quality of life and be pain-free with his family," according to the Giants.

World Baseball Classic
Because of his Italian heritage, Scutaro was given the option of playing for either Italy or Venezuela in the 2006 World Baseball Classic. He chose to play for Venezuela as a utility infielder. He again represented Venezuela in the 2009 World Baseball Classic and 2013 World Baseball Classic. Venezuela won the bronze medal in 2009, but in 2013 earned an early exit after a loss to Puerto Rico 6–3. However, Venezuela won against newcomers Spain to earn a direct qualification for the 2017 World Baseball Classic.

title: Marco Scutaro


text:
Blaenavon

Blaenavon (Blaenafon) is a town and community in Torfaen county borough, Wales, high on a hillside on the source of the Afon Lwyd. It is within the boundaries of the historic county of Monmouthshire and the preserved county of Gwent. The population is 6,055.

Parts of the town and surrounding country form the Blaenavon Industrial Landscape, selected as a World Heritage Site by UNESCO in 2000.

History

Blaenavon literally means "head of the river" or loosely "river's source" in the Welsh language. Blaenavon grew around an ironworks opened in 1788 by the West Midlands industrialist Thomas Hill and his partners, Thomas Hopkins and Benjamin Pratt. The businessmen invested £40,000 into the ironworks project and erected three blast furnaces. Hopkins, as a result of operating the Cannock Wood Forge, Staffordshire, was in contact with skilled and experienced ironworkers, and managed to persuade many of them to migrate to Blaenavon to help establish the new ironworks. In 1836 Robert William Kennard formed the Blaenavon Coal and Iron Company, which subsequently bought the Blaenavon Ironworks.

Blaenavon House, a mansion constructed in 1798 by Thomas Hopkins, was repurposed as a hospital in 1924, supported by the subscriptions of local iron and coal workers. In the 1940s the hospital site was given by the then owners of the site, the National Coal Board, to the UK Ministry of Health; it was run as a cottage hospital until 1985. When the hospital closed the building was sold by the local authority and refurbished as a nursing home for the elderly. In 1995 the building was listed as a Grade 2 listed building. Following the closure of the nursing home in 2007, the building was left empty. It was badly vandalised and stripped of its lead work, slate roof and original interiors, and was placed on the Buildings At Risk register. In 2016 a fire caused severe damage to the ballroom wing and adjoining extension. The House was sold in 2017 to private owners and is currently undergoing restoration as a family home once again.

The Municipal Offices in Lion Street were the home of Blaenavon Urban District Council until local government reorganisation in 1974.

Governance
Blaenavon is a community represented by Blaenavon Town Council and is an electoral ward of Torfaen County Borough Council. Blaenavon is twinned with Coutras in France.

Geography
The town lies near the source of the Afon Lwyd river, north of Cwmbran.

Demography
The population of Blaenavon has declined gradually at each ten-year census since the closure of the ironworks in 1900. It had fallen to 8,451 by 1961 and fell more rapidly after closure of the coal mine in 1980. Part of this decline was not emigration but a decrease in birth rate.

Economy
The Blaenavon Coal and Iron Company developed the Big Pit coalworks with adjoining steel works particularly for rail manufacture. The steel-making and coal mining industries followed, boosting the town's population to over 20,000 at one time before 1890. Since 1988, part of this site has been the Big Pit National Coal Museum.

Culture and community
Government, publishers and mainly Welsh writers sought in 2003 to attract more visitors by introducing Blaenavon as Wales' second "book town" (the first being Hay-on-Wye on the English border). However, the project did not succeed. This can be attributed to a combination of the town's remote location and the established competition from Hay. Many thriving community groups serve and improve the town, including Future Blaenavon, which has helped to create a community garden at the bottom of the town.

Landmarks
Parts of the town and surrounding country form the Blaenavon Industrial Landscape, selected as a World Heritage Site by UNESCO in 2000. Attractions in the town include the Big Pit National Coal Museum (an Anchor Point of the European Route of Industrial Heritage), Blaenavon Ironworks, the Pontypool and Blaenavon Railway and Blaenavon World Heritage Centre. The town has a male voice choir, a town band, and many historical walks through the local mountains.

Transport
A railway viaduct was constructed in 1790; the structure disappeared and was unearthed in a 2001 episode of the archaeology television programme Time Team. The Pontypool and Blaenavon Railway is a scenic attraction rich in geological and historical interest. Blaenavon lost both of its passenger railway stations — Blaenavon High Level station closed in 1941, and the last train from Blaenavon (Low Level) (to Newport via Pontypool Crane Street) ran in April 1962. The lower line had already been closed for more than a year before the Beeching Axe took place. The lower line's passenger service was among many in Gwent (Monmouthshire) which Ministry of Transport de-classified papers reveal were axed because of rail congestion in the Newport area following the newly opened Llanwern steelworks.

Education
Following Samuel Hopkins' death in 1815, his sister Sarah Hopkins of Rugeley, who had inherited much money from her late brother, erected Blaenavon Endowed School in his memory. Which has since been permanently closed.
 * Blaenavon Heritage VC Primary School & Nursery
 * Busy Bees Nursery

Religious sites
St Peter's Church was constructed in 1804, gifted to the parish by Thomas Hill and Samuel Hopkins.

Sport

 * Forgeside RFC
 * Forgeside AFC
 * Blaenavon RFC
 * Blaenavon Blues AFC
 * Blaenavon Bowls Club

Blaenavon Golf Club (now defunct) was founded in 1906. The club closed in 1937.

Notable people
Notable people born in Blaenavon include the Broadway and film actor E. E. Clive, award-winning mystery writer Dorothy Simpson, and international rugby union players Mark Taylor, Ken Jones (also an Olympic athlete), John Perkins, Chris Huish and Terry Cobner.

Nick Thomas-Symonds, elected MP for Torfaen in 2015, was brought up in the town.

title: Blaenavon


text:
Bohr compactification

In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G. Its importance lies in the reduction of the theory of uniformly almost periodic functions on G to the theory of continuous functions on H. The concept is named after Harald Bohr who pioneered the study of almost periodic functions, on the real line.

Definitions and basic properties
Given a topological group G, the Bohr compactification of G is a compact Hausdorff topological group Bohr(G) and a continuous homomorphism

 * b: G → Bohr(G)

which is universal with respect to homomorphisms into compact Hausdorff groups; this means that if K is another compact Hausdorff topological group and

 * f: G → K

is a continuous homomorphism, then there is a unique continuous homomorphism

 * Bohr(f): Bohr(G) → K

such that f = Bohr(f) ∘ b.

Theorem. The Bohr compactification exists and is unique up to isomorphism.

We will denote the Bohr compactification of G by Bohr(G) and the canonical map by

 * $$ \mathbf{b}: G \rightarrow \mathbf{Bohr}(G). $$

The correspondence G ↦ Bohr(G) defines a covariant functor on the category of topological groups and continuous homomorphisms.

The Bohr compactification is intimately connected to the finite-dimensional unitary representation theory of a topological group. The kernel of b consists exactly of those elements of G which cannot be separated from the identity of G by finite-dimensional unitary representations.

The Bohr compactification also reduces many problems in the theory of almost periodic functions on topological groups to that of functions on compact groups.

A bounded continuous complex-valued function f on a topological group G is uniformly almost periodic if and only if the set of right translates gf where

 * $$ [{}_g f ] (x) = f(g^{-1} \cdot x) $$

is relatively compact in the uniform topology as g varies through G.

Theorem. A bounded continuous complex-valued function f on G is uniformly almost periodic if and only if there is a continuous function f1 on Bohr(G) (which is uniquely determined) such that

 * $$ f = f_1 \circ \mathbf{b}. $$

Maximally almost periodic groups
Topological groups for which the Bohr compactification mapping is injective are called maximally almost periodic (or MAP groups). For example all Abelian groups, all compact groups, and all free groups are MAP. In the case G is a locally compact connected group, MAP groups are completely characterized: They are precisely products of compact groups with vector groups of finite dimension.

title: Bohr compactification


text:
Dissipation factor

In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or durability of oscillation.

Explanation
Electrical potential energy is dissipated in all dielectric materials, usually in the form of heat. In a capacitor made of a dielectric placed between conductors, the typical lumped element model includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance (ESR) as shown below. The ESR represents losses in the capacitor. In a good capacitor the ESR is very small, and in a poor capacitor the ESR is large. However, ESR is sometimes a minimum value to be required. Note that the ESR is not simply the resistance that would be measured across a capacitor by an ohmmeter. The ESR is a derived quantity with physical origins in both the dielectric's conduction electrons and dipole relaxation phenomena. In dielectric only one of either the conduction electrons or the dipole relaxation typically dominates loss. For the case of the conduction electrons being the dominant loss, then

 * $$ \text{ESR} = \frac{\sigma}{\varepsilon \omega^2 C} $$

where

 * $$ \sigma $$ is the dielectric's bulk conductivity,
 * $$ \varepsilon $$ is the lossless permittivity of the dielectric, and
 * $$ \omega = 2\pi f$$ is the angular frequency of the AC current i,
 * $$ C $$ is the lossless capacitance.

If the capacitor is used in an AC circuit, the dissipation factor due to the non-ideal capacitor is expressed as the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor, or

 * $$ \text{DF} = \frac{i^2 \text{ESR}}{i^2 \left|X_c\right|} = \omega C\, \text{ESR} = \frac{\sigma}{\varepsilon\omega} = \frac{1}{Q} $$

When representing the electrical circuit parameters as vectors in a complex plane, known as phasors, a capacitor's dissipation factor is equal to the tangent of the angle between the capacitor's impedance vector and the negative reactive axis, as shown in the adjacent diagram. This gives rise to the parameter known as the loss tangent tan δ where

 * $$ \frac{1}{Q} = \tan(\delta) = \frac{\text{ESR}}{\left|X_c\right|} = \text{DF} $$

Alternatively, $$\text{ESR}$$ can be derived from frequency at which loss tangent was determined and capacitance

 * $$ \text{ESR} = \frac{1}{\omega C}\tan(\delta) $$

Since the $$\text{DF}$$ in a good capacitor is usually small, $$\delta \sim \text{DF}$$, and $$\text{DF}$$ is often expressed as a percentage.

$$\text{DF}$$ approximates to the power factor when $$\text{ESR}$$ is far less than $$X_c$$, which is usually the case.

$$\text{DF}$$ will vary depending on the dielectric material and the frequency of the electrical signals. In low dielectric constant (low-κ), temperature compensating ceramics, $$\text{DF}$$ of 0.1–0.2% is typical. In high dielectric constant ceramics, $$\text{DF}$$ can be 1–2%. However, lower $$\text{DF}$$ is usually an indication of quality capacitors when comparing similar dielectric material.

title: Dissipation factor


text:
Talk:Battle of Puebla

There are a lot of anonymous remarks being entered below. Please sign your comments! Magi Media 03:02, 27 June 2006 (UTC)Magi Media

Stamp out stampede
The article on Cinco de mayo mentions that the Battle of Puebla included a stampede of cattle by local peasants. Any truth to this claim? If so, why is it not mentioned here?

 * Because it is a false statement. I have access to the Mexican military historic archive and I'll do my best effort to bring founded info to this page as soon as I can.

 * This overstated stampede account was retained in the discussion section of the CdM article because it is a discussion. Details of the battle in the article were minimized to give more testimony to the day as a modern celebration. But there is no other historical account that talks of a stampede. The French were overrun by a cunning yet legitimate band of Mexican fighters (not peasants with machetes and pitchforks) who got lucky that day. The French also beat themselves at the hands of an overconfident, cocky General Lorencz. Napoleon III retaliated by sending in 29,000 new troops. I'm afraid that a little of the Hollywood romance tale has gotten into many of the accounts for this battle. Magi Media 03:02, 27 June 2006 (UTC)Magi Media

 * "...who got lucky that day.". Hmmm, there's no historical account of that either. "Hollywood romance tale"? Care to elaborate? Never heard of one about May 5th. Oleksandr 05:51, 13 April 2007 (UTC)

 * You're being either naive or out-of-country. The Mexican army had no business overwhelming the French. They got lucky. And the idea that the French were beat off by a bunch of peasants with farm tools and a loosed herd of cattle is something that you see in a Zorro movie. --Magi Media 02:38, 14 April 2007 (UTC)
 * Neither, but it doesn't matter. Wikipedia needs facts, not user's dogma. Naive is: editing without having read first Neutral_point_of_view, or worse, disregarding it. Oleksandr 07:32, 8 May 2007 (UTC)

Enough with the bashings. Going back to the article, no it was not by luck nor by design that the Mexicans won the battle, the French attacked and as any city would, the Mexicans defended. The French General WAS overconfident and the Mexican army did use strategy to win the battle, of course Mexican courage played an enormous role in it. Meli Ruiz

Generally inaccurate
General Don Porfirio Diaz Mori did not lead a cavalry charge in the battle of Puebla. This article mentions that the General did so, but it does not specify as to what battle of Puebla was it. There was one in the 5th of May (famous 5 de Mayo) in which the General was in charge of a brigade that repelled the French forces that attacked the land between the two fortresses of Loreto and Guadalupe. The General's Brigade stopped the French, pulled them back and then chased them despite being ordered by General Zaragoza to hold their ground. General Diaz was praised for bravery for his contributions in the Battle of Puebla (5th of May). This can all be found in the Biography written by General Bernardo Reyes.

There was another Battle of Puebla which was the siege of Puebla later on after it had been taken by the French, in this Battle General Díaz DID lead a fierce cavalry charge against artillery IIRC.

 * Of the accounts I have read, I find that it was a General Felix Diaz who lead the May 5 cavalry attack. General Porfirio Diaz is listed as in charge of the San Luis Potosi Infantry Brigade Magi Media 04:45, 21 May 2006 (UTC)Magi Media

Numbers
The numbers of combatants and casualties in the template were obvious nonsense. I have changed them to the numbers in the Spanish page, which are plausible, but I don't have particular knowledge of this battle so they may need checking. seglea 20:27, 3 May 2006 (UTC)

 * Of the accounts I read I have found a list of the numbers now posted. The French troop count was specific to each unit. The Mexican count had no specific record. The body counts were near accurate. Magi Media 04:48, 21 May 2006 (UTC)Magi Media

The numbers of French troops is 6,000 with 2,000 Mexicans Supposedly number of Mexicans is 30,000 Bergmanucsd (talk) 03:24, 5 May 2017 (UTC)BergmanUCSD

March of the Machetes
I would like once and for all to put a tactical bent on the idea that the Battle of Puebla was fought by peasants wielding machetes. The only place you see such a thing is in a Zorro movie. And the idea that 6,000 French troops were rebuffed by a bunch of croppers is ridiculous.

If you look at the portrayal of the battle as expressed in all the historical accounts, the French never got near the town. That's the only place where you might see street fighting with machetes. But there was a Mexican garrison there, with supposed French allegiance, would turned on the French as well. They may have gotten the locals excited, but there was no real reason for them to join 4,500 regular forces doing real military stuff.

Lorencz attacked from the north on the hillside fortifications. He was rebuffed two times by gunfire, not cutlery. In the third attack he was outmaneuvered by the Mexicans. I'm not going to doubt that any of the regular Mexican military, as well as the French, had some sort of knife. THEY'RE CALLED SABERS. But the Mexican forces were equipped with muskets.

When the French were caught in the pincer movement, a well-known tactic, they retreated (we laughingly call it "advance in retrograde" in the military) back north and were flanked again by Mexican soldiers on the road. This overpowering would not have been done with knives. THEY GOT THEIR ASSES SHOT. 460 dead French soldiers were not killed by machetes,,,they were seriously rained on.

I'll give you this: adding up all the tactical blunders that Lorencz made, he could have been overrun by a plattoon of weedwhackers. --Magi Media (talk) 03:17, 4 January 2011 (UTC)

General Problems
This article is rather poorly written. Sentence structure is sub-par, and even includes sentence fragments such as "Add to that the fact that negotiations for the withdrawal were breaking down," which appears at the end of the second paragraph under "The battle". I have no idea how this entry is able to rate a "B" on the quality scale, particularly considering the possible historical inaccuracies pointed out in previous discussion. In my opinion, the entire article needs to be significantly rewritten and expanded in greater detail, with a more neutral tone and full references. 208.69.225.39 17:28, 24 April 2007 (UTC) JMMP

 * Despite many good faith edits, in many ways seems to have gotten worse over the past year or so. It has a large portion of unreferenced text and some POV language. I'd suggest a major rewrite; some portions of historic versions might be of useful. -- Infrogmation 01:10, 5 May 2007 (UTC)
 * Amen! —The preceding unsigned comment was added by 204.69.190.75 (talk) 08:03, 5 May 2007 (UTC).

May 7th rewrite
I presume it is work in progress. Keep it up. Oleksandr 07:32, 8 May 2007 (UTC)

Wording
Alas you could as well revise your choice of phrasing. Content like: The following account is a corroboration of several historical accounts that hold this account to be most factual: is redundant, yet of minor impact so it doesn't need a tag (Template_messages/Cleanup). Oleksandr 07:32, 8 May 2007 (UTC)

 * You're right! It looked like Pres. Bush wrote that.--Magi Media 13:22, 16 May 2007 (UTC)

The "Followup" section
The "Followup" section needs some work. I don't know the subject well enough to fix it myself.

It finishes talking about the battle, and then proceeds to talk about Maximilian being executed on May such and such, and that the Republic was restored. The problem is, Maximilian didn't even arrive in Mexico until a few years later, and was executed a year or so (I think) after that.

The way the "Followup" section currently reads, one would assume that the Battle of Puebla led directly to Maximilian's execution and the Mexican Republic being restored, all in the span of a few weeks, which isn't the case. --DarthBinky (talk) 19:21, 5 May 2008 (UTC)

 * Ok, so the dates have been fixed, but it still seems to imply that this battle led to the end of the French intervention and Maximilian's reign, when I'm pretty sure it did not. It describes the battle, but then goes on to talk about the end of Max's reign- it doesnt' actually mention what the battle accomplished (or didn't accomplish), it just goes on to talk about somethign that is fairly unrelated.

 * As far as I can remember, this battle just slowed down (but did not stop) the French invasion and gave the Mexicans a big morale boost; other than that, it really didn't accomplish much- the French eventually took Puebla, then occupied Mexico and installed Max. It should mention the actual results of the battle itself, and the stuff about the end of Max can probably be removed.  Unless I'm way wrong, but I don't think I am. --DarthBinky (talk) 15:44, 14 May 2008 (UTC)

 * Since it's been like six months since I last checked this and there's been no change, I took it upon myself to edit the section. It will probably need more work, and definitely need sources (what I wrote was based upon the content of French intervention in Mexico), but I think it more accurately reflects the actual outcome of the battle.  I also tweaked some wording- for example, there was a throwaway sentence that talked about how wonderful and brave the Mexicans were (they very well may have been, but it's a subjective statement); and it mentioned in like three different places that the battle is commemorated by Cinco de Mayo (once should be sufficient).--DarthBinky (talk) 18:57, 8 December 2008 (UTC)

Regarding Cinco de Mayo as Holiday, Im afraid this information is incorrect, the Batalla de Puebla day is INDEED a holiday, and all schools and most workplaces close down.--189.182.23.248 (talk) 05:01, 8 May 2009 (UTC)

Was the battle of Puebla decisive ?
The decisiveness of the battle has been first added by User:Matt Yeager with this comment "are you kidding? probably the biggest victory in Mexican history", lol. This point of view was not sourced of course. I reverted this POV, as the Mexican victory at Puebla has led to nothing (the French invasion continued and Puebla captured). Hence this battle has not been factually decisive. Definition of the word decisive : "Settling an issue; producing a definite result". This was NOT the case at Puebla. Your own source (Washington Post ) confirms my point and contraries yours : "It wasn't a Major Strategic Victory in the Struggle Against the French". My source says EXACTLY the same thing : "The Battle of Puebla was not very important to Mexico from a military standpoint." / "Although the Battle of Puebla amounted to little from a military sense – it merely postponed the inevitable victory of the French army,". It hardly can be described as decisive, it merely was a boost up for the republican morale. UltimaRatio (talk) 15:25, 9 June 2011 (UTC)

 * You are confusing significance with result, and --maybe unknowingly-- engaging in Original Research. And, BTW, rather than reverting someone's edits, as you did with Matt Yeager's as you stated above, try asking for a citation first, and if not provided within a reasonable time then revert: it's just common sense and common courtesy.My name is Mercy11 (talk) 17:56, 10 June 2011 (UTC), and I approve this message.

 * You are the only one here confusing result and significance. As stated above, the battle of Puebla had no decisive result as the invasion continued and Puebla was captured later. My point of view is sourced : "It wasn't a Major Strategic Victory in the Struggle Against the French", "The Battle of Puebla was not very important to Mexico from a military standpoint.", or "Although the Battle of Puebla amounted to little from a military sense – it merely postponed the inevitable victory of the French army,". Yours is not. You're confusing with the significance of the battle : sure, it became a symbolic Mexican victory (David against Goliath like) and it became a national myth in Mexico, but that's not the point. The point is that the result of the battle was very limited. UltimaRatio (talk) 16:20, 11 June 2011 (UTC)

 * The battle was decisive: If you are going to use the argument (which, to start with, is your argument and thus OR) that the battle was not a decisive Mexico victory based on the fact that Mexico was captured later (by the French within the context of the French intervention in Mexico) then you would have to accomodate the fact the battle was decisive based on the fact that Mexico was "re-captured" back from the French later yet by the Mexicans still within the scope of the French intervention in Mexico. Please do not remove the "decisive" and related comments from the article unless you can come up with sources that state your point. My name is Mercy11 (talk) 19:36, 14 June 2011 (UTC), and I approve this message.
 * My point of view is not "OR", it is sourced by four different quotes. While you have no supporting evidence. Have you even read the link you gave ??? It states that this battle was not decisive : "It wasn't a Major Strategic Victory in the Struggle Against the French". Unless you come with some more consistent arguments, I'll have to restore the previous version of the article. UltimaRatio (talk) 19:57, 14 June 2011 (UTC). See also : "Puebla was not a brilliant tactical triumph" .UltimaRatio (talk) 20:30, 14 June 2011 (UTC)

"Size of armies" edits by Wikigi
Wikigi, please stop changing the figures on the sizes of the armies, making it look like the Mexican army was twice as large as the French army (12,000 Mexican to 6,500 French), instead of the other way around. You and I discussed this at great lengths in October 2012, HERE. Your French source just isn't what every other source states. Every reference to troop numbers states the Mexicans were significantly outnumbered. As such your edit is incorrect.

Your edit also introduced a contradiction in that the lead states "but the Mexican victory at Puebla against a much better equipped and larger French army..." but, with your edit, the infobox now states "Mexican forces: Between 4,500[3] and 12,000 soldiers VS. French forces: 6,500 soldiers". 12,000 Mexican to 6,500 French is not a smaller Mexican army against a larger French army.

If you want to dispute this, you can follow the steps in WP:DISPUTE. Mercy11 (talk) 02:30, 9 May 2014 (UTC)
 * Once again, the OTHER sources your are referring to are all Mexican. You cannot turn a blind eye to French sources just because they don't suit your personal views on History, whatever your expertise on the matter is (you must have led some extensive research on this particular event..). At least, Your Honour is "allowing" the information to remain one way or another in the article, unlike what you did a couple years ago when all was deleted and I thank you for that.. On our side of the pond, these published documents are as good as the ones published in Mexico and that's how it should be. - Wikigi | talk to me | 07:17, 9 May 2014 (UTC)

 * Your argument is invalid because Mexican or not, no authority - from the mainstream press and historians to the US Congress - state that the Mexican army was smaller than the French army. No offense, but you really need to get that thru your head. The mainstream of the world is stating that there were far fewer Mexican troops than French troops, and the article needs to state that and not some different statement lacking weight. From there, the article needs to be consistent and not contradict itself. Please give that some thought.

 * For clarification, the problem with your sources is not that they are French. The problem is not one of the nationality of the sources. All sources are welcome despite their nationality so long as they are secondary and reliable. The problem is that your sources are WP:PRIMARY, and thus invalid. Still, since you appear hung up of the nationality issue, if you want a listing of non-Mexican sources that state the Mexicans were far few than the French, just say the word.

 * You made a footnote comment in the article stating that there are sources that state there were 12,000 Mexican troops. This being an encyclopedia, I believe that such footnote reference is as far as the article needs to take the difference in troop numbers issue because anything beyond that would most likely run into conflict with WP:OR because those footnote sources are Primary. That said, changing the troop number in the infobox is not negotiable because, per WP:IBX, the infobox exists "to summarize key facts that appear in the article" - and, per WP:RS, facts must be sourced by reliable secondary sources when there is a challenge.

 * Pond or not, I have no agenda here. I am neither Mexican nor French (nor American). I am looking at the secondary sources and they all state there were fewer Mexican that French troops. They also state the French was the most powerful army in the world and that the defeat (short-lived as it was) stunned politicians and world leaders of the time. Sort of what would happen today if the Americans invaded Cuba, Vietnam, or North Korea,,, and the Cubans, Vietnamese or Koreans defeat the Americans... Mercy11 (talk) 02:39, 10 May 2014 (UTC)
 * I beg your pardon? I specifically provided a primary source (General Gustave Léon Niox book) AND a secondary source (Peter Hicks, Fondation Napoléon) for this very reason. So if "that" is the basis for your argument you just proved yourself wrong. Footnote is fine anyway, it just needed to be mentioned. Now since you are bringing up Vietnam, the Vietnamese won a war already.. just saying.. and guess what? the numbers of casualties, or armed forces on each side, vary wildly from one source to the other, pretty much like numbers for the more recents US wars in Iraq and Afghanistan.. - Wikigi | talk to me | 11:00, 12 May 2014 (UTC)

 * Of course the Vietnamese won a war already (and the Cubans foiled American attempts at an invasion, and the Koreans left a sour taste on American military officers given the armistice that the American - the most powerful army in the world nowadays - had to settle for). You and I are both affirming the same thing as to that. I don't see disagreement among us two in those comparable (to a point at least) military conflicts. In any event, as to the primary source you point out, again, we can't use them in Wikipedia. I appreciate your understanding. As to Peter Hicks' article published by Fondation Napoléon, I too agree with you that it would rank as a secondary, and thus, an admissible, reliable source. The only problem that would I point out is that it is the only dissenting voice out there in terms of the numbers on the Mexican size. Hopefully we can both agree that a footnote indicating that Hicks has different numbers for the Mexican side is sufficient under the circumtances. Mercy11 (talk) 02:16, 14 May 2014 (UTC)

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title: Talk:Battle of Puebla