title: Gauss–Legendre method

abstract:
In numerical analysis and scientific computing, the Gauss–Legendre methods are a family of numerical methods for ordinary differential equations. Gauss–Legendre methods are implicit Runge–Kutta methods. More specifically, they are collocation methods based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method based on s points has order 2s. All Gauss–Legendre methods are A-stable. The Gauss–Legendre method of order two is the implicit midpoint rule. Its Butcher tableau is:
  - The Gauss–Legendre method of order four has Butcher tableau:
  - The Gauss–Legendre method of order six has Butcher tableau:
  - The computational cost of higher-order Gauss–Legendre methods is usually excessive, and thus, they are rarely used.

text:
# Gauss–Legendre method

In numerical analysis and scientific computing, the **Gauss–Legendre methods** are a family of numerical methods for ordinary differential equations. Gauss–Legendre methods are implicit Runge–Kutta methods. More specifically, they are collocation methods based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method based on *s* points has order 2*s*.

All Gauss–Legendre methods are A-stable.

The Gauss–Legendre method of order two is the implicit midpoint rule. Its Butcher tableau is:

| 1/2 | 1/2 |
| --- | --- |
|  | 1 |

The Gauss–Legendre method of order four has Butcher tableau:

| $\tfrac {1}{2}-{\tfrac {1}{6}{\sqrt {3}}}$ | $\tfrac {1}{4}$ | $\tfrac {1}{4}-{\tfrac {1}{6}{\sqrt {3}}}$ |
| --- | --- | --- |
| $\tfrac {1}{2}+{\tfrac {1}{6}{\sqrt {3}}}$ | $\tfrac {1}{4}+{\tfrac {1}{6}{\sqrt {3}}}$ | $\tfrac {1}{4}$ |
|  | $\tfrac {1}{2}$ | $\tfrac {1}{2}$ |

The Gauss–Legendre method of order six has Butcher tableau:

| $\tfrac {1}{2}-{\tfrac {1}{10}{\sqrt {15}}}$ | $\tfrac {5}{36}$ | $\tfrac {2}{9}-{\tfrac {1}{15}{\sqrt {15}}}$ | $\tfrac {5}{36}-{\tfrac {1}{30}{\sqrt {15}}}$ |
| --- | --- | --- | --- |
| $\tfrac {1}{2}$ | $\tfrac {5}{36}+{\tfrac {1}{24}{\sqrt {15}}}$ | $\tfrac {2}{9}$ | $\tfrac {5}{36}-{\tfrac {1}{24}{\sqrt {15}}}$ |
| $\tfrac {1}{2}+{\tfrac {1}{10}{\sqrt {15}}}$ | $\tfrac {5}{36}+{\tfrac {1}{30}{\sqrt {15}}}$ | $\tfrac {2}{9}+{\tfrac {1}{15}{\sqrt {15}}}$ | $\tfrac {5}{36}$ |
|  | $\tfrac {5}{18}$ | $\tfrac {4}{9}$ | $\tfrac {5}{18}$ |

The computational cost of higher-order Gauss–Legendre methods is usually excessive, and thus, they are rarely used.

## Intuition

Gauss-Legendre Runge-Kutta (GLRK) methods solve an ordinary differential equation $\dot {x}=f(x)$ with $x(0)=x\_{0}$. The distinguishing feature of GLRK is the estimation of $\textstyle x(h)-x\_{0}=\int \_{0}^{h}dt\\,f(x(t))$ with Gaussian quadrature.

$x(h)=x(0)+{\frac {h}{2}\sum \_{i=1}^{\ell }w\_{i}k\_{i}+O(h^{2\ell }),}$

where $k\_{i}=f(x(hc\_{i}))$ are the sampled velocities, $w\_{i}$ are the quadrature weights, $\textstyle c\_{i}={\frac {1}{2}h(1+r\_{i})}$ are the abscissas, and $r\_{i}$ are the roots $P\_{\ell }(r\_{i})=0$ of the Legendre polynomial of degree $\ell $. A further approximation is needed, as $k\_{i}$ is still impossible to evaluate. To maintain truncation error of order $O(h^{2\ell })$, we only need $k\_{i}$ to order $O(h^{2\ell -1})$. The Runge-Kutta implicit definition $\textstyle k\_{i}=f{\left(x\_{0}+h\sum \_{j}a\_{ij}k\_{j}\right)}$ is invoked to accomplish this. This is an implicit constraint that must be solved by a root finding algorithm like Newton's method. The values of the Runge-Kutta parameters $a\_{ij}$ can be determined from a Taylor series expansion in $h$.

## Practical example

The Gauss-Legendre methods are implicit, so in general they cannot be applied exactly. Instead one makes an educated guess of $k\_{i}$, and then uses Newton's method to converge arbitrarily close to the true solution. Below is a Matlab function which implements the Gauss-Legendre method of order four.

```
% starting point
x = [ 10.5440; 4.1124; 35.8233];

dt = 0.01;
N = 10000;
x_series = [x];
for i = 1:N
  x = gauss_step(x, @lorenz_dynamics, dt, 1e-7, 1, 100);
  x_series = [x_series x];
end

plot3( x_series(1,:), x_series(2,:), x_series(3,:) );
set(gca,'xtick',[],'ytick',[],'ztick',[]);
title('Lorenz Attractor');
return;

function [td, j] = lorenz_dynamics(state)
  % return a time derivative and a Jacobian of that time derivative
  x = state(1);
  y = state(2);
  z = state(3);

  sigma = 10;
  beta  = 8/3;
  rho   = 28;

  td = [sigma*(y-x); x*(rho-z)-y; x*y-beta*z];

  j = [-sigma, sigma, 0;
        rho-z, -1, -x;
        y, x, -beta];
end

function x_next = gauss_step( x, dynamics, dt, threshold, damping, max_iterations )
  [d,~] = size(x);
  sq3 = sqrt(3);
  if damping > 1 || damping <= 0
    error('damping should be between 0 and 1.')
  end

  % Use explicit Euler steps as initial guesses
  [k,~] = dynamics(x);
  x1_guess = x + (1/2-sq3/6)*dt*k;
  x2_guess = x + (1/2+sq3/6)*dt*k;
  [k1,~] = dynamics(x1_guess);
  [k2,~] = dynamics(x2_guess);

  a11 = 1/4;
  a12 = 1/4 - sq3/6;
  a21 = 1/4 + sq3/6;
  a22 = 1/4;

  error = @(k1, k2) [k1 - dynamics(x+(a11*k1+a12*k2)*dt); k2 - dynamics(x+(a21*k1+a22*k2)*dt)];
  er = error(k1, k2);
  iteration=1;
  while (norm(er) > threshold && iteration < max_iterations)
    fprintf('Newton iteration %d: error is %f.\n', iteration, norm(er) );
    iteration = iteration + 1;

    [~, j1] = dynamics(x+(a11*k1+a12*k2)*dt);
    [~, j2] = dynamics(x+(a21*k1+a22*k2)*dt);

    j = [eye(d) - dt*a11*j1, -dt*a12*j1;
         -dt*a21*j2, eye(d) - dt*a22*j2];

    k_next = [k1;k2] - damping * linsolve(j, er);
    k1 = k_next(1:d);
    k2 = k_next(d+(1:d));

    er = error(k1, k2);
  end
  if norm(er) > threshold
    error('Newton did not converge by %d iterations.', max_iterations);
  end
  x_next = x + dt / 2 * (k1 + k2);
end

```

This algorithm is surprisingly cheap. The error in $k\_{i}$ can fall below $10^{-12}$ in as few as 2 Newton steps. The only extra work compared to explicit Runge-Kutta methods is the computation of the Jacobian.

## Time-symmetric variants

At the cost of adding an additional implicit relation, these methods can be adapted to have time reversal symmetry. In these methods, the averaged position $(x\_{f}+x\_{i})/2$ is used in computing $k\_{i}$ instead of just the initial position $x\_{i}$ in standard Runge-Kutta methods. The method of order 2 is just an implicit midpoint method.

$$k\_{1}=f\left({\frac {x\_{f}+x\_{i}{2}\right)}}$$

$$x\_{f}=x\_{i}+hk\_{1}$$

The method of order 4 with 2 stages is as follows.

$$k\_{1}=f\left({\frac {x\_{f}+x\_{i}{2}-{\frac {\sqrt {3}{6}hk\_{2}\right)}}}}$$

$$k\_{2}=f\left({\frac {x\_{f}+x\_{i}{2}+{\frac {\sqrt {3}{6}hk\_{1}\right)}}}}$$

$$x\_{f}=x\_{i}+{\frac {h}{2}(k\_{1}+k\_{2})}$$

The method of order 6 with 3 stages is as follows.

$$k\_{1}=f\left({\frac {x\_{f}+x\_{i}{2}-{\frac {\sqrt {15}{15}hk\_{2}-{\frac {\sqrt {15}{30}hk\_{3}\right)}}}}}}$$

$$k\_{2}=f\left({\frac {x\_{f}+x\_{i}{2}+{\frac {\sqrt {15}{24}hk\_{1}-{\frac {\sqrt {15}{24}hk\_{3}\right)}}}}}}$$

$$k\_{3}=f\left({\frac {x\_{f}+x\_{i}{2}+{\frac {\sqrt {15}{30}hk\_{1}+{\frac {\sqrt {15}{15}hk\_{2}\right)}}}}}}$$

$$x\_{f}=x\_{i}+{\frac {h}{18}(5k\_{1}+8k\_{2}+5k\_{3})}$$

* Iserles, Arieh (1996), *A First Course in the Numerical Analysis of Differential Equations*, Cambridge University Press, ISBN 978-0-521-55655-2.


title: Gauss–Lucas theorem

abstract: In complex analysis, a branch of mathematics, the Gauss–Lucas theorem gives a geometric relation between the roots of a polynomial P and the roots of its derivative P'. The set of roots of a real or complex polynomial is a set of points in the complex plane. The theorem states that the roots of P' all lie within the convex hull of the roots of P, that is the smallest convex polygon containing the roots of P. When P has a single root then this convex hull is a single point and when the roots lie on a line then the convex hull is a segment of this line. The Gauss–Lucas theorem, named after Carl Friedrich Gauss and Félix Lucas, is similar in spirit to Rolle's theorem.

text:
# Gauss–Lucas theorem

In complex analysis, a branch of mathematics, the **Gauss–Lucas theorem** gives a geometric relation between the roots of a polynomial P and the roots of its derivative P'. The set of roots of a real or complex polynomial is a set of points in the complex plane. The theorem states that the roots of P' all lie within the convex hull of the roots of P, that is the smallest convex polygon containing the roots of P. When P has a single root then this convex hull is a single point and when the roots lie on a line then the convex hull is a segment of this line. The Gauss–Lucas theorem, named after Carl Friedrich Gauss and Félix Lucas, is similar in spirit to Rolle's theorem.

## Formal statement

If P is a (nonconstant) polynomial with complex coefficients, all zeros of P' belong to the convex hull of the set of zeros of P.

## Special cases

It is easy to see that if $P(x)=ax^{2}+bx+c$ is a second degree polynomial, the zero of $P'(x)=2ax+b$ is the average of the roots of P. In that case, the convex hull is the line segment with the two roots as endpoints and it is clear that the average of the roots is the middle point of the segment.

For a third degree complex polynomial P (cubic function) with three distinct zeros, Marden's theorem states that the zeros of P' are the foci of the Steiner inellipse which is the unique ellipse tangent to the midpoints of the triangle formed by the zeros of P.

For a fourth degree complex polynomial P (quartic function) with four distinct zeros forming a concave quadrilateral, one of the zeros of P lies within the convex hull of the other three; all three zeros of P' lie in two of the three triangles formed by the interior zero of P and two others zeros of P.

In addition, if a polynomial of degree n of real coefficients has n distinct real zeros $x\_{1}\<x\_{2}\<\cdots \<x\_{n},$ we see, using Rolle's theorem, that the zeros of the derivative polynomial are in the interval $\[x\_{1},x\_{n}\]$ which is the convex hull of the set of roots.

The convex hull of the roots of the polynomial

$$p\_{n}x^{n}+p\_{n-1}x^{n-1}+\cdots +p\_{0}$$

particularly includes the point

$$-{\frac {p\_{n-1}{n\cdot p\_{n}.}}}$$

## Proof

**Proof**

By the fundamental theorem of algebra, $P$ is a product of linear factors as

$$P(z)=\alpha \prod \_{i=1}^{n}(z-a\_{i})$$

where the complex numbers $a\_{1},a\_{2},\ldots ,a\_{n}$ are the – not necessarily distinct – zeros of the polynomial P, the complex number α is the leading coefficient of P and n is the degree of P.

For any root $z$ of $P'$, if it is also a root of $P$, then the theorem is trivially true. Otherwise, we have for the logarithmic derivative

$$0={\frac {P^{\prime }(z)}{P(z)}=\sum \_{i=1}^{n}{\frac {1}{z-a\_{i}=\sum \_{i=1}^{n}{\frac {{\overline {z}-{\overline {a\_{i}{|z-a\_{i}|^{2}.}}}}}}}}}$$

Hence

$\sum \_{i=1}^{n}{\frac {\overline {z}{|z-a\_{i}|^{2}=\sum \_{i=1}^{n}{\frac {\overline {a\_{i}{|z-a\_{i}|^{2}}}}}}}}$.

Taking their conjugates, and dividing, we obtain $z$ as a convex sum of the roots of $P$:

$$z=\sum \_{i=1}^{n}{\frac {|z-a\_{i}|^{-2}{\sum \_{j=1}^{n}|z-a\_{j}|^{-2}a\_{i}}}}$$


title: Methanobacteriales

abstract: Methanobacteriales is an order of archaeans in the class Methanobacteria. Species within this order differ from other methanogens in that they can use fewer catabolic substrates and have distinct morphological characteristics, lipid compositions, and RNA sequences. Their cell walls are composed of pseudomurein. Most species are Gram-positive with rod-shaped bodies and some can form long filaments. Most of them use formate to reduce carbon dioxide, but those of the genus Methanosphaera use hydrogen to reduce methanol to methane.

text:
# Methanobacteriales

**Methanobacteriales** is an order of archaeans in the class Methanobacteria. Species within this order differ from other methanogens in that they can use fewer catabolic substrates and have distinct morphological characteristics, lipid compositions, and RNA sequences. Their cell walls are composed of pseudomurein. Most species are Gram-positive with rod-shaped bodies and some can form long filaments. Most of them use formate to reduce carbon dioxide, but those of the genus *Methanosphaera* use hydrogen to reduce methanol to methane.

## Phylogeny

The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) and National Center for Biotechnology Information (NCBI).

| 16S rRNA based LTP\_06\_2022 | 53 marker proteins based GTDB 08-RS214 |
| --- | --- |
|  |  |

## Further reading

### Scientific journals

### Scientific books

* Boone, DR (2001). "Class I. Methanobacteria class. nov.". In DR Boone; RW Castenholz (eds.). *Bergey's Manual of Systematic Bacteriology*. Vol. 1: The Archaea and the deeply branching and phototrophic Bacteria (2nd ed.). New York: Springer Verlag. pp. 169. ISBN 978-0-387-98771-2.
* Murray, RGE (1984). "The higher taxa, or, a place for everything...". In NR Krieg; JG Holt (eds.). *Bergey's Manual of Systematic Bacteriology*. Vol. 1 (1st ed.). Baltimore: The Williams & Wilkins Co. pp. 31–34.

## InfoBox

| Methanobacteriales | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Archaea |
| Kingdom: | Euryarchaeota |
| Class: | Methanobacteria |
| Order: | Methanobacteriales<br>Balch and Wolfe 1981 |
|
| Families | |
|  | |


title: Gaël Aymon

abstract:
Gaël Aymon is an author, screenwriter, film director and producer born in Paris, France. Having attended the acting schools of Les Cours Florent and the Studio Pygmalion, Gael Aymon first embarks on a career in acting and directing.
He has worked as a producer and distributor for the cinema and theatre. He was first published as a children's author in 2010. His books have received numerous awards and have been translated into Chinese, Korean, Romanian, Italian, Spanish, Catalan, German and Portuguese (Brasil). In 2023 and 2024, he is one of the nominees for the International Astrid Lindgren Memorial Award.

text:
# Gaël Aymon

**Gaël Aymon** is an author, screenwriter, film director and producer born in Paris, France.

Having attended the acting schools of Les Cours Florent and the Studio Pygmalion, Gael Aymon first embarks on a career in acting and directing. He has worked as a producer and distributor for the cinema and theatre.

He was first published as a children's author in 2010. His books have received numerous awards and have been translated into Chinese, Korean, Romanian, Italian, Spanish (Spain and Mexico), Catalan, German and Portuguese (Brasil).

In 2023 and 2024, he is one of the nominees for the International Astrid Lindgren Memorial Award.

## Books

### For teenagers and young adults

* *Forever 17* (Nathan - Novel - 2024)
* *A night of my childhood* (Nathan - Novel - 2023)
* *The Apprentice Storyteller* (L'Ecole des loisirs - Novel - 2022)
* *Grim, son of the swamp* (Nathan - Novel - 2021)
* *Silent Boy* (Nathan - Novel - 2020)
* *And your life will be mine* (Nathan - Novel - 2020)
* *My brother soul* (Actes Sud Junior - Novel- 2018)
* *The planet of the 7 sleepers* (Nathan - Novel - 2018)
* *Golden Valley* (Gallimard Jeunesse - Novel - 2016)
* *The forgotten heroes* \- Volume II "The Masters" (Actes Sud Junior - Novel- 2016)
* *The forgotten heroes* \- Volume I "The gates of oblivion" (Actes Sud Junior - Novel- 2015)
* *Forgetting Camille* (Actes Sud Junior - Novel - Rentrée littéraire 2014)
* *My reputation* (Actes Sud Junior – Novel – 2013 / new edition Gallimard 2022)

### For children

* *My 2nd brain* (L'Ecole des Loisirs - 2024)
* *Really scary!* (Nathan - 2022)
* *SOS little mermaids* \- Volume I to VI (Nathan - 2021-2022)
* *Sleeping Beauty* (Nathan - 2020)
* *The golden years* \- Volume VIII (Nathan - 2020)
* *The beauty and the beast wityh diamond tears* (Gautier-Languereau - 2019)
* *The golden years* \- Volume VI & VII (Nathan - 2019)
* *The golden years* \- Volume III, IV & V (Nathan - 2018)
* *Snow White* (Nathan - 2018)
* *The golden years* \- Volume I & II (Nathan - 2017)
* *The tale of the three flakes* (Bayard Editions - J'aime Lire poche - 2015)
* *Snowdrop ans thye 3 ogresses* (Éditions Talents Hauts \- 2014) – supported by Amnesty International
* *The wold's mightiest secret* (Les éditions du Ricochet – 2014)
* *The son of the giants* ("Le fils des géants" – Éditions Talents Hauts – 2013) – supported by Amnesty International
* *Scarlet Slippers* ("Les souliers écarlates" – Éditions Talents Hauts – 2012) – supported by Amnesty International
* *An Upside Down Birthday* ("L'anniversaire à l'envers" – Éditions Talents Hauts – 2012)
* *Tales of Another Type* ("Contes d'un autre genre" – Éditions Talents Hauts – 2011)
* *Giga-Boy* (Éditions Talents Hauts – 2011))
* *A Space in the Playground* ("Une place dans la cour" – Éditions Talents Hauts\- 2011)
* *Princess Candy-Floss* ("La princesse Rose-praline" – Éditions Talents Hauts\- 2010)

## Awards

Full list here : http://gaelaymon.com/ressources/

*Silent Boy*

* Prix Louis Mathis 2021

*Et ta vie m'appartiendra*

* Prix Lire Elire 2021

*Oublier Camille*

* Programme 2016 de l’Éducation Nationale, lectures cursives jeunesse, classes de 4e, « Dire l’amour, dire l’absence »
* Prix littéraire Au cœur des page, Nort-sur-Erdre 2019
* Prix des collégiens de Clamart 2016

*Ma réputation*

* Prix littéraire Marguerite-Bahuet 2017
* Prix littéraire "slam ta lecture " 2017
* Prix de la ville Cherbourg-Octeville 2015
* Prix Gr’Aisne de critique 2014-2015
* Prix Jacaranda 2016 (Maroc)

*Perce-Neige et les trois ogresses*

* Prix Littéraire du Val de l'Aurence 2016

*Une place dans la cour*

* Prix Tartines Fraises 2013

## InfoBox

| Gaël Aymon | |
| --- | --- |
| GAEL AYMON by Pascal Ito 2022 | |
| Born | (1973-12-12) 12 December 1973<br>Paris, France |
| Occupation | Novelist |
| Genre | Children's literature |
| Notable works | * "My reputation" * "Forever 17" * "And your life will be mine" * "Silent Boy" * "Tales of another type" |
| Website | |
| gaelaymon.com | |


title: Gaël Duhayindavyi

abstract: Gaël Duhayindavyi is a Burundian professional footballer who plays as a midfielder for Rwandan side Mukura Victory Sports and the Burundi national team.

text:
# Gaël Duhayindavyi

**Gaël Duhayindavyi** (born 3 October 1990) is a Burundian professional footballer who plays as a midfielder for Rwandan side Mukura Victory Sports and the Burundi national team.

## International career

He was called up by national team coach Lofty Naseem to represent Burundi in the 2014 African Nations Championship held in South Africa.

### International goals

*Scores and results list Burundi's goal tally first.*

| No | Date | Venue | Opponent | Score | Result | Competition |
| --- | --- | --- | --- | --- | --- | --- |
| 1. | 11 March 2017 | Prince Louis Rwagasore Stadium, Bujumbura, Burundi | Djibouti | **5**–0 | 7–0 | Friendly |
| 2. | 10 June 2017 | Prince Louis Rwagasore Stadium, Bujumbura, Burundi | South Sudan | **2**–0 | 3–0 | 2019 Africa Cup of Nations qualification |

## InfoBox

Gaël Duhayindavyi
| Personal information | | | |
| --- | --- | --- | --- |
| Date of birth | (1990-10-03) 3 October 1990 | | |
| Place of birth | Bujumbura, Burundi | | |
| Height | 1.83 m (6 ft 0 in) | | |
| Position(s) | Midfielder | | |
| Team information | | | |
| Current team | Mukura Victory Sports | | |
| Senior career\* | | | |
| Years | **Team** | **Apps** | **(Gls)** |
| 0000–2013 | Atlético Olympic |  |  |
| 2013–2015 | LLB Académic |  |  |
| 2015–2017 | Vital'O |  |  |
| 2017– | Mukura Victory Sports |  |  |
| International career | | | |
| 2011– | Burundi | 48 | (2) |
| \*Club domestic league appearances and goals<br>‡ National team caps and goals, correct as of 10 May 2021 | | | |


title: Gastroplakaeis schultzei

abstract: Gastroplakaeis schultzei is a moth species in the family of Lasiocampidae found in Nigeria.

text:
# Gastroplakaeis schultzei

***Gastroplakaeis schultzei*** is a moth species in the family of Lasiocampidae found in Nigeria.

## InfoBox

| *Gastroplakaeis schultzei* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Lepidoptera |
| Family: | Lasiocampidae |
| Genus: | *Gastroplakaeis* |
| Species: | ***G. schultzei*** |
| Binomial name | |
| ***Gastroplakaeis schultzei***<br>Aurivillius, 1905 | |
|


title: Metz-en-Couture

abstract: Metz-en-Couture is a commune in the Pas-de-Calais department in the Hauts-de-France region of France.

text:
# Metz-en-Couture

**Metz-en-Couture** is a commune in the Pas-de-Calais department in the Hauts-de-France region of France.

## Geography

Metz-en-Couture is situated 25 miles (40 km) southeast of Arras, at the junction of the D7 and the D17 roads.

## Population

Historical population
| Year | Pop. | ±% p.a. |
| --- | --- | --- |
| 1968 | 714 |  |
| 1975 | 647 | −1.40% |
| 1982 | 575 | −1.67% |
| 1990 | 605 | +0.64% |
| 1999 | 602 | −0.06% |
| 2007 | 628 | +0.53% |
| 2012 | 655 | +0.85% |
| 2017 | 664 | +0.27% |
| Source: INSEE | | |

## Places of interest

## InfoBox

| Metz-en-Couture | |
| --- | --- |
| Commune | |
| View of Metz-en-Couture from the fields | |
|  | |
| Location of Metz-en-Couture | |
| Metz-en-CoutureMetz-en-Couture | |
| Coordinates: 50°04′06″N 3°03′52″E / 50.0683°N 3.0644°E / 50.0683; 3.0644 | |
| Country | France |
| Region | Hauts-de-France |
| Department | Pas-de-Calais |
| Arrondissement | Arras |
| Canton | Bapaume |
| Intercommunality | CC Sud-Artois |
| Government | |
| Mayor (20202026) | Michel Lalisse |
| Area**1** | 10.73 km2 (4.14 sq mi) |
| Population (2021) | 609 |
| Density | 57/km2 (150/sq mi) |
| Time zone | UTC+01:00 (CET) |
| Summer (DST) | UTC+02:00 (CEST) |
| INSEE/Postal code | 62572 /62124 |
| Elevation | 90–134 m (295–440 ft)
(avg. 136 m or 446 ft) |
| **1** French Land Register data, which excludes lakes, ponds, glaciers \> 1 km2 (0.386 sq mi or 247 acres) and river estuaries. | |


title: Metz, Wisconsin

abstract: Metz is an unincorporated community in Waushara, and Winnebago counties, Wisconsin, United States. Metz is located 6.5 miles south of Fremont, in the towns of Bloomfield, and Wolf River.

text:
# Metz, Wisconsin

**Metz** is an unincorporated community in Waushara, and Winnebago counties, Wisconsin, United States. Metz is located 6.5 miles south of Fremont, in the towns of Bloomfield, and Wolf River.

## InfoBox

| Metz, Wisconsin | |
| --- | --- |
| Unincorporated community | |
| Metz, WisconsinMetz, Wisconsin | |
| Coordinates: 44°12′49″N 88°53′11″W / 44.21361°N 88.88639°W / 44.21361; -88.88639 | |
| Country | United States |
| State | Wisconsin |
| Counties | Waushara and Winnebago |
| Elevation | 237 m (778 ft) |
| Time zone | UTC-6 (Central (CST)) |
| Summer (DST) | UTC-5 (CDT) |
| Area code(s) | 715 & 534 |
| GNIS feature ID | 1577727 |


title: Metz-le-Comte

abstract: Metz-le-Comte is a commune in the Nièvre department in central France.

text:
# Metz-le-Comte

**Metz-le-Comte** is a commune in the Nièvre department in central France.

## Demographics

On 1 January 2019, the estimated population was 160.

## InfoBox

| Metz-le-Comte | |
| --- | --- |
| Commune | |
| A general view of Metz-le-Comte | |
| Location of Metz-le-Comte | |
| Metz-le-ComteMetz-le-Comte | |
| Coordinates: 47°23′31″N 3°38′24″E / 47.3919°N 3.64000°E / 47.3919; 3.64000 | |
| Country | France |
| Region | Bourgogne-Franche-Comté |
| Department | Nièvre |
| Arrondissement | Clamecy |
| Canton | Clamecy |
| Intercommunality | Tannay-Brinon-Corbigny |
| Government | |
| Mayor (20202026) | Jean-Claude Gauthier |
| Area**1** | 14.37 km2 (5.55 sq mi) |
| Population (2021) | 172 |
| Density | 12/km2 (31/sq mi) |
| Time zone | UTC+01:00 (CET) |
| Summer (DST) | UTC+02:00 (CEST) |
| INSEE/Postal code | 58165 /58190 |
| Elevation | 157–314 m (515–1,030 ft) |
| **1** French Land Register data, which excludes lakes, ponds, glaciers \> 1 km2 (0.386 sq mi or 247 acres) and river estuaries. | |


title: Metz, South Africa

abstract: Metz is a town in Mopani District Municipality in the Limpopo province of South Africa.

text:
# Metz, South Africa

**Metz** is a town in Mopani District Municipality in the Limpopo province of South Africa.

## InfoBox

| Metz | |
| --- | --- |
| MetzMetz | |
| Coordinates: 24°14′42″S 30°28′26″E / 24.245°S 30.474°E / -24.245; 30.474 | |
| Country | South Africa |
| Province | Limpopo |
| District | Mopani |
| Municipality | Maruleng |
| Area | |
| Total | 7.94 km2 (3.07 sq mi) |
| Population (2011) | |
| Total | 6,350 |
| Density | 800/km2 (2,100/sq mi) |
| Racial makeup (2011) | |
| Black African | 99.8% |
| Coloured | 0.1% |
| First languages (2011) | |
| Northern Sotho | 95.7% |
| Tsonga | 1.2% |
| Other | 3.2% |
| Time zone | UTC+2 (SAST) |


title: Metz, West Virginia

abstract: Metz is an unincorporated community in Marion County, West Virginia, United States. Metz is located along U.S. Route 250, 3.5 miles (5.6 km) north-northwest of Mannington. Metz had a post office, which closed on August 27, 2011.

text:
# Metz, West Virginia

**Metz** is an unincorporated community in Marion County, West Virginia, United States. Metz is located along U.S. Route 250, 3.5 miles (5.6 km) north-northwest of Mannington. Metz had a post office, which closed on August 27, 2011.

## History

Metz was founded by Jacob Metz in the early 1800s, well before the state of West Virginia was created in 1863. West Virginia was created by counties in Virginia that had remained loyal to the Union during the Civil War. Metz was never part of a Confederate state. The village of Metz was first known as "Bee Hive Station", because Jacob kept many bee hives. In 1850, representatives of the Baltimore & Ohio Railroad approached Jacob about buying land for a needed rights-of-way. Jacob agreed to give them the land providing they build a station and name it for him. Metz Crossing was shortened to just "Metz" and remains so even today.

## Climate

The climate in this area is characterized by relatively high temperatures and evenly distributed precipitation throughout the year. According to the Köppen Climate Classification system, Metz has a Humid subtropical climate, abbreviated "Cfa" on climate maps.

| Climate data for Metz, West Virginia | | | | | | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Month | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Year |
| Mean daily maximum °C (°F) | 4
(39) | 6
(43) | 12
(53) | 19
(66) | 23
(74) | 28
(82) | 29
(85) | 29
(84) | 26
(78) | 19
(67) | 12
(54) | 6
(42) | 18
(64) |
| Mean daily minimum °C (°F) | −8
(17) | −7
(19) | −4
(25) | 1
(34) | 7
(44) | 12
(53) | 14
(58) | 14
(57) | 9
(49) | 3
(37) | −2
(29) | −6
(21) | 3
(37) |
| Average precipitation mm (inches) | 94
(3.7) | 81
(3.2) | 100
(4.1) | 97
(3.8) | 120
(4.6) | 110
(4.4) | 130
(5.1) | 110
(4.3) | 91
(3.6) | 76
(3) | 89
(3.5) | 91
(3.6) | 1,190
(46.8) |
| Source: Weatherbase | | | | | | | | | | | | | |

## InfoBox

| Metz, West Virginia | |
| --- | --- |
| Unincorporated community | |
| Metz Church of God of Prophecy | |
| Metz, West VirginiaMetz, West Virginia | |
| Coordinates: 39°34′49″N 80°22′11″W / 39.58028°N 80.36972°W / 39.58028; -80.36972 | |
| Country | United States |
| State | West Virginia |
| County | Marion |
| Elevation | 1,001 ft (305 m) |
| Time zone | UTC-5 (Eastern (EST)) |
| Summer (DST) | UTC-4 (EDT) |
| ZIP code | 26585 |
| Area code(s) | 304 & 681 |
| GNIS feature ID | 1554500 |


title: MetroCard (disambiguation)

abstract:
MetroCard is a fare card used on subways, buses, and other public transport in the New York metropolitan area. Other fare cards known as the METROcard, MetroCard or Metrocard:
  - metroCARD, launched in 2012–2013 on Adelaide Metro buses, trams, and trains in Adelaide, Australia
  - METROcard, which was used on the Metro Monorail and light rail in Sydney, Australia
  - MetroCard, used in several Tokyo subway systems in Japan, replaced in 1988–2007 by the Pasmo RFID card
  - Metrocard, used on buses on public transport routes in Christchurch and Timaru, New Zealand, under the "Metro" branding
  - MetroCard, used on the West Yorkshire Metro in West Yorkshire, England
  - MetroCard, used on the Merseytravel network in the Liverpool City Region

text:
# MetroCard (disambiguation)

MetroCard is a fare card used on subways, buses, and other public transport in the New York metropolitan area. Other fare cards known as the **METROcard**, **MetroCard** or **Metrocard**:

* metroCARD, launched in 2012–2013 on Adelaide Metro buses, trams, and trains in Adelaide, Australia
* METROcard, which was used on the Metro Monorail and light rail in Sydney, Australia
* MetroCard, used in several Tokyo subway systems in Japan, replaced in 1988–2007 by the Pasmo RFID card
* Metrocard, used on buses on public transport routes in Christchurch and Timaru, New Zealand, under the "Metro" branding
* MetroCard, used on the West Yorkshire Metro in West Yorkshire, England
* MetroCard, used on the Merseytravel network in the Liverpool City Region


title: Michael's bond

abstract: Michael's bond was a decree enacted by Michael the Brave that bonded the Wallachian serfs to the estate where they were living at that time. Its exact meaning has been a matter of debate in Romanian historiography: the decree may have bonded some formerly free peasants, it may have only legislated the existing order, or it may have banned the return of runaway serfs to their previous estates.

text:
# Michael's bond

**Michael's bond** (Romanian: *Legătura lui Mihai*) was a decree enacted by Michael the Brave that bonded the Wallachian serfs to the estate where they were living at that time.

Its exact meaning has been a matter of debate in Romanian historiography: the decree may have bonded some formerly free peasants, it may have only legislated the existing order, or it may have banned the return of runaway serfs to their previous estates.

## Sources

Some 18th century documents talk about a measure, named either *așezământ* (foundation) or *legătură* (bond), taken by Michael the Brave about the peasants in bondage living in villages owned by the boyars, the monasteries or the state.

The earliest document dates from April 24, 1613, through which Hospodar Radu Mihnea reinforces to the postelnics brothers Pârvu and Radu from Slăvitești the rights to two runaway serfs, who were claimed by their former owner, Ghinea the deacon. The decree is explained as bonding "for eternity" the serfs to wherever place they lived at the time of the legislation.

## Historiography

The 1613 document was considered by Nicolae Bălcescu to be a proof that Michael introduced serfdom to Wallachia, being forced by the landlords. A. D. Xenopol considered that it was merely a sanctioning of an existing practice. Constantin Giurescu argued that serfdom already existed for some time, so the measure only meant to abolish the right of landlords to retrieve the serfs who fled to other estates during the Sinan Pasha expedition against Michael the Brave. Michael may have had an urgent need for money to pay the mercenaries and the investigations and returning of the serfs to their original estates may have delayed the paying of taxes. Ioan C. Filitti supported the conclusions of Giurescu, but argued that the decree may have been used to make serfs from previously free peasants who settled in villages during the war of 1595. Petre P. Panaitescu considered that the decree meant the bonding of peasants to the land, the abolition of the right to change estate and that peasants who previously had a contract with the landlord were assimilated with serfs, using as argument a treaty prior to Sinan's expedition.

Constantin C. Giurescu and Dinu C. Giurescu argued that while Michael did not introduce nor strengthened serfdom in Wallachia, the increases in taxes meant that previously free peasants were forced to sell or lost their land, and with it, they lost their freedom, becoming serfs. Some villages became property of the boyars or they were taken over by the Hospodar for not paying their taxes. Michael himself bought 149 villages, of which 113 of formerly free peasants, for at least a quarter of which the peasants complained that they were made serfs unwillingly.

* Giurescu, Constantin C.; Giurescu, Dinu C. (1976). *Istoria Românilor*. Vol. 2. Editura Științifică și Enciclopedică.


title: Gateway AnyKey

abstract: The Gateway AnyKey is a programmable computer keyboard that was sold exclusively by Gateway 2000, Inc., as an option for some of their desktop computers. Introduced in the spring of 1991, the keyboard was manufactured in at least five known versions and incarnations by Tucson, Arizona–based Maxi Switch, Inc., a subsidiary of the Lite-On Technology Corporation. It was also sold by Maxi Switch themselves, as the ProKey II. The AnyKey proved popular, especially among power users and computer programmers, and soon gained a cult following. The AnyKey is no longer manufactured, Gateway having discontinued it by 1998 at the latest. The AnyKey keyboard is easily distinguished from other generic keyboards by its wide footprint—20 inches (51 cm)—necessitated by an extra double column of function keys on the left side, a unique eight directional arrow keys as opposed to the traditional inverted T, and a quartet of extra keys directly above the numeric pad that control the programmable aspects of the keyboard. They are labeled "Program Macro", "Suspend Macro", "Repeat Rate", and "Remap", reading left to right. All versions of the AnyKey are white or very light gray with some keys in a darker gray.

text:
# Gateway AnyKey

The **Gateway AnyKey** is a programmable computer keyboard that was sold exclusively by Gateway 2000, Inc., as an option for some of their desktop computers. Introduced in the spring of 1991, the keyboard was manufactured in at least five known versions and incarnations by Tucson, Arizona–based Maxi Switch, Inc., a subsidiary of the Lite-On Technology Corporation. It was also sold by Maxi Switch themselves, as the **ProKey II** (later the **ProKey 124**). The AnyKey proved popular, especially among power users and computer programmers, and soon gained a cult following. The AnyKey is no longer manufactured, Gateway having discontinued it by 1998 at the latest.

The AnyKey keyboard is easily distinguished from other generic keyboards by its wide footprint—20 inches (51 cm)—necessitated by an extra double column of function keys on the left side, a unique eight directional arrow keys as opposed to the traditional inverted T, and a quartet of extra keys directly above the numeric pad that control the programmable aspects of the keyboard. They are labeled "Program Macro", "Suspend Macro", "Repeat Rate", and "Remap", reading left to right. All versions of the AnyKey are white or very light gray with some keys (notably the programming keys, extra function keys, and arrows) in a darker gray.

## Features and construction

The AnyKey is a 124-key PC keyboard, comprising the usual complement of 101 keys as well as 23 additional keys. The keyboard includes twelve extra function keys, four programming keys, and four additional arrow keys for diagonal input, as well as one blank key in the center of the eight way arrow key area that normally acts as a second space bar but which can be reprogrammed.

The AnyKey has a fourth indicator light labeled "Program", located to the right of the Num Lock, Caps Lock, and Scroll Lock lights. Revisions of its design that predate the advent of the Windows key and Menu key in 1995 have an asterisk (\*), backslash (\\), or number sign (#) in the positions of these keys, depending on the intended locale.

A unique feature of the AnyKey is its hardware programmability. The keyboard contains an internal controller as well as an EEPROM chip that can store user-defined macros. Any key on the keyboard can be programmed to contain a macro of arbitrary length or can be programmed to act like any other key on the keyboard (remapped). This is done on the hardware level inside the keyboard's controller itself. No driver software is required to use the AnyKey's programming functionality, as the keyboard's own controller dictates which key-press codes are sent to the attached computer. A utility for MS-DOS exists to quickly remap the entire keyboard to a predefined configuration or save its current configuration to a file, but it is not required to use or program the keyboard. The AnyKey's EEPROM memory will retain its data even if the keyboard is unplugged indefinitely, so settings and programming are not lost if the computer is powered down, unplugged, or if the keyboard is unplugged or moved to a different computer.

The AnyKey was originally available only with an AT-style connector at the end of its 60-inch cable. Gateway provided a simple adapter with the purchase of an AnyKey, allowing it to be used with the PS/2 port, which Gateway started including in their machines circa 1991. As its design predates the implementation of the USB standard, no USB AnyKey keyboard was ever produced. However, a PS/2 to USB converter will allow the AnyKey to be used with modern USB systems.

The AnyKey is built out of a plastic chassis that, at 20 inches (51 cm) wide, is quite large compared to most modern keyboards, primarily owing to the extra columns of keys on the left side. It is also slightly thicker than most keyboard casings of the present era and features a distinctive wedge shape similar to contemporaneous keyboard offerings by Dell. As with many keyboards, there are two plastic feet that can be flipped down from the upper corners to tilt the keyboard into a suitable typing position. There is also a long central plastic foot, on some versions, that can be flipped down to tilt the keyboard to a less severe angle than the two outside feet. The AnyKey uses rubber dome key switches, imparting a smooth, "mushy" key feel versus that of mechanical offerings, such as IBM's popular Model M keyboard.

## Programming

The AnyKey keyboard is extensively programmable. This takes two forms: remapping, and macro programming. The only keys on the AnyKey that cannot be programmed in at least some way are those used to control the programming itself—"Program Macro", "Suspend Macro", "Repeat Rate", and "Remap". Any *other* key on the keyboard—including letters, numbers, arrow keys, and even special keys like modifiers such as Shift, Alt, Ctrl, Enter, and the Space Bar—can be programmed.

### Remapping

A key can be remapped (copied to a different location on the keyboard) by pressing the Remap key once, pressing the key to be copied, and then pressing the new key that will serve as the new destination for the old key's command. The Program light on the keyboard will flash as long as it is awaiting remapping commands. Multiple keys can be remapped without pressing Remap again. The Program light will continue blinking after one key has been remapped and the keyboard will await more remapping commands with the same method as before. On each keypress, the Remap light will pause, flashing momentarily to signal that a keypress has been registered. Pressing Remap again before completing a remapping cancels the operation. Pressing Remap after at least one remapping has been completed will save all the remappings but will cancel an incomplete one if it is in progress.

After remapping, the old key will retain its original function even after being remapped elsewhere, effectively creating two copies of the same key. After it is remapped somewhere else, the original or "old" key can be remapped to a different function or have a macro programmed to it.

To restore a remapped key to its original function, press the Remap key and then press the remapped key twice. This is known as "remapping a key to itself". Pressing the Remap key will cause the Program light to begin flashing, indicating that the very next key that is pressed will be remapped.

### Macros

Any key can also be programmed with a macro and can be combined with key modifiers Alt, and/or Ctrl (e.g. `Ctrl`+`Alt`+`Q`, `Ctrl`+`Alt`+`F1`). Macros are multiple presses of various keys in sequence of arbitrary length. The extra function keys on the left of the keyboard are essentially reserved for having macros programmed to them, though they mirror the function of the function keys along the top of the keyboard before they are programmed. The keyboard treats both sets of function keys as separate, however. Remapping or programming one of the function keys will not change the function of its counterpart.

A macro is programmed to a key by pressing the Program Macro key once (depending on the revision of the keyboard, the Ctrl key may also need to be held down), pressing the key that will have the macro assigned to it once, and then entering the commands to be programmed. Any sequence of key presses is valid input, including letters, numbers, keys used in conjunction with Shift, Alt, and Ctrl, function keys, cursor movement, remapped keys, and even *other keys programmed with macros*. The Program light flashes as long as the keyboard is accepting programming input. It pauses momentarily when the key to be assigned the macro is pressed to indicate that the keypress was picked up. Pressing Program Macro for a second time ends the programming session and saves the macro to the target key. Pressing it again before entering any programming input cancels the operation.

A key can be cleared of its macro by pressing Program Macro and then pressing the key twice. Pressing a programmed key will "play back" all the keypresses that were programmed into it at the current repeat rate of the keyboard.

The Program light normally remains solidly on or off depending on whether the keyboard is set to use macros, which can be toggled by pressing the Suspend Macro key. The state of the Program light does not reflect whether there are any macros programmed into the keyboard, merely whether the keyboard is in macro mode.

Pressing the Suspend Macro key will cause the Program light to go out and will cause all keys programmed with macros to behave with their usual functions instead of their programmed macros. Keys that have been remapped do not reset themselves while macros are suspended. Pressing Suspend Macro again relights the Program light and restores the macros to all programmed keys.

A DOS utility, ANYKEY.EXE, was offered by Gateway for saving and uploading AnyKey key mappings and macros. It offers three functions: Saving key mappings and settings from the keyboard's non-volatile memory to a file, uploading settings from the file to the keyboard's nonvolatile memory, and checking the file's integrity. It must run in DOS, and it may require the keyboard be connected through a PS/2 or AT-style 5-pin-DIN socket, though a PS/2-to-USB adapter seems to work well for normal keyboard usage.

### Resetting

Holding the Control and Alt keys and pressing the Suspend Macro key clears all of the keyboard's programming. The Program light will flash while the keyboard erases its memory. Afterwards, it will go dark and all keys will be reset to their original function, all macros deleted, and all remappings reset. Holding down the Suspend Macro key while powering on the computer will also reset all keys to their original function.

### Quirks

The AnyKey also has a user-programmable repeat rate (the rate at which a key will repeat its function on the computer if it is held down) that is handled by the controller inside the board and therefore overrides the BIOS or operating system controlled repeat rate on the attached computer. (On Linux, this has been known to conflict with the included kbdrate utility.) The repeat rate is set by pressing the Repeat Rate key and then one of the top-row function keys, with F1 being the slowest rate and F8 being the fastest—then press "Repeat Rate" again.

The programmability of the AnyKey results in complex rules being forged pertaining to its behavior. For example, the Num Lock, Caps Lock, and Scroll Lock keys cannot have macros assigned to them, but they can be included in other macros. These keys can be remapped and remapped to others, however.

The keyboard can be programmed to call up and execute software programs in the computer, but the user must compensate for the time it takes the computer to execute the program via inserting a delay of 1–5 seconds before entering a subsequent series of commands.

Despite the fact that "AnyKey" is in the name, there is no "Any" key on these keyboards. In customer service lore, the blank key in the center of the AnyKey's arrow key cluster often served as a stand-in for the nonexistant "Any" key, however.

## History

Gateway bundled or offered the AnyKey keyboards with most of their desktop systems from 1991 to around 1998. The keyboard featured advanced programmability, making it possible for novice users to reprogram the AnyKey keyboards in unintentional and arcane ways.

Manufacturing of the AnyKey ceased circa 1998, and Gateway stopped offering them shortly thereafter. Neither Maxi Switch, Gateway, nor Lite-On currently offer any product labeled as or comparable to the AnyKey.

## InfoBox

| Gateway AnyKey | |
| --- | --- |
| A Gateway AnyKey keyboard, manufactured circa 1994 | |
| Part no. | 2189014 (prefix) |
| Branding | Gateway 2000 |
| Manufacturer | Maxi Switch |
| Features | Reprogramability (key remapping and macros) |
| Layouts | Standard 101-key layout plus 23 additional keys (124 total) |
| Keyswitches | Rubber domes |
| Keycaps | Dye-sublimated (white/grey keycaps) or pad-printed (black) PBT |
| Interface | PS/2, AT |
| Introduced | 1991 |
| Discontinued | c. 1998 |


title: Ged McNamee

abstract: Gerard McNamee is an English former footballer who works at Sunderland as the academy's Head of Recruitment.

text:
# Ged McNamee

**Gerard McNamee** (born 16 August 1960) is an English former footballer who works at Sunderland as the academy's Head of Recruitment.

## Playing career

McNamee came through the youth system at Hartlepool United before signing his first professional contract in 1980. His time as a player with Pools was blighted by injury and he made just four appearances in three seasons, scoring once against York City.

After leaving Hartlepool, McNamee went onto play for Consett as well as various other North-East non-league sides.

## Coaching career

McNamee began working for Manchester United's regional development centre in Durham in 1992. In 1995, McNamee began running the Durham branch of Manchester United's Centre of Excellence before moving to Sunderland A.F.C. in 1997 where he became the club's Centre of Excellence Director.

In 2004, Sunderland manager Mick McCarthy moved McNamee into the position of the club's Academy Manager. He would remain in that position with the Black Cats until 2016 when he stepped down following a restructure of the club's academy. During McNamee's time as Academy Manager, Sunderland produced players such as Jordan Henderson, Jordan Pickford, Jack Colback and Duncan Watmore.

McNamee returned to football in February 2018 working as a voluntary coach at National League club Hartlepool United as part of caretaker manager Matthew Bates' backroom staff. Following Bates' appointment as first-team manager in May 2018, McNamee's position of first team coach became a full-time paid role. In October 2019, McNamee departed the club alongside manager Craig Hignett.

In January 2020, McNamee returned to Sunderland as the academy's Head of Recruitment.

## Personal life

McNamee's son, Tom, previously played for Sunderland but failed to make a first-team appearance before moving onto Blyth Spartans in 2015.

## InfoBox

Ged McNamee
| Personal information | | | |
| --- | --- | --- | --- |
| Full name | Gerard McNamee | | |
| Date of birth | (1960-08-16) 16 August 1960 | | |
| Place of birth | Consett, England | | |
| Position(s) | Midfielder | | |
| Senior career\* | | | |
| Years | **Team** | **Apps** | **(Gls)** |
| 1980–1983 | Hartlepool United | 4 | (1) |
|  | Consett |  |  |
| \*Club domestic league appearances and goals | | | |


title: Tottenham Lock

abstract: Tottenham Lock (No17) is a paired lock on the River Lee Navigation in the London Borough of Haringey, England and is located near Tottenham, London. Like other locks as far as Ponders End it is large enough to take barges of up to 130 tons. The primary lock has been upgraded to mechanical operation, but the secondary west lock is operated manually. Tottenham Lock was originally nearer to Stonebridge, but was relocated to its current location when the cut was created, creating a junction just south of the lock.

text:
# Tottenham Lock

**Tottenham Lock** (No17) is a paired lock on the River Lee Navigation in the London Borough of Haringey, England and is located near Tottenham, London. Like other locks as far as Ponders End it is large enough to take barges of up to 130 tons. The primary lock has been upgraded to mechanical operation, but the secondary west lock is operated manually.

Tottenham Lock was originally nearer to Stonebridge, but was relocated to its current location when the cut was created, creating a junction just south of the lock.

## Transport

The nearest London Underground station is Tottenham Hale at Ferry Lane. The towpath is open to pedestrians and cyclists which forms part of the Lea Valley Walk.

## Recreation

Angling is allowed on the River Lee Navigation upstream of the lock. Information from the River Lea Anglers Club.

## InfoBox

| Tottenham Lock | |
| --- | --- |
| Tottenham Lock | |
|  | |
| 51°35′17″N 0°03′23″W / 51.588050°N 0.056375°W / 51.588050; -0.056375 | |
| Waterway | River Lee Navigation |
| County | London Borough of Haringey
Greater London |
| Maintained by | Canal & River Trust |
| Operation | Mechanical/Manual |
| Length | 95 feet (29 m) |
| Width | 19 feet 6 inches (5.9 m) |
| Fall | 6 feet 9 inches (2.1 m) |
| Distance to
Bow Creek | 7.3 miles (11.7 km) |
| Distance to
Hertford Castle Weir | 20.7 miles (33.3 km) |


abstract: Vehicular traffic can be either free or congested. Traffic occurs in time and space, i.e., it is a spatiotemporal process. However, usually traffic can be measured only at some road locations. For efficient traffic control and other intelligent transportation systems, the reconstruction of traffic congestion is necessary at all other road locations at which traffic measurements are not available. Traffic congestion can be reconstructed in space and time based on Boris Kerner’s three-phase traffic theory with the use of the ASDA and FOTO models introduced by Kerner. Kerner's three-phase traffic theory and, respectively, the ASDA/FOTO models are based on some common spatiotemporal features of traffic congestion observed in measured traffic data.

text:
# Traffic congestion reconstruction with Kerner's three-phase theory

Vehicular traffic can be either free or congested. Traffic occurs in time and space, i.e., it is a spatiotemporal process. However, usually traffic can be measured only at some road locations (for example, via road detectors, video cameras, probe vehicle data, or phone data). For efficient traffic control and other intelligent transportation systems, the reconstruction of traffic congestion is necessary at all other road locations at which traffic measurements are not available. Traffic congestion can be reconstructed in space and time (Fig. 1) based on Boris Kerner’s three-phase traffic theory with the use of the ASDA and FOTO models introduced by Kerner. Kerner's three-phase traffic theory and, respectively, the ASDA/FOTO models are based on some *common* spatiotemporal features of traffic congestion observed in measured traffic data.

## Common spatiotemporal empirical features of traffic congestion

### Definition

Common spatiotemporal empirical features of traffic congestion are those spatiotemporal features of traffic congestion, which are qualitatively the same for different highways in different countries measured during years of traffic observations. In particular, common features of traffic congestion are independent on weather, road conditions and road infrastructure, vehicular technology, driver characteristics, day time, etc.

Kerner's definitions \[S\] and \[J\], respectively, for the synchronized flow and wide moving jam phases in congested traffic are examples of common spatiotemporal empirical features of traffic congestion.

### Propagation of wide moving jams through highway bottlenecks

In empirical observations, traffic congestion occurs usually at a highway bottleneck as a result of traffic breakdown in an initially free flow at the bottleneck. A highway bottleneck can result from on- and off-ramps, road curves and gradients, road works, etc.

In congested traffic (this is a synonym term to traffic congestion), a phenomenon of the propagation of a moving traffic jam (moving jam for short) is often observed. A moving jam is a local region of low speed and great density that propagates upstream as a whole localized structure. The jam is limited spatially by two jam fronts. At the downstream jam front, vehicles accelerate to a higher speed downstream of the jam. At the upstream jam front, vehicles decelerate while approaching the jam.

A wide moving jam is a moving jam that exhibits the characteristic jam feature \[J\], which is a *common* spatiotemporal empirical feature of traffic congestion. The jam feature \[J\] defines the wide moving jam traffic phase in congested traffic as follows.

#### Definition \[J\] for wide moving jam

A wide moving jam is a moving traffic jam, which exhibits the characteristic jam feature \[J\] to propagate through any bottlenecks while maintaining the mean velocity of the downstream jam front denoted by $v\_{g}$.

Kerner's jam feature \[J\] can be explained as follows. The motion of the downstream jam front results from acceleration of drivers from a standstill within the jam to traffic flow downstream of the jam. After a vehicle has begun to accelerate escaping from the jam, to satisfy safety driving, the following vehicle begins to accelerate with a time delay. We denote the mean value of this time delay in vehicle acceleration at the downstream jam front by $\tau \_{del,jam}^{(a)}$. Because the average distance between vehicles within the jam, including average vehicle length, equals $\frac {1}{\rho \_{max}}$ (where $\rho \_{max}$ is the average vehicle density within the jam), the mean velocity of the downstream jam front $v\_{g}$ is

$v\_{g}=-{\frac {1}{\rho \_{max}\tau \_{del,jam}^{(a)}\qquad \qquad (1)}}$.

When traffic parameters (percentage of long vehicles, weather, driver characteristics, etc.) do not change over time, $\tau \_{del,jam}^{(a)}$ and $\rho \_{max}$ are constant in time. This explains why the mean velocity of the downstream jam front $v\_{g}$ (1) is the characteristic parameter that does not depend on the flow rates and densities upstream and downstream of the jam.

### Catch effect: pinning of downstream front of synchronized flow at bottleneck

In contrast with the jam feature \[J\], the mean velocity of the downstream front of synchronized flow is not self-maintained during the front propagation. This is the *common* feature of synchronized flow that is one of the two phases of traffic congestion.

A particular case of this common feature of synchronized flow is that the downstream synchronized flow front is usually caught at a highway bottleneck. This pinning of the downstream front of synchronized flow at the bottleneck is called the *catch effect*. Note that at this downstream front of synchronized flow, vehicles accelerate from a lower speed within synchronized flow upstream of the front to a higher speed in free flow downstream of the front.

#### Definition \[S\] for synchronized flow

Synchronized flow is defined as congested traffic that does not exhibit the jam feature \[J\]; in particular, the downstream front of synchronized flow is often fixed at the bottleneck.

Thus Kerner's definitions \[J\] and \[S\] for the wide moving jam and synchronized flow phases of his three-phase traffic theory are indeed associated with common empirical features of traffic congestion.

### Empirical example of wide moving jam and synchronized flow

Vehicle speeds measured with road detectors (1 min averaged data) illustrate Kerner's definitions \[J\] and \[S\] (Fig. 2 (a, b)). There are two spatiotemporal patterns of congested traffic with low vehicle speeds in Fig. 2 (a). One pattern of congested traffic propagates upstream with almost constant mean velocity of the downstream pattern front through the freeway bottleneck. According to the definition \[J\] this pattern of congested traffic belongs to the "wide moving jam" traffic phase. In contrast, the downstream front of the other pattern of the congested traffic is fixed at the bottleneck. According to the definition \[S\] this pattern of congested traffic belongs to the "synchronized flow" traffic phase (Fig. 2 (a) and (b)).

## ASDA and FOTO models

The FOTO (**F**orecasting **o**f **t**raffic **o**bjects) model reconstructs and tracks regions of synchronized flow in space and time. The ASDA (**A**utomatische **S**tau**d**ynamik**a**nalyse: Automatic Tracking of Moving Jams) model reconstructs and tracks wide moving jams. The ASDA/FOTO models are devoted to *on-line* applications without calibration of model parameters under different environment conditions, road infrastructure, percentage of long vehicles, etc.

### General features

Firstly, the ASDA/FOTO models identify the synchronized flow and wide moving jam phases in measured data of congested traffic. One of the empirical features the synchronized flow and wide moving jam phases used in the ASDA/FOTO models for traffic phase identification is as follows: Within a wide moving jam, both the speed and flow rate are very small (Fig. 2 (c-f)). In contrast, whereas the speed with the synchronized flow phase is considerably lower than in free flow (Fig. 2 (c, e)), the flow rate in synchronized flow can be as great as in free flow (Fig. 2 (d, f)).

Secondly, based on the abovementioned common features of wide moving jams and synchronized flow, the FOTO model tracks the downstream and upstream fronts of synchronized flow denoted by $x\_{down}^{(syn)}(t)$, $x\_{up}^{(syn)}(t)$, where $t$ is time (Fig. 3). The ASDA model tracks the downstream and upstream fronts of wide moving jams denoted by $x\_{down}^{(jam)}(t)$, $x\_{up}^{(jam)}(t)$ (Fig. 3). This tracking is carried out between road locations at which the traffic phases have initially been identified in measured data, i.e., when synchronized flow and wide moving jams cannot be measured.

In other words, the tracking of synchronized flow by the FOTO model and wide moving jams by the ASDA model is performed at road locations at which *no* traffic measurements are available, i.e., the ASDA/FOTO models make the forecasting of the front locations of the traffic phases in time. The ASDA/FOTO models enable us to predict the merging and/or the dissolution of one or more initially different synchronized flow regions and of one or more initially different wide moving jams that occur between measurement locations.

### ASDA/FOTO models for data measured by road detectors

#### Cumulative flow approach for FOTO

While the downstream front of synchronized flow at which vehicles accelerate to free flow is usually fixed at the bottleneck (see Fig. 2 (a, b)), the upstream front of synchronized flow at which vehicles moving initially in free flow must decelerate approaching synchronized flow can propagate upstream. In empirical (i.e., measured) traffic data, the velocity of the upstream front of synchronized flow depends usually considerably both on traffic variables within synchronized flow downstream of the front and within free flow just upstream of this front. A good correspondence with empirical data is achieved, if a time-dependence of the location of the synchronized flow front is calculated by the FOTO model with the use of a so-called cumulative flow approach:

$x\_{up}^{(syn)}(t)=\mu {\frac {1}{n}\int \_{0}^{t}(q\_{S}(t)-q\_{F}(t))dt,\ \ t\geq t\_{0}\qquad \qquad (2)}$

where $q\_{F}$ and $q\_{S}$ \[vehicles/h\] are respectively the flow rates upstream and downstream of the synchronized flow front, $\mu $ is a model parameter \[m/vehicles\], and $n$ is the number of road lanes.

#### Two approaches for jam tracking with ASDA

There are two main approaches for the tracking of wide moving jams with the ASDA model:

1. The use of the Stokes-shock-wave formula.
2. The use of a characteristic velocity of wide moving jams.

##### The use of the Stokes-shock-wave formula in ASDA

The current velocity $v^{(jam)}$ of a front of a wide moving jam is calculated though the use of the shock-wave formula derived by Stokes in 1848:

$v^{(jam)}(t)={\frac {q\_{2}(t)-q\_{1}(t)}{\rho \_{2}(t)-\rho \_{1}(t)}\qquad \qquad (3)}$,

where $q\_{1}$ and $\rho \_{1}$ the flow rate and density upstream of the jam front that velocity should be found; $q\_{2}$ and $\rho \_{2}$ are the flow rate and density downstream of this jam front. In (3) *no any* relationship, in particular, *no* fundamental diagram is used between the flow rates $q\_{1}$, $q\_{2}$ and vehicle densities $\rho \_{1}$, $\rho \_{2}$ found from measured data independent of each other.

##### The use of a characteristic velocity of wide moving jams

If measured data are not available for the tracking of the downstream jam front with the Stokes-shock-wave formula (3), the formula

$v\_{down}^{(jam)}=v\_{g}\qquad \qquad (4)$

is used in which $v\_{g}$ is the characteristic velocity of the downstream jam front associated with Kerner's jam feature \[J\] discussed above. This means that after the downstream front of a wide moving jam has been identified at a time instant $t=t\_{1}$, the location of the downstream front of the jam can be estimated with formula

$x(t)-x(t\_{1})=v\_{g}(t-t\_{1}),\ \ t\>t\_{1}\qquad \qquad (5)$

The characteristic jam velocity is illustrated in Fig. 4. Two wide moving jams propagate upstream while maintaining the mean velocity of their downstream fronts. There are two jams following each other in this empirical example.

However, in contrast with the mean velocity of the downstream jam front, the mean velocity of the upstream jam front depends on the flow rate and density in traffic flow upstream of the jam. Therefore, in a general case the use of formula (5) can lead to a great error by the estimation of the mean velocity of the upstream jam front.

In many data measured on German highways has been found $v\_{g}\approx -15{\mbox{km/h}}$. However, although the mean velocity $v\_{g}$ of the downstream jam front is independent of the flow rates and densities upstream and downstream of the jam, $v\_{g}$ can depend considerably on traffic parameters like the percentage of long vehicles in traffic, weather, driver characteristics, etc. As a result, the mean velocity $v\_{g}$ found in different data measured over years of observations varies approximately within the range $-12\>v\_{g}\>-20{\mbox{km/h}}$.

#### On-line applications of ASDA/FOTO models in traffic control centres

Reconstruction and tracking of spatiotemporal congested patterns with the ASDA/FOTO models is done today online permanently in the traffic control centre of the federal state Hessen (Germany) for 1200 km of freeway network. Since April 2004 measured data of nearly 2500 detectors are automatically analyzed by ASDA/FOTO. The resulting spatiotemporal traffic patterns are illustrated in a space-time diagram showing congested pattern features like Fig. 5. The online system has also been installed in 2007 for North Rhine-Westphalia freeways. The raw traffic data are transferred to WDR, the major public radio broadcasting station from North Rhine-Westphalia in Cologne, who offers traffic messages to the end customer (e. g., radio listener or driver) via broadcast channel RDS. The application covers a part of the whole freeway network with 1900 km of freeway and more than 1000 double loop detectors. In addition, since 2009 ASDA/FOTO models are online in the northern part of Bavaria.

#### Average traffic flow characteristics and travel time

In addition to spatiotemporal reconstruction of traffic congestion (Figs. 1 and 5), the ASDA/FOTO models can provide average traffic flow characteristics within synchronized flow and wide moving jams. In turn, this permits the estimation of either travel time on a road section or travel time along any vehicle trajectory (see examples of trajectories 1–4 in Fig. 5).

### ASDA/FOTO models for data measured by probe vehicles

Firstly, the ASDA and FOTO models identify transition points for phase transitions along the trajectory of a probe vehicle. Each of the transition points is associated to the front separating spatially two of the three different traffic phases each other (free flow (F), synchronized flow (S), wide moving jam (J)). After the transition points have been found, the ASDA/FOTO models reconstruct regions of synchronized flow and wide moving jams in space and time with the use of empirical features of these traffic phases discussed above (see Figs. 2 and 4).

1. Boris S. Kerner, Kirschfink H, Rehborn H; Method for the automatic monitoring of traffic including the analysis of back-up dynamics, Deutsches Patent DE19647127C2, USA patent: US 5861820 (Filed: 1996)
2. Boris S. Kerner, Rehborn H., Traffic surveillance method and vehicle flow control in a road network, Deutsche Patentoffenlegung DE19835979A1, USA patent: US 6587779B1 (Filed: 1998)
3. Boris S. Kerner, M. Aleksić, U. Denneler; Verfahren und Vorrichtung zur Verkehrszustandsüberwachung, Deutsches Patent DE19944077C1 (Filed: 1999)
4. Boris S. Kerner; Method for monitoring the condition of traffic for a traffic network comprising effective narrow points, Deutsche Patentoffenlegung DE19944075A1; USA patent: US 6813555B1; Japan: JP 2002117481 (Filed: 1999)
5. Boris S. Kerner Deutsches Patent DE10036789A1; Method for determining the traffic state in a traffic network with effective bottlenecks, USA patent: US 6522970B2 (Filed: 2000)
6. Boris S. Kerner, "Experimental Features of Self-Organization in Traffic Flow", Physical Review Letters, 81, 3797-3400 (1998)
7. Boris S. Kerner, "The physics of traffic", Physics World Magazine 12, 25-30 (August 1999)
8. Boris S. Kerner, "Congested Traffic Flow: Observations and Theory", Transportation Research Record, Vol. 1678, pp. 160-167 (1999) Archived 9 December 2012 at archive.today
9. George G. Stokes, "On a difficulty in the theory of sound", Philosophical Magazine, 33, pp 349-356 (1848)
10. B.S. Kerner, H. Rehborn, J. Palmer, S.L. Klenov, Using probe vehicle to generate jam warning messages, Traffic Engineering and Control Vol 52, No 3 141-148 (2011)
11. J. Palmer, H. Rehborn, B.S. Kerner, ASDA and FOTO Models based on Probe Vehicle Data, Traffic Engineering and Control Vol 52 No 4, 183-191 (2011)

## Bibliography

* Kerner B. S., Konhäuser P. (1994). Structure and parameters of clusters in traffic flow, Physical Review E, Vol. 50, 54
* Kerner B. S., Rehborn H. (1996). Experimental features and characteristics of traffic jams. Physical Review E, Vol. 53, 1297
* Kerner B. S., Rehborn H. (1996). Experimental properties of complexity in traffic flow. Physical Review E, Vol. 53, R4257
* Kerner B. S., Kirschfink H., Rehborn H. (1997) Automatische Stauverfolgung auf Autobahnen, Straßenverkehrstechnik, No. 9, pp 430–438
* Kerner B. S., Rehborn H. (1998) Messungen des Verkehrsflusses: Charakteristische Eigenschaften von Staus auf Autobahnen, Internationales Verkehrswesen, 5/1998, pp 196–203
* Kerner B. S., Rehborn H., Aleksić M., Haug A., Lange R. (2000) Verfolgung und Vorhersage von Verkehrsstörungen auf Autobahnen mit "ASDA" und "FOTO" im online-Betrieb in der Verkehrsrechnerzentrale Rüsselsheim, Straßenverkehrstechnik, No. 10, pp 521–527
* Kerner B. S., Rehborn H., Aleksić M., Haug A. (2001) Methods for Tracing and Forecasting of Congested Traffic Patterns on Highways, Traffic Engineering and Control, 09/2001, pp 282–287
* Kerner B. S., Rehborn H., Aleksić M., Haug A., Lange R. (2001) Online Automatic tracing and forecasting of traffic patterns with models "ASDA" and "FOTO", Traffic Engineering and Control, 11/2001, pp 345–350
* Kerner B. S., Rehborn H., Aleksić M., Haug A. (2004): Recognition and Tracing of Spatial-Temporal Congested Traffic Patterns on Freeways, Transportation Research C, 12, pp 369–400
* Palmer J., Rehborn H. (2007) ASDA/FOTO based on Kerner's Three-Phase Traffic Theory in North-Rhine Westfalia (in German), Straßenverkehrstechnik, No. 8, pp 463–470
* Palmer J., Rehborn H., Mbekeani L. (2008) Traffic Congestion Interpretation Based on Kerner's Three-Phase Traffic Theory in USA, In: Proceedings 15th World Congress on ITS, New York
* Palmer J., Rehborn H. (2009) Reconstruction of congested traffic patterns using traffic state detection in autonomous vehicles based on Kerner's three-phase traffic theory, In: Proceedings of. 16th World Congress on ITS, Stockholm
* Rehborn H, Klenov S.L. (2009) Traffic Prediction of Congested Patterns, In: R. Meyers (Ed.): Encyclopedia of Complexity and Systems Science, Springer New York, 2009, pp 9500–9536
* Boris S. Kerner, Rehborn H, Klenov S L, Palmer J, Prinn M (2009) Verfahren zur Verkehrszustandsbestimmung in einem Fahrzeug, (Method for traffic state detection in a vehicle), German Patent publication DE 10 2008 003 039 A1.

## Further reading


title: Traffic count

abstract: A traffic count is a count of vehicular or pedestrian traffic, which is conducted along a particular road, path, or intersection. A traffic count is commonly undertaken either automatically, or manually by observers who visually count and record traffic on a hand-held electronic device or tally sheet. Traffic counts can be used by local councils to identify which routes are used most, and to either improve that road or provide an alternative if there is an excessive amount of traffic. Also, some geography fieldwork involves a traffic count. Traffic counts provide the source data used to calculate the Annual Average Daily Traffic (AADT), which is the common indicator used to represent traffic volume. Traffic counts are useful for comparing two or more roads, and can also be used alongside other methods to find out where the central business district (CBD) of a settlement is located. Traffic counts that include speeds are used in speed limit enforcement efforts, highlighting peak speeding periods to optimise speed camera use and educational efforts.

text:
# Traffic count

A **traffic count** is a count of vehicular or pedestrian traffic, which is conducted along a particular road, path, or intersection. A traffic count is commonly undertaken either automatically (with the installation of a temporary or permanent electronic traffic recording device), or manually by observers who visually count and record traffic on a hand-held electronic device or tally sheet. Traffic counts can be used by local councils to identify which routes are used most, and to either improve that road or provide an alternative if there is an excessive amount of traffic. Also, some geography fieldwork involves a traffic count. Traffic counts provide the source data used to calculate the Annual Average Daily Traffic (AADT), which is the common indicator used to represent traffic volume. Traffic counts are useful for comparing two or more roads, and can also be used alongside other methods to find out where the central business district (CBD) of a settlement is located. Traffic counts that include speeds are used in speed limit enforcement efforts, highlighting peak speeding periods to optimise speed camera use and educational efforts.

## Counting methods

To permanently or temporarily monitor the usage of a road, an electronic traffic counter can be installed or placed to measure road usage continuously or for a short period of time. Most modern equipment called ATR's (Automatic Traffic Recorders) store count and/or classification data recorded in memory in a timestamp or interval fashion that can be downloaded and viewed in software or via a count display on some equipment. In some instances people either draw up a table and/or use a tally to keep a record of vehicles which pass manually as an alternative to ATR's.

## Traffic counter devices

A **traffic counter** is a device, often electronic in nature, used to count, classify, and/or measure the speed of vehicular traffic passing along a given roadway. The device is usually deployed in near proximity to the roadway and uses an on-road medium, such as pneumatic road tubes laid across the roadway, piezo-electric sensors embedded in the roadway, inductive loops cut into the roadway, or a combination of these to detect the passing vehicles. Pneumatic road tubes are generally used for temporary studies to study a sample of traffic, while piezo-electric sensors and inductive loops are used for permanent studies which can ascertain seasonal traffic trends and are often used in congestion monitoring on major roads. One of the first traffic counting units, called **traffic recorders**, was introduced in 1937, operated off a strip laid across the street, and used a six volt battery. Each hour it printed off a paper strip with the total for that hour. A newer type of temporary sensor consists of a metal detector and data recorder in a single package, adhered to the pavement in the center of a driving lane, unlike the pneumatic tube detector which cannot differentiate between lanes.

Recently, off-road technologies have been developed. These devices generally use some sort of transmitted energy such as radar waves or infrared beams to detect vehicles passing over the roadway. These methods are generally employed where vehicle speeds and volume are required without classification which require on-road sensors. Other off-road technologies are video image detection systems. A portable digital camera unit can be mounted to a pole and computer vision software is used to analyze traffic pattern including traffic counts.

Traffic count software can now also classify vehicles - recording numbers of cars, trucks, bikes etc as well as total numbers - as well as registering how many travelled that way before.

### Bicycle and pedestrian traffic counting devices

Technologies for counting bicycles on roads, or bicycles and pedestrians along sidewalks or shared-use paths have progressed with the increased emphasis on the economic, environmental and social benefits of multi-modal traffic networks. Non-motorized modes of traffic are often surveyed using the same types of sensors used for motorized vehicles; in some cases tuned to be more sensitive to actuation (e.g. Pneumatic tubes, Piezoelectric, inductive loop detectors, Passive and Active Infrared, Video, Magnetometers, et al.).

In 2004, the American private-sector firm Alta Planning and Design, in partnership with the Institute of Transportation Engineers (ITE) initiated the National Bicycle and Pedestrian Documentation Program (NBPD) as an effort to promote greater data collection for non-motorized transportation modes, establish a consistent model for data collection, and address the lack of data access and shared research.

In 2013, the US Department of Transportation, Federal Highway Administration (FHWA) expanded and created a chapter on non-motorized counting for the Traffic Monitoring Guide (TMG) designed to guide planning agencies in the collection of their data.

1. "FHWA Traffic Monitoring Guide". June 2013. Retrieved March 2015
2. Atagi, Colin (4 January 2017). "Caltrans checks dangerous intersection's traffic". *The Desert Sun*. Retrieved 8 October 2021.
3. "Strip Across Road Counts Cars and Registers Hourly Total" *Popular Mechanics*, July 1936
4. Evaluation of Microwave Radar Trailers for Nonintrusive Traffic Measurements." Transportation Research Record: Journal of the Transportation Research Board 1917 (2005): 127-40. Transportation Research Record: Journal of the Transportation Research Board Online.
5. Middleton, D.R., R.T. Parker, and R.R. Longmire. "Investigation of Vehicle Detector Performance and ATMS Interface.", Texas Transportation Institute 0-4750-2 (2007). Texas Transportation Institute.
6. Antoniou, Constantinos; Balakrishna, Ramachandran; Koutsopoulos, Haris N. (November 2011). "A Synthesis of emerging data collection technologies and their impact on traffic management applications" (PDF). *European Transport Research Review*. **3** (3): 139–148. Bibcode:2011ETRR....3..139A. doi:10.1007/s12544-011-0058-1. S2CID 59450394. Retrieved 8 October 2021.
7. Kawamura, Kazuya; Sriraj, P.S. (2016). "Building Freight-friendly Environment". *Transportation Research Procedia*. **12**: 119–131. doi:10.1016/j.trpro.2016.02.052. Retrieved 8 October 2021.
8. Vehicle Detection: Ten Ways to Count Traffic, Retail Sensing, Retrieved 2023.06.21
9. Ryus, Paul; Ferguson, Erin; Laustsen, Kelly M.; Schneider, Robert J.; Proulx, Frank R.; Hull, Tony; Miranda-Moreno, Luis (2014). *National Cooperative Highway Research Program ~ Report 797: Guidebook on Pedestrian and Bicycle Volume Data Collection* (PDF). Washington, D.C.: Transportation Research Board. ISBN 978-0-309-30826-7. Retrieved 2015-11-18.
10. "National Bicycle and Pedestrian Documentation Program". Alta Planning & Design. 2015.
11. Denney, Charlie. "National Bicycle & Pedestrian Documentation Project" (PDF). Advocacy Advance. Retrieved 2015-11-18.


title: Traffic court

abstract:
Traffic court is a specialized judicial process for handling traffic ticket cases. In the United States, people who are given a citation by a police officer can plead guilty and pay the indicated fine directly to the court house, by mail, or on the Internet. A person who wishes to plead not guilty or otherwise contest the charges is required to appear in court on the predetermined date on the citation, where they may argue before the judge or negotiate with the prosecutor before being called to appear in front of the judge. Most prosecutors will not negotiate with someone who does not have a lawyer. The person may also request a trial by a written declaration in the following states: California, Florida, Hawaii, Indiana, Louisiana, Nebraska, Ohio, Oregon, and Wyoming.
In the case of a trial by written declaration, the accused does not have to be present in the courtroom; they may just explain the reason to defense for the case. Officers are required to turn in their declaration. The judge will then make a decision based on the declarations and evidence from both sides. After the written trial, the accused is allowed to request a new in-person hearing if they are not satisfied with the outcome of the written trial, by filing a trial de novo request. More serious charges, such as a DUI or instances where the person in question may be responsible for injuries to another, may require the person to appear in court regardless of their plea. Some municipalities process guilty pleas of this nature without the presence of an actual judge, whereas others may require one to appear in court. Often these charges are handled by the larger criminal court. Each state handles traffic matters in its own way. In most of New York State, for example, traffic matters are heard in the court for the city, town, or village where the alleged violation happened. The town and village courts are known as Justice Courts. Each municipality is free to decide how to handle traffic cases. A similar process is followed in Tennessee, though many southern states have varying procedures for paying the fine as a form of pleading guilty. New York City traffic matters are heard in a special court called Traffic Violations Bureau, with a very different process. New Jersey handles traffic matters in the Municipal Court System, with the most serious cases heard in Superior Court. In Virginia, traffic court is general district court and speeding as low as 81 mph in a 70 is misdemeanor reckless driving. In Washington, D.C., traffic tickets are handled by the Department of Motor Vehicles. In California, tickets are handled in Superior Court. Massachusetts tickets are heard in District Courts. In the City of Chicago, traffic tickets issued by Chicago Police Officers with no possibility of jail time are handled by the City's Law Department, frequently by law students. All other traffic violations are dealt with by the Cook County State's Attorney.

text:
# Traffic court

**Traffic court** is a specialized judicial process for handling traffic ticket cases. In the United States, people who are given a citation by a police officer can plead guilty and pay the indicated fine directly to the court house, by mail, or on the Internet. A person who wishes to plead not guilty or otherwise contest the charges is required to appear in court on the predetermined date on the citation, where they may argue before the judge or negotiate with the prosecutor before being called to appear in front of the judge. Most prosecutors will not negotiate with someone who does not have a lawyer. The person may also request a trial by a written declaration in the following states: California, Florida, Hawaii, Indiana, Louisiana, Nebraska, Ohio, Oregon, and Wyoming. In the case of a trial by written declaration, the accused does not have to be present in the courtroom; they may just explain the reason to defense for the case. Officers are required to turn in their declaration. The judge will then make a decision based on the declarations and evidence from both sides. After the written trial, the accused is allowed to request a new in-person hearing if they are not satisfied with the outcome of the written trial, by filing a trial de novo request.

More serious charges, such as a DUI or instances where the person in question may be responsible for injuries to another, may require the person to appear in court regardless of their plea. Some municipalities process guilty pleas of this nature without the presence of an actual judge, whereas others may require one to appear in court. Often these charges are handled by the larger criminal court.

Each state handles traffic matters in its own way. In most of New York State, for example, traffic matters are heard in the court for the city, town, or village where the alleged violation happened. The town and village courts are known as Justice Courts. Each municipality is free to decide how to handle traffic cases. A similar process is followed in Tennessee, though many southern states have varying procedures for paying the fine as a form of pleading guilty. New York City traffic matters (and those of a few other locations) are heard in a special court called Traffic Violations Bureau, with a very different process. New Jersey handles traffic matters in the Municipal Court System, with the most serious cases heard in Superior Court. In Virginia, traffic court is general district court and speeding as low as 81 mph in a 70 is misdemeanor reckless driving. In Washington, D.C., traffic tickets are handled by the Department of Motor Vehicles. In California, tickets are handled in Superior Court. Massachusetts tickets are heard in District Courts. In the City of Chicago, traffic tickets issued by Chicago Police Officers with no possibility of jail time are handled by the City's Law Department, frequently by law students. All other traffic violations (including those issued by state police) are dealt with by the Cook County State's Attorney.

1. "Trial by Declaration: Fight a Traffic Ticket Without Going to Court". 13 May 2008.
2. "California Courts Online - the most comprehensive resource on California court information" (PDF). 5 October 2021.
3. "Vehicle Code Section 40902". *www.dmv.ca.gov*. Archived from the original on 2001-02-11.
4. Park, Sean. "How Tennessee Handles Traffic Court". The Park Law Firm. Retrieved 15 July 2015.
5. "General District Courts".
6. "Virginia Reckless Driving Lawyer".
7. "Municipal Department Overview".


abstract: Totto-Chan: The Little Girl at the Window Totto-Chan: The Little Girl at the Window is a 2023 Japanese animated biographical film written and directed by Shinnouske Yakuwa with Yōsuke Suzuki as a co-writer; the film is based on an autobiographical novel of the same title by Tetsuko Kuroyanagi. Produced by Shin-Ei Animation and distributed by Toho, it tells Kuroyanagi's story as a child of going to Tomoe Gakuen, and learning new things as Japan descends into war. The film stars Liliana Ohno as the voice of Totto, alongside Koji Yakusho, Shun Oguri, Anne Watanabe, and Karen Takizawa. It was released in Japan on December 8, 2023.

text:
# Totto-Chan: The Little Girl at the Window (film)

***Totto-Chan: The Little Girl at the Window*** (Japanese: 窓ぎわのトットちゃん, Hepburn: *Madogiwa no Totto-chan*) is a 2023 Japanese animated biographical film written and directed by Shinnouske Yakuwa with Yōsuke Suzuki as a co-writer; the film is based on an autobiographical novel of the same title by Tetsuko Kuroyanagi. Produced by Shin-Ei Animation and distributed by Toho, it tells Kuroyanagi's story as a child (nicknamed Totto) of going to Tomoe Gakuen, and learning new things as Japan descends into war. The film stars Liliana Ohno as the voice of Totto, alongside Koji Yakusho, Shun Oguri, Anne Watanabe, and Karen Takizawa. It was released in Japan on December 8, 2023.

## Synopsis

Totto-chan attends Tomoe Gakuen at a young age, and learns new things as Japan descends into war.

## Voice cast

| Character | Japanese voice cast |
| --- | --- |
| Totto-chan | Liliana Ohno |
| Sōsaku Kobayashi | Koji Yakusho |
| Moritsuna Kuroyanagi | Shun Oguri |
| Cho Kuroyanagi | Anne Watanabe |
| Miss Oishi | Karen Takizawa |
|

## Production

In March 2023, it was announced that an anime film adaptation of Tetsuko Kuroyanagi's autobiographical novel *Totto-Chan: The Little Girl at the Window* was in development, with Shinnouske Yakuwa writing and directing the film at Shin-Ei Animation, Yōsuke Suzuki co-writing the screenplay with Yakuwa, and Shizue Kaneko designing the characters. In July of that year, it was announced that Liliana Ohno was to voice Totto-chan. In September of that year, it was announced that Koji Yakusho, Shun Oguri, Anne Watanabe, and Karen Takizawa were cast for the film. The theme song for the film is "You Know What" (あのね, *Ano ne*) by Aimyon.

## Release

The film was released in theaters in Japan on December 8, 2023.

## Reception

### Box office

The film debuted at number 6 out of top 10 in the Japanese box office in its opening weekend, and later dropped to number 8 in its second week.

### Critical reception

Richard Eisenbeis of Anime News Network gave the film "A" rating, and stated "It's got fantastic characters, a powerful message about childhood education, and a unique exploration of the consequences of war through a child's eyes".

### Accolades

The film was nominated for the 47th Japan Academy Film Prize for "Best Animation Film" category.

## InfoBox

| Totto-Chan: The Little Girl at the Window | |
| --- | --- |
| Theatrical release poster | |
|  | |
| **Kanji** | 窓ぎわのトットちゃん |
|  | |
| Revised Hepburn | Madogiwa no Totto-chan |
|  | |
|  | |
| Directed by | Shinnosuke Yakuwa |
| Screenplay by | * Shinnosuke Yakuwa * Yōsuke Suzuki |
| Based on | *Totto-Chan: The Little Girl at the Window*
by Tetsuko Kuroyanagi |
| Produced by | * Rena Takahashi * Keiji Takagawa |
| Starring |  |
| Cinematography | Kentaro Minegishi |
| Edited by | Toshihiko Kojima |
| Music by | Yuji Nomi |
| Production
company | Shin-Ei Animation |
| Distributed by | Toho Co., Ltd. |
| Release date | * December 8, 2023 (2023-12-08) |
| Running time | 114 minutes |
| Country | Japan |
| Language | Japanese |


title: Tottington railway station

abstract: Tottington Railway station served the town of Tottington in Greater Manchester, England. It opened in 1882 and continued to serve passengers until the line closed to passengers in 1952 and freight in 1963.

text:
# Tottington railway station

**Tottington Railway station** served the town of Tottington in Greater Manchester (then Lancashire), England. It opened in 1882 and continued to serve passengers until the line closed to passengers in 1952 and freight in 1963.

## History

The Bury and Tottington District Railway opened from a junction to the north of Bury to a terminus at Holcombe Brook on 6 November 1882. Among the original stations was that at Tottington, situated 2+12 miles (4.0 km) from Bury.

The station closed when passenger services were withdrawn from the Holcombe Brook line on 5 May 1952; goods trains continued to serve Tottington until 19 August 1963.

| Preceding station |  | Disused railways |  | Following station |
| --- | --- | --- | --- | --- |
| Knowles Halt |  | L&YR
Bury to Holcombe Brook Line |  | Sunny Wood Halt |

## InfoBox

| Tottington | |
| --- | --- |
| General information | |
| Location | Tottington, Bury
England |
| Coordinates | 53°36′50″N 2°20′15″W / 53.61394°N 2.33753°W / 53.61394; -2.33753 |
| Grid reference | SD777131 |
| Other information | |
| Status | Disused |
| History | |
| Original company | Bury and Tottington District Railway |
| Pre-grouping | Lancashire and Yorkshire Railway |
| Post-grouping | London, Midland and Scottish Railway |
| Key dates | |
| 6 November 1882 (1882-11-06) | Station opened |
| 5 May 1952 (1952-05-05) | Station closed for passengers |
| 19 August 1963 | closed for freight |
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abstract: Mexico competed at the 2023 World Aquatics Championships in Fukuoka, Japan from 14 to 30 July.

text:
# Mexico at the 2023 World Aquatics Championships

**Mexico** competed at the 2023 World Aquatics Championships in Fukuoka, Japan from 14 to 30 July.

## Medalists

## Athletes by discipline

The following is the list of number of competitors participating at the Championships per discipline.

| Sport | Men | Women | Total |
| --- | --- | --- | --- |
| Artistic swimming | 2 | 11 | 13 |
| Diving | 7 | 7 | 14 |
| High diving | 3 | 1 | 4 |
| Open water swimming | 3 | 3 | 6 |
| Swimming | 5 | 6 | 11 |
| Total | 20 | 28 | **48** |

* Moesha Johnson was compete in both open water swimming and indoor swimming.

## Artistic swimming

Men

| Athlete | Event | Preliminaries | | Final | |
| --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank |
| Joel Benavides | Solo technical routine | 163.5466 | 7 **Q** | 170.7166 | 7 |

Women

| Athlete | Event | Preliminaries | | Final | |
| --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank |
| Nuria Diosdado
Joana Jiménez | Duet technical routine | 244.2000 | 6 **Q** | 222.5667 | 9 |
| | Duet free routine | DNS | | | |

Mixed

| Athlete | Event | Preliminaries | | Final | |
| --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank |
| **Itzamary González
Diego Villalobos** | Duet technical routine | 228.0075 | 2 **Q** | 223.6066 | 4 |
| | Duet free routine | 166.4040 | 5 **Q** | 192.5500 |  |
| Daniela Estrada
Luisa Rodríguez
Joana Jiménez
Glenda Inzunza
Itzamary González
Nuria Diosdado
Jessica Sobrino
Pamela Toscano | Team acrobatic routine | 202.4533 | 7 **Q** | 215.7267 | 4 |
| Nuria Diosdado
María Fernanda Arellano
Regina Alferez
Joana Jiménez
Daniela Estrada
Pamela Toscano
Jessica Sobrino
Itzamary González | Team technical routine | 219.5325 | 9 **Q** | 257.1380 | 6 |

## Diving

Mexico entered 14 divers.

Men

| Athlete | Event | Preliminaries | | Semifinals | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank | Points | Rank |
| Diego Balleza | 10 m platform | 361.65 | 21 | Did not advance | | | |
| Juan Celaya | 1 m springboard | 362.30 | 10 **Q** |  | | 406.25 | 4 |
| Rodrigo Diego | 3 m springboard | 419.65 | 7 **Q** | 446.45 | 6 **Q** | 439.80 | 5 |
|
| **Osmar Olvera** | 1 m springboard | 395.85 | 2 **Q** |  | | 428.85 |  |
| | 3 m springboard | 443.70 | 4 **Q** | 471.00 | 4 **Q** | 507.50 |  |
| Randal Willars | 10 m platform | 411.55 | 9 **Q** | 477.55 | 4 **Q** | 465.55 | 8 |
| Juan Celaya
Rodrigo Diego | 3 m synchro springboard | 382.08 | 5 **Q** |  | | 369.75 | 11 |
| **Kevin Berlín
Randal Willars** | 10 m synchro platform | 411.78 | 3 **Q** |  | | 434.16 |  |

Women

| Athlete | Event | Preliminaries | | Semifinals | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank | Points | Rank |
| Gabriela Agúndez | 10 m platform | 286.45 | 17 **Q** | 336.55 | 4 **Q** | 325.35 | 4 |
| Carolina Mendoza | 3 m springboard | 276.15 | 18 **Q** | 289.75 | 13 | Did not advance | | | |
| Alejandra Orozco | 10 m platform | 318.30 | 6 **Q** | 315.50 | 6 **Q** | 313.40 | 7 |
| Paola Pineda | 1 m springboard | 214.25 | 31 |  | | Did not advance | |
| **Aranza Vázquez** | 1 m springboard | 262.20 | 3 **Q** |  | | 285.05 |  |
| | 3 m springboard | 218.70 | 39 | Did not advance | | | |
| Arantxa Chávez
Paola Pineda | 3 m synchro springboard | 282.30 | 4 **Q** |  | | 274.50 | 7 |
| Gabriela Agúndez
Alejandra Orozco | 10 m synchro platform | 290.70 | 5 **Q** |  | | 291.18 | 4 |

Mixed

| Athlete | Event | Final | |
| --- | --- | --- | --- |
| | | Points | Rank |
| Jahir Ocampo
Aranza Vázquez | 3 m synchro springboard | 273.90 | 6 |
| **Diego Balleza
Viviana del Ángel** | 10 m synchro platform | 313.44 |  |
| **Gabriela Agúndez
Jahir Ocampo
Randal Willars
Aranza Vázquez** | Team event | 455.35 |  |

## High diving

| Athlete | Event | Points | Rank |
| --- | --- | --- | --- |
| Alejandra Aguilar | Women's high diving | 204.75 | 15 |
| Sergio Guzmán | Men's high diving | 361.35 | 10 |
| Yolotl Martínez | Men's high diving | 290.90 | 16 |
| Jonathan Paredes | Men's high diving | 352.50 | 11 |

## Open water swimming

Mexico entered 6 open water swimmers.

Men

| Athlete | Event | Time | Rank |
| --- | --- | --- | --- |
| Daniel Delgadillo | Men's 10 km | 1:54:12.7 | 29 |
| Santiago Gutiérrez | Men's 5 km | 1:01:21.9 | 52 |
| Paulo Strehlke | Men's 5 km | 56:46.6 | 16 |
| | Men's 10 km | 1:53:04.4 | 11 |

Women

| Athlete | Event | Time | Rank |
| --- | --- | --- | --- |
| Paulina Alanis | Women's 10 km | 2:13:16.7 | 44 |
| Alejandra Hoyos | Women's 5 km | 1:05:55.5 | 44 |
| Martha Sandoval | Women's 5 km | 1:02:26.6 | 32 |
| | Women's 10 km | 2:03:44.8 | 19 |

Mixed

| Athlete | Event | Time | Rank |
| --- | --- | --- | --- |
| Paulina Alanis
Daniel Delgadillo
Martha Sandoval
Paulo Strehlke | Team relay | 1:16:52.7 | 15 |

## Swimming

Mexico entered 11 swimmers.

Men

| Athlete | Event | Heat | | Semifinal | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Time | Rank | Time | Rank | Time | Rank |
| Diego Camacho | 50 metre backstroke | 26.04 | 38 | Did not advance | | | |
| | 100 metre backstroke | 55.80 | 35 | Did not advance | | | |
| Miguel de Lara | 50 metre breaststroke | 27.38 | 17 | Did not advance | | | |
| | 100 metre breaststroke | 1:01.02 | 25 | Did not advance | | | |
| | 200 metre breaststroke | 2:12.40 | 22 | Did not advance | | | |
| Jorge Iga | 50 metre freestyle | 22.64 | 46 | Did not advance | | | |
| | 100 metre freestyle | 49.24 | 37 | Did not advance | | | |
| | 200 metre freestyle | 1:46.89 | 19 | Did not advance | | | |
| | 50 metre butterfly | 24.05 | 45 | Did not advance | | | |
| | 100 metre butterfly | 52.39 | 29 | Did not advance | | | |
| Héctor Ruvalcaba | 200 metre butterfly | 1:57.80 | 22 | Did not advance | | | |
| | 200 metre individual medley | 2:03.87 | 31 | Did not advance | | | |
| | 400 metre individual medley | 4:21.25 **NR** | 18 |  | | Did not advance | |
| Diego Camacho
Miguel de Lara
Jorge Iga
Andres Dupont | 4 × 100 m medley relay | 3:37.25 | 18 |  | | Did not advance | |

Women

| Athlete | Event | Heat | | Semifinal | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Time | Rank | Time | Rank | Time | Rank |
| Miranda Grana | 100 metre backstroke | 1:02.91 | 37 | Did not advance | | | |
| María José Mata | 200 metre freestyle | 2:00.30 | 29 | Did not advance | | | |
| | 200 metre butterfly | 2:09.50 | 11 **Q** | 2:09.33 | 12 | Did not advance | |
| Athena Meneses | 200 metre backstroke | 2:15.14 | 26 | Did not advance | | | |
| | 100 metre butterfly | 1:00.95 | 32 | Did not advance | | | |
| Tayde Revilak | 50 metre freestyle | 25.48 | 27 | Did not advance | | | |
| Melissa Rodríguez | 50 metre breaststroke | 32.05 | 34 | Did not advance | | | |
| | 100 metre breaststroke | 1:09.16 | 33 | Did not advance | | | |
| | 200 metre breaststroke | 2:30.57 | 25 | Did not advance | | | |
| Tayde Sansores | 50 metre backstroke | 28.91 | 32 | Did not advance | | | |
| | 50 metre butterfly | 26.82 | 29 | Did not advance | | | |
| Miranda Grana
Melissa Rodríguez
María José Mata
Athena Meneses | 4 × 100 m medley relay | 4:06.85 **NR** | 22 |  | | Did not advance | |

Mixed

| Athlete | Event | Heat | | Final | |
| --- | --- | --- | --- | --- | --- |
| | | Time | Rank | Time | Rank |
| Jorge Iga
Andres Dupont
Athena Meneses
Tayde Revilak | 4 × 100 m freestyle relay | 3:30.77 | 19 | Did not advance | |
| Miranda Grana
Miguel de Lara
Athena Meneses
Andres Dupont | 4 × 100 m medley relay | 3:53.38 | 18 | Did not advance | |

## InfoBox

| Mexico at the
2023 World Aquatics Championships | |
| --- | --- |
| Flag of Mexico | |
| FINA code | MEX |
| National federation | Mexican Swimming Federation |
| in Fukuoka, Japan | |
| Competitors | 48 in 5 sports |
| Medals
Ranked 19th | Gold 0 Silver 5 Bronze 2 Total 7 |
| World Aquatics Championships appearances | |
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