text:
Bernoulli process

In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The component Bernoulli variables Xi are identically distributed and independent. Prosaically, a Bernoulli process is a repeated coin flipping, possibly with an unfair coin (but with consistent unfairness). Every variable Xi in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided die); this generalization is known as the Bernoulli scheme.

The problem of determining the process, given only a limited sample of Bernoulli trials, may be called the problem of checking whether a coin is fair.

Definition
A Bernoulli process is a finite or infinite sequence of independent random variables X1, X2, X3, ..., such that

 * for each i, the value of Xi is either 0 or 1;
 * for all values of $i$, the probability p that Xi = 1 is the same.

In other words, a Bernoulli process is a sequence of independent identically distributed Bernoulli trials.

Independence of the trials implies that the process is memoryless. Given that the probability p is known, past outcomes provide no information about future outcomes. (If p is unknown, however, the past informs about the future indirectly, through inferences about p.)

If the process is infinite, then from any point the future trials constitute a Bernoulli process identical to the whole process, the fresh-start property.

Interpretation
The two possible values of each Xi are often called "success" and "failure". Thus, when expressed as a number 0 or 1, the outcome may be called the number of successes on the ith "trial".

Two other common interpretations of the values are true or false and yes or no. Under any interpretation of the two values, the individual variables Xi may be called Bernoulli trials with parameter p.

In many applications time passes between trials, as the index i increases. In effect, the trials X1, X2, ... Xi, ... happen at "points in time" 1, 2, ..., i, .... That passage of time and the associated notions of "past" and "future" are not necessary, however. Most generally, any Xi and Xj in the process are simply two from a set of random variables indexed by {1, 2, ..., n}, the finite cases, or by {1, 2, 3, ...}, the infinite cases.

One experiment with only two possible outcomes, often referred to as "success" and "failure", usually encoded as 1 and 0, can be modeled as a Bernoulli distribution. Several random variables and probability distributions beside the Bernoullis may be derived from the Bernoulli process:

 * The number of successes in the first n trials, which has a binomial distribution B(n, p)
 * The number of failures needed to get r successes, which has a negative binomial distribution NB(r, p)
 * The number of failures needed to get one success, which has a geometric distribution NB(1, p), a special case of the negative binomial distribution

The negative binomial variables may be interpreted as random waiting times.

Formal definition
The Bernoulli process can be formalized in the language of probability spaces as a random sequence of independent realisations of a random variable that can take values of heads or tails. The state space for an individual value is denoted by $$2=\{H,T\} .$$

Borel algebra
Consider the countably infinite direct product of copies of $$2=\{H,T\}$$. It is common to examine either the one-sided set $$\Omega=2^\mathbb{N}=\{H,T\}^\mathbb{N}$$ or the two-sided set $$\Omega=2^\mathbb{Z}$$. There is a natural topology on this space, called the product topology. The sets in this topology are finite sequences of coin flips, that is, finite-length strings of H and T (H stands for heads and T stands for tails), with the rest of (infinitely long) sequence taken as "don't care". These sets of finite sequences are referred to as cylinder sets in the product topology. The set of all such strings forms a sigma algebra, specifically, a Borel algebra. This algebra is then commonly written as $$(\Omega, \mathcal{B})$$ where the elements of $$\mathcal{B}$$ are the finite-length sequences of coin flips (the cylinder sets).

Bernoulli measure
If the chances of flipping heads or tails are given by the probabilities $$\{p,1-p\}$$, then one can define a natural measure on the product space, given by $$P=\{p, 1-p\}^\mathbb{N}$$ (or by $$P=\{p, 1-p\}^\mathbb{Z}$$ for the two-sided process). In another word, if a discrete random variable X has a Bernoulli distribution with parameter p, where 0 ≤ p ≤ 1, and its probability mass function is given by

 * $$pX(1)=P(X=1)=p$$ and $$pX(0)=P(X=0)=1-p$$.

We denote this distribution by Ber(p).

Given a cylinder set, that is, a specific sequence of coin flip results $$[\omega_1, \omega_2,\cdots\omega_n]$$ at times $$1,2,\cdots,n$$, the probability of observing this particular sequence is given by

 * $$P([\omega_1, \omega_2,\cdots ,\omega_n])= p^k (1-p)^{n-k}$$

where k is the number of times that H appears in the sequence, and n−k is the number of times that T appears in the sequence. There are several different kinds of notations for the above; a common one is to write
 * $$P(X_1=x_1, X_2=x_2,\cdots, X_n=x_n)= p^k (1-p)^{n-k}$$

where each $$X_i$$ is a binary-valued random variable with $$x_i=[\omega_i=H]$$ in Iverson bracket notation, meaning either $$1$$ if $$\omega_i=H$$ or $$0$$ if $$\omega_i=T$$. This probability $$P$$ is commonly called the Bernoulli measure.

Note that the probability of any specific, infinitely long sequence of coin flips is exactly zero; this is because $$\lim_{n\to\infty}p^n=0$$, for any $$0\le p<1$$. A probability equal to 1 implies that any given infinite sequence has measure zero. Nevertheless, one can still say that some classes of infinite sequences of coin flips are far more likely than others, this is given by the asymptotic equipartition property.

To conclude the formal definition, a Bernoulli process is then given by the probability triple $$(\Omega, \mathcal{B}, P)$$, as defined above.

Law of large numbers, binomial distribution and central limit theorem
Let us assume the canonical process with $$ H $$ represented by $$ 1 $$ and $$ T $$ represented by $$ 0 $$. The law of large numbers states that the average of the sequence, i.e., $$ \bar{X}_{n}:=\frac{1}{n}\sum_{i=1}^{n}X_{i} $$, will approach the expected value almost certainly, that is, the events which do not satisfy this limit have zero probability. The expectation value of flipping heads, assumed to be represented by 1, is given by $$p$$. In fact, one has
 * $$\mathbb{E}[X_i]=\mathbb{P}([X_i=1])=p,$$

for any given random variable $$X_i$$ out of the infinite sequence of Bernoulli trials that compose the Bernoulli process.

One is often interested in knowing how often one will observe H in a sequence of n coin flips. This is given by simply counting: Given n successive coin flips, that is, given the set of all possible strings of length n, the number N(k,n) of such strings that contain k occurrences of H is given by the binomial coefficient
 * $$N(k,n) = {n \choose k}=\frac{n!}{k! (n-k)!}$$

If the probability of flipping heads is given by p, then the total probability of seeing a string of length n with k heads is
 * $$\mathbb{P}([S_n=k]) = {n\choose k} p^k (1-p)^{n-k}, $$

where $$ S_n=\sum_{i=1}^{n}X_i $$. The probability measure thus defined is known as the Binomial distribution.

As we can see from the above formula that, if n=1, the Binomial distribution will turn into a Bernoulli distribution. So we can know that the Bernoulli distribution is exactly a special case of Binomial distribution when n equals to 1.

Of particular interest is the question of the value of $$S_{n}$$ for a sufficiently long sequences of coin flips, that is, for the limit $$n\to\infty$$. In this case, one may make use of Stirling's approximation to the factorial, and write
 * $$n! = \sqrt{2\pi n} \;n^n e^{-n}

\left(1 + \mathcal{O}\left(\frac{1}{n}\right)\right)$$

Inserting this into the expression for P(k,n), one obtains the Normal distribution; this is the content of the central limit theorem, and this is the simplest example thereof.

The combination of the law of large numbers, together with the central limit theorem, leads to an interesting and perhaps surprising result: the asymptotic equipartition property. Put informally, one notes that, yes, over many coin flips, one will observe H exactly p fraction of the time, and that this corresponds exactly with the peak of the Gaussian. The asymptotic equipartition property essentially states that this peak is infinitely sharp, with infinite fall-off on either side. That is, given the set of all possible infinitely long strings of H and T occurring in the Bernoulli process, this set is partitioned into two: those strings that occur with probability 1, and those that occur with probability 0. This partitioning is known as the Kolmogorov 0-1 law.

The size of this set is interesting, also, and can be explicitly determined: the logarithm of it is exactly the entropy of the Bernoulli process. Once again, consider the set of all strings of length n. The size of this set is $$2^n$$. Of these, only a certain subset are likely; the size of this set is $$2^{nH}$$ for $$H\le 1$$. By using Stirling's approximation, putting it into the expression for P(k,n), solving for the location and width of the peak, and finally taking $$n\to\infty$$ one finds that

 * $$H=-p\log_2 p - (1-p)\log_2(1-p)$$

This value is the Bernoulli entropy of a Bernoulli process. Here, H stands for entropy; not to be confused with the same symbol H standing for heads.

John von Neumann posed a question about the Bernoulli process regrading the possibility of a given process being isomorphic to another, in the sense of the isomorphism of dynamical systems. The question long defied analysis, but was finally and completely answered with the Ornstein isomorphism theorem. This breakthrough resulted in the understanding that the Bernoulli process is unique and universal; in a certain sense, it is the single most random process possible; nothing is 'more' random than the Bernoulli process (although one must be careful with this informal statement; certainly, systems that are mixing are, in a certain sense, "stronger" than the Bernoulli process, which is merely ergodic but not mixing. However, such processes do not consist of independent random variables: indeed, many purely deterministic, non-random systems can be mixing).

Dynamical systems
The Bernoulli process can also be understood to be a dynamical system, as an example of an ergodic system and specifically, a measure-preserving dynamical system, in one of several different ways. One way is as a shift space, and the other is as an odometer. These are reviewed below.

Bernoulli shift
One way to create a dynamical system out of the Bernoulli process is as a shift space. There is a natural translation symmetry on the product space $$\Omega=2^\mathbb{N}$$ given by the shift operator
 * $$T(X_0, X_1, X_2, \cdots) = (X_1, X_2, \cdots)$$

The Bernoulli measure, defined above, is translation-invariant; that is, given any cylinder set $$\sigma\in\mathcal{B}$$, one has
 * $$P(T^{-1}(\sigma))=P(\sigma)$$

and thus the Bernoulli measure is a Haar measure; it is an invariant measure on the product space.

Instead of the probability measure $$P:\mathcal{B}\to\mathbb{R}$$, consider instead some arbitrary function $$f:\mathcal{B}\to\mathbb{R}$$. The pushforward
 * $$f\circ T^{-1}$$

defined by $$\left(f\circ T^{-1}\right)(\sigma) = f(T^{-1}(\sigma))$$ is again some function $$\mathcal{B}\to\mathbb{R}.$$ Thus, the map $$T$$ induces another map $$\mathcal{L}_T$$ on the space of all functions $$\mathcal{B}\to\mathbb{R}.$$ That is, given some $$f:\mathcal{B}\to\mathbb{R}$$, one defines
 * $$\mathcal{L}_T f = f \circ T^{-1}$$

The map $$\mathcal{L}_T$$ is a linear operator, as (obviously) one has $$\mathcal{L}_T(f+g)= \mathcal{L}_T(f) + \mathcal{L}_T(g)$$ and $$\mathcal{L}_T(af)= a\mathcal{L}_T(f)$$ for functions $$f,g$$ and constant $$a$$. This linear operator is called the transfer operator or the Ruelle–Frobenius–Perron operator. This operator has a spectrum, that is, a collection of eigenfunctions and corresponding eigenvalues. The largest eigenvalue is the Frobenius–Perron eigenvalue, and in this case, it is 1. The associated eigenvector is the invariant measure: in this case, it is the Bernoulli measure. That is, $$\mathcal{L}_T(P)= P.$$

If one restricts $$\mathcal{L}_T$$ to act on polynomials, then the eigenfunctions are (curiously) the Bernoulli polynomials! This coincidence of naming was presumably not known to Bernoulli.

The 2x mod 1 map
[[Image:Exampleergodicmap.svg|thumb|The map T : [0,1) → [0,1), $$x \mapsto 2x \bmod 1$$ preserves the [[Lebesgue measure]].]]

The above can be made more precise. Given an infinite string of binary digits $$b_0, b_1, \cdots$$ write
 * $$y=\sum_{n=0}^\infty \frac{b_n}{2^{n+1}}.$$

The resulting $$y$$ is a real number in the unit interval $$0\le y\le 1.$$ The shift $$T$$ induces a homomorphism, also called $$T$$, on the unit interval. Since $$T(b_0, b_1, b_2, \cdots) = (b_1, b_2, \cdots),$$ one can see that $$T(y)=2y\bmod 1.$$ This map is called the dyadic transformation; for the doubly-infinite sequence of bits $$\Omega=2^\mathbb{Z},$$ the induced homomorphism is the Baker's map.

Consider now the space of functions in $$y$$. Given some $$f(y)$$ one can find that
 * $$\left[\mathcal{L}_T f\right](y) = \frac{1}{2}f\left(\frac{y}{2}\right)+\frac{1}{2}f\left(\frac{y+1}{2}\right)$$

Restricting the action of the operator $$\mathcal{L}_T$$ to functions that are on polynomials, one finds that it has a discrete spectrum given by
 * $$\mathcal{L}_T B_n= 2^{-n}B_n$$

where the $$B_n$$ are the Bernoulli polynomials. Indeed, the Bernoulli polynomials obey the identity
 * $$\frac{1}{2}B_n\left(\frac{y}{2}\right)+\frac{1}{2}B_n\left(\frac{y+1}{2}\right) = 2^{-n}B_n(y)$$

The Cantor set
Note that the sum
 * $$y=\sum_{n=0}^\infty \frac{b_n}{3^{n+1}}$$

gives the Cantor function, as conventionally defined. This is one reason why the set $$\{H,T\}^\mathbb{N}$$ is sometimes called the Cantor set.

Odometer
Another way to create a dynamical system is to define an odometer. Informally, this is exactly what it sounds like: just "add one" to the first position, and let the odometer "roll over" by using carry bits as the odometer rolls over. This is nothing more than base-two addition on the set of infinite strings. Since addition forms a group (mathematics), and the Bernoulli process was already given a topology, above, this provides a simple example of a topological group.

In this case, the transformation $$T$$ is given by
 * $$T\left(1,\dots,1,0,X_{k+1},X_{k+2},\dots\right) = \left(0,\dots,0,1,X_{k+1},X_{k+2},\dots \right).$$

It leaves the Bernoulli measure invariant only for the special case of $$p=1/2$$ (the "fair coin"); otherwise not. Thus, $$T$$ is a measure preserving dynamical system in this case, otherwise, it is merely a conservative system.

Bernoulli sequence
The term Bernoulli sequence is often used informally to refer to a realization of a Bernoulli process. However, the term has an entirely different formal definition as given below.

Suppose a Bernoulli process formally defined as a single random variable (see preceding section). For every infinite sequence x of coin flips, there is a sequence of integers

 * $$\mathbb{Z}^x = \{n\in \mathbb{Z} : X_n(x) = 1 \} \, $$

called the Bernoulli sequence associated with the Bernoulli process. For example, if x represents a sequence of coin flips, then the associated Bernoulli sequence is the list of natural numbers or time-points for which the coin toss outcome is heads.

So defined, a Bernoulli sequence $$\mathbb{Z}^x$$ is also a random subset of the index set, the natural numbers $$\mathbb{N}$$.

Almost all Bernoulli sequences $$\mathbb{Z}^x$$ are ergodic sequences.

Randomness extraction
From any Bernoulli process one may derive a Bernoulli process with p = 1/2 by the von Neumann extractor, the earliest randomness extractor, which actually extracts uniform randomness.

Basic von Neumann extractor
Represent the observed process as a sequence of zeroes and ones, or bits, and group that input stream in non-overlapping pairs of successive bits, such as (11)(00)(10)... . Then for each pair,
 * if the bits are equal, discard;
 * if the bits are not equal, output the first bit.

This table summarizes the computation. For example, an input stream of eight bits 10011011 would by grouped into pairs as (10)(01)(10)(11). Then, according to the table above, these pairs are translated into the output of the procedure: (1)(0)(1) (=101).

In the output stream 0 and 1 are equally likely, as 10 and 01 are equally likely in the original, both having probability p(1−p) = (1−p)p. This extraction of uniform randomness does not require the input trials to be independent, only uncorrelated. More generally, it works for any exchangeable sequence of bits: all sequences that are finite rearrangements are equally likely.

The von Neumann extractor uses two input bits to produce either zero or one output bits, so the output is shorter than the input by a factor of at least 2. On average the computation discards proportion p2 + (1 − p)2 of the input pairs(00 and 11), which is near one when p is near zero or one, and is minimized at 1/4 when p = 1/2 for the original process (in which case the output stream is 1/4 the length of the input stream on average).

Von Neumann (classical) main operation pseudocode:

Iterated von Neumann extractor
This decrease in efficiency, or waste of randomness present in the input stream, can be mitigated by iterating the algorithm over the input data. This way the output can be made to be "arbitrarily close to the entropy bound".

The iterated version of the von Neumann algorithm, also known as advanced multi-level strategy (AMLS), was introduced by Yuval Peres in 1992. It works recursively, recycling "wasted randomness" from two sources: the sequence of discard-non-discard, and the values of discarded pairs (0 for 00, and 1 for 11). It relies on the fact that, given the sequence already generated, both of those sources are still exchangeable sequences of bits, and thus eligible for another round of extraction. While such generation of additional sequences can be iterated infinitely to extract all available entropy, an infinite amount of computational resources is required, therefore the number of iterations is typically fixed to a low value – this value either fixed in advance, or calculated at runtime.

More concretely, on an input sequence, the algorithm consumes the input bits in pairs, generating output together with two new sequences:

(If the length of the input is odd, the last bit is completely discarded.) Then the algorithm is applied recursively to each of the two new sequences, until the input is empty.

Example: The input stream from above, 10011011, is processed this way:

From the step of 1 on, the input becomes the new sequence1 of the last step to move on in this process. The output is therefore (101)(1)(0) (=10110), so that from the eight bits of input five bits of output were generated, as opposed to three bits through the basic algorithm above. The constant output of exactly 2 bits per round (compared with a variable 0 to 1 bits in classical VN) also allows for constant-time implementations which are resistant to timing attacks.

Von Neumann–Peres (iterated) main operation pseudocode: Another tweak was presented in 2016, based on the observation that the Sequence2 channel doesn't provide much throughput, and a hardware implementation with a finite number of levels can benefit from discarding it earlier in exchange for processing more levels of Sequence1.

title: Bernoulli process


text:
Lagardère Group

Lagardère S.A., Co., Ltd. is an international group with operations in over 40 countries. Based in the 16th arrondissement of Paris, the group was founded and created in 1992 by Jean-Luc Lagardère under the name Matra, Hachette & Lagardère.

Headed by Arnaud Lagardère, it is focused around two priority divisions: Lagardère Publishing and Lagardère Travel Retail. While its book and e-publishing division (Lagardère Publishing) includes the major imprint Hachette Livre, its Travel Retail unit includes store retail, largely in airports and railway stations.

The group's business scope also comprises other activities, mainly including Lagardère News (Paris Match, Le Journal du Dimanche, Europe 1, Europe 2, RFM and the Elle brand licence), Lagardère Live Entertainment (production of concerts and shows and venue management) and Lagardère Paris Racing (sports club).

On November 21, 2023, Vivendi completed the purchase of a majority stake (60%) in Lagardère.

Hachette and Matra, the foundation of Lagardère
The starting point for what would become the Lagardère Group was Louis Hachette's acquisition of Parisian bookstore Brédif in 1826. Hachette published magazines dedicated to public entertainment (Le Journal pour Tous ["Everyone's Newspaper"], 1855) and also took part in publishing the Dictionnaire de la Langue française ("Dictionary of the French Language") with his friend Littré, starting in 1863. In 1953, Hachette launched Le Livre de Poche with Henri Filipacchi.

Created in 1945, Matra (Mechanics/Aviation/Traction) was the company behind several technological projects, including creating a twin-engine aeroplane prototype able to travel at 800 km/h and breaking the sound barrier at Mach 1.4 in vertical flight for the first time in Europe. In 1990, Matra Espace and the aerospace division of Gec Marconi came together to create Matra Marconi Space. Matra Hautes Technologies joined the aerospace industry and officially became Aerospatiale Matra on June 11, 1999. EADS, or the European Aeronautic Defence and Space Company, later Airbus, was founded on July 10, 2000, from the merger of Aérospatiale Matra SA, Aeronautics SA, and DaimlerChrysler Aerospace AG. It officially launched the A380 program that same year. The aircraft would make its first flight in 2005.

Jean-Luc Lagardère and the birth of the group
In 1963, Jean-Luc Lagardère was appointed Chief Executive Officer of Matra, with 1,450 employees. In 1981, he became head of Hachette. In 1988, the group acquired Grolier Encyclopedias in the USA, its first overseas acquisition. In 1992, after a major year-long restructuring, Matra Hachette and Lagardère group were created. In 1990, Jean-Luc Lagardère turned to television and became head of La Cinq, which had been suffering from financial problems since it began operations in 1986. The network's financial problems would worsen after Lagardère took control, and La Cinq ultimately ceased operations on 12 April 1992 (it would be replaced by France 5 in late 1994).

Arnaud Lagardère and the group's refocus on media
In 1994, Hachette Livre launched the first multimedia encyclopedia, Axis. Also in 1994, Matra Hachette Multimedia presented EPSIS, the first image-substitution process for advertising. In 1998, Hachette Multimedia was born of the consolidation of the multimedia division of Hachette Livre and Grolier Interactive (online educational services). A strategic agreement signed in 2000 by Lagardère and Deutsche Telekom to provide Internet service led to the merger of T-Online and Club-Internet.

In 1995, Hachette acquired UCS, Canada's leading newsstand chain, and became the third largest operator in the international retail press trade. In 1996, Hachette Livre acquired the Hatier Group. In 1997, Hachette Livre won a string of literary prizes, including the Prix Goncourt and the Prix de l'Académie française with La Bataille (The Battle) by Patrick Rambaud (Grasset). That same year, Europe 1 and Club-Internet launched Europe Info. In 2000, Hachette Distribution Services created Relay, an international brand specializing in selling media products at public points of sale. That same year, Lagardère and Canal+ got into digital television. In 2001, Lagardère acquired the Virgin Stores brand and Virgin Megastore in France. Hachette Filipacchi Médias has continued its growth by taking a 42% stake in the Marie-Claire Group.

From a conglomerate to a media-diversified group
With the death of Jean-Luc Lagardère on March 14, 2003, Arnaud Lagardère was appointed General Partner of Lagardère SCA. That same year, Lagardère sold off its interest in Renault as well as its automotive engineering business. In 2004, the Group acquired Vivendi Universal Publishing. After antitrust review, Lagardère kept 40% of the company, including the imprints Larousse, Dalloz, Dunod, Nathan, Armand Colin and Sedes, as well as the Spanish division Grupo Anaya. The remainder was sold in 2004 under the name of Editis. Lagardère took advantage of the growth of TNT to launch the youth channel Gulli in partnership with France Télévisions.

In 2006, Arnaud Lagardère created Lagardère Sports, a new subsidiary of the Group specializing in sports economics and sporting rights. Lagardère also became the new franchisee of the Croix-Catelan (Bois de Boulogne, Paris) and the Rue Eblé sports and recreation sites, for a twenty-year period. On May 31, 2010, Lagardère Sports changed its name and became Lagardère Unlimited, a new branch of the group specializing in the sport industry and entertainment.

On July 8, 2015, Lagardère Services was renamed Lagardère Travel Retail. On September 15 of that year, agencies of the Lagardère Group announced that they were being renamed under a common corporate brand: Lagardère Sports and Entertainment. This new brand would replace the brand of Lagardère Unlimited as one of the four divisions of the Lagardère Group. In addition, all sports marketing agencies within this division, including Sportfive, World Sport Group, IEC in Sports, Sports Marketing and Management and Lagardère Unlimited Inc., would be unified under a single commercial brand, Lagardère Sports, with all entertainment businesses under the brand Lagardère Live Entertainment.

2010 shareholders meeting
Seventeen years after the creation of the limited partnership disputed by an American activist, the SCA (the French limited partnership with shares) was confirmed by nearly 80% of shareholders at the Shareholders Meeting on April 27, 2010.

Agreement between Lagardère SCA and Hearst Corporation
On March 28, 2011, Lagardère SCA signed a contract to sell its international magazine business, totaling 102 titles, to Hearst Corporation for €651 million. The transaction included a Master License Agreement (MLA) relating to the ELLE trademark in the 15 countries affected by the transfer, in return for which the Group would receive an annual recurring royalty payment. Lagardère would retain complete ownership of its magazine business operations in France and of its ELLE trademark throughout the world. The closing of the transaction remained subject to approval by local partners in certain countries as well as to certain customary governmental approvals and antitrust clearances in certain jurisdictions.

Sale of endurance sports division to WTC
In January 2016, Lagardère sold the endurance sports division to the World Triathlon Corporation. The transaction included the ITU World Triathlon Series races in Hamburg, Abu Dhabi, Kapstadt, Leeds and Stockholm; other running events like the Hamburg-Marathon, Hawkes Bay International Marathon, Marathon de Bordeaux, Queenstown Marathon and The Music Runs; and cycling events like the Cyclassics Hamburg, Velothon Berlin, Velothon Wales, Velothon Copenhagen, Velothon Stockholm and Velothon Stuttgart.

Sale of most of the media assets and sports agency
Since the first half of 2018, a plan to sell the Group's media assets (excluding Paris Match, Le Journal du Dimanche, Europe 1, Europe 2, RFM and the Elle brand licence) was underway at Lagardère Active. The Group had already divested a large number of assets, including international radio operations, the main digital assets (including e-Health), and the interest in Marie Claire. In 2019, Lagardère finalised the sale of most of the magazine publishing titles in France, the TV businesses, the stake in Mezzo and Disney Hachette Presse.

The Lagardère group finalized the sale of 75% of Lagardère Sports (excluding Lagardère Live Entertainment) to Hamburg-based private equity firm H.I.G. Capital on April 22, 2020.

In May 2020, the Group resisted a demand for the replacement of most of the board members, submitted by Amber Capital, its new largest shareholder. In August, peer French media conglomerate Vivendi raised its stake in the Group to 23.5%, the highest among all shareholders, including Amber (which raised its own by 2% to 20%). It made a pact with the fund in which the two jointly requested four seats, three for Amber and one for Vivendi, on the board.

In November 2020, Lagardère Studios their entertainment television division of Lagardère Activie was sold to French-based media production and distribution company Mediawan. In July 2021, Lagardère Sports was fully divested by the sale of remaining 25% to H.I.G. Capital.

Recent acquisitions
Lagardère Publishing acquired Perseus Books (2016), Bookouture (2017), La Plage (2018), Worthy Publishing Group (2018), Gigamic (2019), Blackrock Games (2019), Short Books (2019), Laurence King Publishing (2020), Workman Publishing (2021) and Welbeck Publishing (2022). Lagardère Travel Retail completed the acquisitions of Paradies (2015), Hojeij Branded Foods (2018), International Duty Free (2019), Creative Table Holdings Ltd (2022), Marché International AG (2022) and Tastes on the Fly (2023).

Self censorship
In 2022 the Financial Times reported that the Lagardère Group's Octopus Books had censored references in books to issues seen as sensitive in China, including information about Taiwan. One book had an entire section about Taiwan cut. The censorship was implemented to allow Octopus to continue to use low cost Chinese book printers.

Management
Until 30 June 2021, the management structure of Lagardère reflects its status as a société en commandite par actions (partnership limited by shares): the firm is led by general and managing partner Arnaud Lagardère, who heads an executive committee comprising two co-managing partners (Pierre Leroy and Thierry Funck-Brentano), spokesperson and chief of external relations Ramzi Khiroun and chief financial officer Sophie Stabile.

Since the conversion of the company into a joint-stock company with a board of directors on 30 June 2021, Arnaud Lagardère was appointed as chairman and chief executive officer and Pierre Leroy as deputy chief executive officer.

Each of the company's two main divisions has its own chairman and CEO, with Lagardère Publishing led by Pierre Leroy and Lagardère Travel Retail by Dag Rasmussen.

The company is overseen by a board of directors, which has been chaired by Arnaud Lagardère since July 2021. Its other members are Virginie Banet, Valérie Bernis, Laura Carrere, Fatima Fikree, Marie Flavion (director representing employees), Pascal Jouen (director representing employees), Arnaud Lagardère, Véronique Morali, Arnaud de Puyfontaine, René Ricol, Nicolas Sarkozy and Pierre Leroy (board advisor).

Lagardère Publishing
Lagardère Publishing is the world's third-largest trade book publisher for the general public and educational markets, operating under the Hachette Livre imprint. The division is a federation of publishing houses which specialise in education, general literature, illustrated books, part works, dictionaries, youth works, book distribution, etc.

Lagardère Publishing creates 17,000 original publications each year and operates predominantly in the three main language groups: English, French and Spanish.

The division also invested in leisure activities adjacent to the world of publishing with the acquisition of companies specialised in mobile games (Neon Play and Brainbow in 2016), board games (Gigamic and Blackrock Games in 2019, La Boîte de Jeu in 2022) and premium stationery (Paperblanks in 2022).

Lagardère Travel Retail
Lagardère Travel Retail is involved in Travel Retail (Travel Essentials, Duty Free & Fashion, and Foodservice). Aelia is a subsidiary of Lagardère that manages 270 duty-free shops in France, the United Kingdom, Poland, Ireland and Spain. In 2013, Aelia had sales of over €1,100 million.

At the end of 2013, Lagardère acquired the Dutch company Gerzon, including Gerzon Schiphol, Gerzon Duty Free and Gerzon Import. Gerzon has a long term concession for Fashion, Leather & Travel and has stores at Amsterdam Schiphol Airport, among them Hermes, Burberry, Victoria's Secret, Ralph Lauren and nine multi brands in Fashion and Leather & Travel. From December 1, 2015, Gerzon would become Lagardère Travel Retail the Netherlands.

In 2015, Lagardère Travel Retail acquired The Paradies Shops in North America, signing the agreement in August and completing the acquisition in October. Paradies and Lagardère Travel Retail in North America combined to become Paradies Lagardère.

In 2018, the division acquired Hojeij Branded Foods (HBF), a food service leader in the travel retail market in North America.

In 2019, Lagardère Travel Retail completed acquisition of International Duty Free (IDF), the travel retail market leader in Belgium, which also has operations in Luxembourg and Kenya.

In November 2022, it was announced Lagardère Travel Retail had acquired the Pfäffikon-headquartered multi-brand international catering company Marché International AG - holding company of Marché Group.

Other activities
Lagardère News: Paris Match, Le Journal du Dimanche, Europe 1, Europe 2, RFM and the Elle brand licence.

Lagardère Live Entertainment: venue operation and management (the Folies Bergère, Casino de Paris, Arkéa Arena, Arena du Pays d'Aix), production of concerts and live shows.

Lagardère Paris Racing: sports club.

Jean-Luc Lagardère Foundation
Since 1989, the Jean-Luc Lagardère Foundation has encouraged and supported creativity and diversity through partnerships in the spheres of culture, solidarity and sport. Each year, the Foundation awards grants to gifted young people with bold, creative projects in the culture and media world.

It has rewarded young film producers like Carole Scotta (founder of Haut et Court movie company), scriptwriters like Phil Ox (who became a producer in France and England), novel writers like Agnes Desarthe, photographers like Emily Buzin and Tiane Doan Na Champassak and journalists like Stephane Edelson (who wrote in 1993 about the economist and banker Muhammad Yunus and the influence of his work on the empowerment of women).

Financial data
(*Excluding non-recurring/non-operating items ) / (**Restated for IFRS 15) / (***Restated for IFRS 16).

Lagardère shares are listed at Euronext Paris.

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

title: Lagardère Group


text:
Bernoulli trial

[[File:Bernoulli_trial_progression.svg|thumb|400px|Graphs of probability P of not observing independent events each of probability p after n Bernoulli trials vs np for various p. Three examples are shown:

Blue curve: Throwing a 6-sided die 6 times gives a 33.5% chance that 6 (or any other given number) never turns up; it can be observed that as n increases, the probability of a 1/n-chance event never appearing after n tries rapidly converges to 0.

Grey curve: To get 50-50 chance of throwing a Yahtzee (5 cubic dice all showing the same number) requires 0.69 × 1296 ~ 898 throws.

Green curve: Drawing a card from a deck of playing cards without jokers 100 (1.92 × 52) times with replacement gives 85.7% chance of drawing the ace of spades at least once.]] In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).

The mathematical formalization and advanced formulation of the Bernoulli trial is known as the Bernoulli process.

Since a Bernoulli trial has only two possible outcomes, it can be framed as a "yes or no" question. For example:

 * Is the top card of a shuffled deck an ace?
 * Was the newborn child a girl? (See human sex ratio.)

Success and failure are in this context labels for the two outcomes, and should not be construed literally or as value judgments. More generally, given any probability space, for any event (set of outcomes), one can define a Bernoulli trial according to whether the event occurred or not (event or complementary event). Examples of Bernoulli trials include:

 * Flipping a coin. In this context, obverse ("heads") conventionally denotes success and reverse ("tails") denotes failure. A fair coin has the probability of success 0.5 by definition. In this case, there are exactly two possible outcomes.
 * Rolling a, where a six is "success" and everything else a "failure". In this case, there are six possible outcomes, and the event is a six; the complementary event "not a six" corresponds to the other five possible outcomes.
 * In conducting a political opinion poll, choosing a voter at random to ascertain whether that voter will vote "yes" in an upcoming referendum.

Definition
Independent repeated trials of an experiment with exactly two possible outcomes are called Bernoulli trials. Call one of the outcomes "success" and the other outcome "failure". Let $$p$$ be the probability of success in a Bernoulli trial, and $$q$$ be the probability of failure. Then the probability of success and the probability of failure sum to one, since these are complementary events: "success" and "failure" are mutually exclusive and exhaustive. Thus, one has the following relations:

p = 1 - q, \quad \quad q = 1 - p, \quad \quad p + q = 1.$$

Alternatively, these can be stated in terms of odds: given probability $$p$$ of success and $$q$$ of failure, the odds for are $$p:q$$ and the odds against are $$q:p.$$ These can also be expressed as numbers, by dividing, yielding the odds for, $$o_f$$, and the odds against, $$o_a$$:

\begin{align} o_f &= p/q = p/(1-p) = (1-q)/q\\ o_a &= q/p = (1-p)/p = q/(1-q). \end{align} $$ These are multiplicative inverses, so they multiply to 1, with the following relations:

o_f = 1/o_a, \quad o_a = 1/o_f, \quad o_f \cdot o_a = 1.$$

In the case that a Bernoulli trial is representing an event from finitely many equally likely outcomes, where $$S$$ of the outcomes are success and $$F$$ of the outcomes are failure, the odds for are $$S:F$$ and the odds against are $$F:S.$$ This yields the following formulas for probability and odds:

\begin{align} p &= S/(S+F)\\ q &= F/(S+F)\\ o_f &= S/F\\ o_a &= F/S. \end{align} $$ Here the odds are computed by dividing the number of outcomes, not the probabilities, but the proportion is the same, since these ratios only differ by multiplying both terms by the same constant factor.

Random variables describing Bernoulli trials are often encoded using the convention that 1 = "success", 0 = "failure".

Closely related to a Bernoulli trial is a binomial experiment, which consists of a fixed number $$n$$ of statistically independent Bernoulli trials, each with a probability of success $$p$$, and counts the number of successes. A random variable corresponding to a binomial experiment is denoted by $$B(n,p)$$, and is said to have a binomial distribution. The probability of exactly $$k$$ successes in the experiment $$B(n,p)$$ is given by:
 * $$P(k)={n \choose k} p^k q^{n-k}$$

where $${n \choose k}$$ is a binomial coefficient.

Bernoulli trials may also lead to negative binomial distributions (which count the number of successes in a series of repeated Bernoulli trials until a specified number of failures are seen), as well as various other distributions.

When multiple Bernoulli trials are performed, each with its own probability of success, these are sometimes referred to as Poisson trials.

Tossing coins
Consider the simple experiment where a fair coin is tossed four times. Find the probability that exactly two of the tosses result in heads.

Solution
For this experiment, let a heads be defined as a success and a tails as a failure. Because the coin is assumed to be fair, the probability of success is $$p = \tfrac{1}{2}$$. Thus, the probability of failure, $$q$$, is given by
 * $$q = 1 - p = 1 - \tfrac{1}{2} = \tfrac{1}{2}$$.

Using the equation above, the probability of exactly two tosses out of four total tosses resulting in a heads is given by:
 * $$\begin{align}

P(2) &= {4 \choose 2} p^{2} q^{4-2} \\ &= 6 \times \left(\tfrac{1}{2}\right)^2 \times \left(\tfrac{1}{2}\right)^2 \\ &= \dfrac {3}{8}. \end{align}$$

Rolling dice
What is probability that when three independent fair six-sided dice are rolled, exactly two yield sixes?

Solution
On one die, the probability of rolling a six, $$p = \tfrac{1}{6}$$. Thus, the probability of not rolling a six, $$q = 1 - p = \tfrac{5}{6}$$.

As above, the probability of exactly two sixes out of three,
 * $$\begin{align}

P(2) &= {3 \choose 2} p^{2} q^{3-2} \\ &= 3 \times \left(\tfrac{1}{6}\right)^2 \times \left(\tfrac{5}{6}\right)^1 \\ &= \dfrac {5}{72} \approx 0.069. \end{align}$$

title: Bernoulli trial


text:
SOGEADE

SOGEADE (Société de gestion de l'aéronautique, de la défense et de l'espace) was a French intermediate holding company. It was dissolved in 2013.

History
SOGEADE was created solely to hold French interests in the newly founded EADS (Airbus), as an intermediate holding company, which were owned by the state of France (through SOGEPA) and Lagardère Group (Désirade). In 2005, SOGEADE had the same shares holding ratio with Daimler AG for 29.9%.

In 2006 Daimler and Lagardère agreed to sell 7.5% shares each to the open public. In 2007 Daimler agreed to sell 7.5% shares of Airbus to Dedalus while Lagardère issued mandatory exchangeable bonds for the 7.5% shares of Airbus to Natixis. In 2013 the French State's portion of ownership was transferred to SOGEPA, while SOGEADE became the wholly owned subsidiary of Lagardère. Soon later Lagardère sold all the shares.

Evolution of shares in EADS

 * 29.9% of EADS at 31 December 2005
 * 29.95% of EADS at 31 March 2007
 * 27.53% of EADS at 31 September 2007
 * 22.50% of EADS at 31 March 2009
 * 22.46% of EADS at 31 December 2009 (183,337,704)
 * 22.46% of EADS at 31 December 2010 (183,337,704)
 * 22.35% of EADS at 31 December 2011 (183,337,704)
 * 22.16% of EADS at 31 December 2012 (183,337,704)
 * 7.4% of Airbus in April 2013 (61,000,000)

Shareholders

 * SOGEPA (0%) (50% at creation, 60% end of 2008, 66.6% in 2009) – Wholly owned by French government
 * Désirade (100%) (50% at creation, 40% end of 2008, 33.3% in 2009) – Wholly owned by Lagardère Group.

title: SOGEADE


text:
SOGEPA

SOGEPA (Societé de Gestion de Participations Aéronautiques) is a French holding company owned completely by the French Republic. It is one of the largest public bodies investing in European aerospace technology, indirectly owning 10.09% shares of Airbus as of 31 September 2023.

It was under supervision of Agence des participations de l'État.

In 2014, SOGEPA became one of the major shareholders of PSA Peugeot Citroën (now Stellantis).

title: SOGEPA


text:
The Memory of Whiteness

The Memory of Whiteness is a science fiction novel written by Kim Stanley Robinson and published in September 1985.

Theme
It shares with the Mars trilogy a focus on human colonization of the Solar System and depicts a grand tour that travels from the outer planets inward toward the Sun, visiting many human colonies along the way. The different human societies on the various planets and planetoids visited are depicted in detail.

Plot summary
The purpose of the tour is to stage concerts by the "Holywelkin Orchestra", a futuristic musical instrument played by a selected master. Readers follow the Orchestra and its entourage together with a journalist, who after some time detects a conspiracy that seems to be connected with a group of gray-clad, sun-worshipping monks. The tour ends near the planet Mercury in a solar station belonging to these "Grays", which controls the white line energy source for the whole Solar System.

Reception
Dave Langford reviewed The Memory of Whiteness for White Dwarf #76, and stated that "this is impressive for its scope and feel of connecting the two cultures: both music and multidimensional physics sound convincing."

Reviews

 * Review by Faren Miller (1985) in Locus, #295 August 1985
 * Review by Stuart Napier (1985) in Fantasy Review, October 1985
 * Review by Don D'Ammassa (1985) in Science Fiction Chronicle, #75 December 1985
 * Review by Doc Kennedy (1985) in Rod Serling's The Twilight Zone Magazine, December 1985
 * Review by Tom Easton (1986) in Analog Science Fiction/Science Fact, January 1986
 * Review by Andrew Andrews (1986) in Science Fiction Review, Spring 1986
 * Review by Algis Budrys (1986) in The Magazine of Fantasy & Science Fiction, February 1986
 * Review by Keith Soltys (1986) in Science Fiction Review, Summer 1986
 * Review by Tom A. Jones (1986) in Vector 132
 * Review by Pascal J. Thomas (1986) inThrust, #24, Summer 1986
 * Review by Ken Lake (1987) in Paperback Inferno, #65
 * Review by Paul Kincaid (1987) in Foundation, #38 Winter 1986/87
 * Review [German] by Norbert Kupper (1988) in Science Fiction Times, April 1988
 * Review by K. V. Bailey (1999) in Vector 206
 * Review? [French] by Claude Ecken (2006) in Galaxies, #39

title: The Memory of Whiteness


text:
Stevens Point, Wisconsin

Stevens Point is a city in and the county seat of Portage County, Wisconsin, United States. Its population was 25,666 as of the 2020 census. It forms the core of the Stevens Point micropolitan statistical area, which had a population of 70,377 in 2020.

The city was incorporated in 1858. Stevens Point is home to the University of Wisconsin–Stevens Point and a campus of Mid-State Technical College.

History
Historically part of the Menominee homelands, a three-mile strip along the Wisconsin River was ceded to the United States in an 1836 treaty. In 1854 the Menominee made its last treaty with the U.S., gathering on a reservation on the Wolf River. In the Menominee language it is called Pasīpahkīhnen which means "It juts out as land" or "point of land".

Stevens Point was named after George Stevens, who operated a grocery and supply business on the Wisconsin River during the extensive logging of interior Wisconsin. The river was used by logging companies to float logs to market. Loggers on the river found this a convenient stopping point, as the river bends slightly and the operation was from far upstream. The town developed from Stevens's post and was named for him.

In 1845, the postal service came to Stevens Point and with this improvement in communications, the population tripled within 20 years.

In 1847, the first plat was laid out of what became the City of Stevens Point, including the Public Square. The town square was originally an area next to the Wisconsin River where professionals, craftsmen, businessmen, and loggers gathered before their river journeys, bringing revenue to the area. As years went by, the area around the town square grew as logging increased.

Most buildings were first built with readily available wood. Many cases of early fires were reported from 1850–1890. Around 1880, buildings began to be built of brick and sandstone.

In 1916, Lyric Theater was built. It was demolished later.

Geography
According to the United States Census Bureau, the city encompasses 18.41 sqmi, including 17.17 sqmi of land 1.24 sqmi of water. The communities of Plover, Whiting and Park Ridge are adjacent to the city. The city's main hydrology includes the Wisconsin River to the west and the Plover River, which joins the Wisconsin from the northeast at a point to the south, and which supplies much of the urban area's water.

2020 census
As of the census of 2020, the population was 25,666. The population density was 1,495.1 PD/sqmi. There were 11,386 housing units at an average density of 663.2 /sqmi. The racial makeup of the city was 85.6% White, 4.8% Asian, 2.7% Black or African American, 0.6% Native American, 1.3% from other races, and 4.9% from two or more races. Ethnically, the population was 4.1% Hispanic or Latino of any race.

The 2020 census population of the city included 40 people incarcerated in adult correctional facilities and 2,595 people in student housing.

According to American Community Survey estimates for 2016-20, the median income for a household in the city was $46,663, and the median income for a family was $73,009. Male full-time workers had a median income of $48,618 versus $32,409 for female workers. The per capita income was $26,127. About 7.0% of families and 19.3% of the population were below the poverty line, including 11.4% of those under 18 and 8.6% of those 65 or older. Of the population 25 and older, 93.4% were high school graduates or higher and 38.1% had a bachelor's degree or higher.

2010 census
As of the 2010 census 26,717 people, 10,598 households, and 4,944 families residing in the city. The population density was 1674.0 PD/sqmi. They occupied 11,220 housing units at an average density of 703.0 /sqmi. The racial makeup of the city was 91.7% White, 0.9% African American, 0.4% Native American, 4.7% Asian, 0.7% from other races, and 1.5% from two or more races. Hispanic or Latino of any race was 2.6% of the population.

Among households, 21.7% had children under the age of 18, 34.9% were married couples living together, 8.5% had a female householder with no husband present, 3.2% had a male householder with no wife present, and 53.3% were non-families. 34.9% of all households were made up of individuals, and 11.2% had someone living alone who was 65 years of age or older. The average household size was 2.21 and the average family size was 2.87.

The median age in the city was 26.5 years. 16% of residents were under the age of 18; 31.3% were between the ages of 18 and 24; 22.3% were from 25 to 44; 18.5% were from 45 to 64; and 12% were 65 years of age or older. The gender makeup of the city was 48.8% male and 51.2% female.

Religion
The mother house of the Sisters of St. Joseph of the Third Order of St. Francis was in Stevens Point. Catholic parishes in the city include Holy Spirit, St. Stephen, St. Casimir, St. Peter, and St. Joseph. Lutheran and other Protestant churches are also present, along with members of the Baháʼí Faith.

A wide variety of Catholic and Protestant churches spread throughout Stevens Point. Many of those churches date back to the early 20th century. Within the past century, other religious groups have made their mark on Stevens Point.

Economy
Major employers in the area include Pixelle Specialty Solutions paper mill, Associated Banc-Corp, Sentry Insurance, Travel Guard (travel and insurance), Donaldson Company, Skyward (software design), Lands' End, Canadian National Railway, Delta Dental of Wisconsin, Worzalla Publishing, Mason Companies (formerly known as Figis), Berkshire Hathaway Travel Protection, Herrschners, and the Stevens Point Brewery.

Companies with corporate headquarters in the city include Sentry Insurance, Ki Mobility, Delta Dental of Wisconsin, and Skyward. Associated Bank, Canadian National, AIG, and the Donaldson Company have regional headquarters in Stevens Point.

Business developments in the area include Crossroads Commons, Portage County Business Park, Venture Drive and Corporate Center, Stevens Point Industrial Park, Eastridge, Parkdale Plazas, Stevens Points East Side and Downtown Stevens Point.

At one time, Midstate Airlines had its headquarters in Stevens Point.

Arts and culture
Stevens Point is home to a community theater group, Central Wisconsin Area Community Theatre (cwACT); a children's museum; and a group of museums run by the Portage County Historical Society, including the Beth Israel Congregation Museum, in the former synagogue. (The synagogue has been defunct since 1985.)

Religion plays a significant role in the community. In 1847, the first recorded religious service was held near the town square with a pastor from Norway. As time went by, more religions joined the town square, and by 1900, Catholic, Lutheran, and Methodist churches and Jewish synagogues were established within one mile of the downtown area.

The Central Wisconsin Symphony Orchestra (CWSO) presents four concerts each season.

Most events happen near the downtown area, many at the town square, which was rebuilt in 2011. These include the annual Riverfront Rendezvous, Corn on the Curb, sculpture park summer celebration, Fourth of July parade, Krazy Days and Gather at the River.

The downtown area was designated a "Wisconsin Main Street Community" and offers specialty shops and restaurants. Buildings in downtown Stevens Point are made from materials including Lake Superior limestone, brick, and red granite. City and county administrative offices are downtown, as are a bank regional headquarters and two insurance companies. Downtown also offers night life on "the Square" that is popular with college students and a farmers' market that has been selling fresh produce for over 100 years. The farmers' market is open early summer through early fall.

Stevens Point hosts the world's largest trivia contest, run by UWSP's radio station, WWSP-FM. The contest, which typically involves over 12,000 contestants on more than 400 teams, is held every year in April and lasts 54 consecutive hours, from Friday to Sunday.

The city was the setting for the first three seasons of the Disney Channel series Liv and Maddie.

Parks and recreation
The area hosts 20 developed parks and a 26 mi bicycle and jogging trail (the Green Circle Trail) that surrounds and winds through the city. The Ice Age National Scenic Trail also runs through the city. An 18-hole Robert Trent Jones, Jr.-designed golf course and country club, SentryWorld, is at the Sentry Insurance Home Office. The Schmeeckle Reserve, a nature reserve, is on the University of Wisconsin–Stevens Point campus. Right outside of Schmeeckle is the Stevens Point Sculpture Park, which displays sculpture by local artists.

The area also has Goerke Park, which includes a football stadium where high school and college athletes compete. An outdoor track is used by the same groups.

The Backwaters Paddle Quest canoe adventure challenge has been held in Stevens Point on the Wisconsin River since 2002, usually during the second week of August. Players paddle their crafts over two days past checkpoints along the river, encountering characters who act out a storyline that continues year to year.

Iverson Park is a recreational park course that lies on the green circle trail and Plover River in Stevens Point. It spans over 100 acres, and contains a swimming area, hiking trails, and canoe and recreation activities rental.

Education

The Stevens Point Area Public School District serves the city, as do the Pacelli Catholic Schools and Point of Discovery School.

Public elementary schools include Bannach, Jefferson School for the Arts, Kennedy, Madison, McDill, McKinley, Roosevelt, Plover-Whiting, and Washington Service-Learning Center. There are two junior high schools, Ben Franklin and P. J. Jacobs, and two high schools, Stevens Point Area Senior High (SPASH) and Charles F. Fernandez Center for Alternative Learning.

Parochial schools include St. Paul Lutheran School (Pre-K–8), St. Joseph Early Childhood Center, St. Stanislaus (K–2) and St. Stephen Elementary (3–5) Schools, St. Peter Middle School, and Pacelli High School.

The city serves as the hub of the Portage County Public Library, which provides educational resources and programming for adults, young adults, and children.

Stevens Point is home to the University of Wisconsin–Stevens Point (UWSP). The university enrolls approximately 7,313 undergraduate and 651 graduate students. Mid-State Technical College (MSTC) is also in the city.

Major highways
Five major roads pass through Stevens Point:

 * Northbound I-39 routes to Wausau. Southbound, it routes to Madison and Bloomington.
 * travels east to Manitowoc and Bay City and west to Fargo.
 * Northbound US 51 routes to Hurley. Southbound, US 51 routes to Baton Rouge, Louisiana.
 * travels east to Green Bay and west to Onalaska.
 * travels east to Rosholt and west to Wisconsin Rapids.

Airport
The city is served by two airports. Commercial service is available through Central Wisconsin Airport (KCWA), midway between Stevens Point and Wausau, in Mosinee. CWA is served by three major airlines. General aviation, charter flights and air cargo operators use the local Stevens Point Municipal Airport (KSTE).

Public transit
Stevens Point Transit system provides public transportation.

Notable people

 * Cole Caufield, NHL player
 * Pat Friday, baseball executive for the Kansas City Athletics
 * Suzy Favor Hamilton, middle distance runner, NCAA champion, 3-time Olympian
 * Sam Hauser, NBA player
 * Joel Hodgson, writer, comedian, and actor; creator of Mystery Science Theater 3000
 * Ian Holland, first class cricketer for Victoria cricket team, and Hampshire County Cricket Club
 * Kathy Kinney, actress and comedian
 * Ben Kissel, former co-host of The Last Podcast on the Left
 * Ross Kolodziej, NFL player and coach
 * Janel McCarville, WNBA player
 * Harry McCurdy, Major League Baseball catcher
 * James Miller, Catholic teacher and missionary
 * Ben Provisor, Olympic wrestler
 * Peggy Rajski, Oscar-winning filmmaker, and activist
 * Ryan Ramczyk, NFL player
 * Rick Reichardt, former MLB player
 * Patrick Rothfuss, author
 * Chris Solinsky, NCAA champion distance runner
 * Garrett Weber-Gale (born 1985), Olympic swimmer
 * Peter Weller, actor, director, and art historian
 * Chet Yorton, professional bodybuilder

Sister cities

 * Gulcz, Greater Poland Voivodeship, Poland
 * Rostov Veliky, Yaroslavl Oblast, Russia

title: Stevens Point, Wisconsin


text:
Viridian design movement

The Viridian Design Movement was an aesthetic movement focused on concepts from bright green environmentalism. The name was chosen to refer to a shade of green that does not quite look natural, indicating that the movement was about innovative design and technology, in contrast with the "leaf green" of traditional environmentalism. The movement tied together environmental design, techno-progressivism, and global citizenship. It was founded in 1998 by Bruce Sterling, a postcyberpunk science fiction author. Sterling always remained the central figure in the movement, with Alex Steffen perhaps the next best-known. Steffen, Jamais Cascio, and Jon Lebkowsky, along with some other frequent contributors to Sterling's Viridian notes, formed the Worldchanging blog. Sterling wrote the introduction to Worldchanging's book (Worldchanging: A Users Guide for the 21st Century), which (according to Ross Robertson) is considered the definitive volume on bright green thinking. Sterling formally closed the Viridian movement in 2008, saying there was no need to continue its work now that bright green environmentalism had emerged.

title: Viridian design movement


text:
Vaux-le-Vicomte

The Château de Vaux-le-Vicomte is a Baroque French château located in Maincy, near Melun, 55 km southeast of Paris in the Seine-et-Marne department of Île-de-France.

Built between 1658 and 1661 for Nicolas Fouquet, Marquis de Belle Île, Viscount of Melun and Vaux, the Superintendent of Finances of Louis XIV, the château was an influential work of architecture in mid-17th-century Europe. At Vaux-le-Vicomte, the architect Louis Le Vau, the landscape architect André Le Nôtre and the painter-decorator Charles Le Brun worked together on a large-scale project for the first time. Their collaboration marked the beginning of the Louis XIV style combining architecture, interior design and landscape design. The garden's pronounced visual axis is an example of this style.

History
Once a small château between the royal residences of Vincennes and Fontainebleau, the estate of Vaux-le-Vicomte was purchased in 1641 by Nicolas Fouquet, an ambitious 26-year-old member of the Parlement of Paris. Fouquet was an avid patron of the arts, attracting many artists with his generosity.

When Fouquet became King Louis XIV's Superintendent of Finances in 1656, he commissioned Le Vau, Le Brun and Le Nôtre to renovate his estate and garden to match his grand ambition. Fouquet's artistic and cultivated personality subsequently brought out the best in the three.

To secure the necessary grounds for the elaborate plans for Vaux-le-Vicomte's garden and castle, Fouquet purchased and demolished three villages. The displaced villagers were then employed in the upkeep and maintenance of the gardens. It was said to have employed 18 thousand workers and cost as much as 16 million livres.

The château and its patron became for a short time a focus for fine feasts, literature and arts. The fabulist and poet Jean de La Fontaine and the playwright Molière were among the artists close to Fouquet. At the inauguration of Vaux-le-Vicomte, a Molière play was performed, along with a dinner event organized by François Vatel and an impressive firework show.

Fête and arrest

The château was lavish, refined and dazzling to behold, but those characteristics proved tragic for its owner: the king had Fouquet arrested shortly after a famous fête that took place on 17 August 1661, where Molière's play 'Les Fâcheux' debuted. The celebration had been too impressive and the superintendent's home too luxurious. Fouquet's intentions were to flatter the king: part of Vaux-le-Vicomte was actually constructed specifically for the king, but Fouquet's plan backfired. Jean-Baptiste Colbert led the king to believe that his minister's magnificence was funded by the misappropriation of public funds. Colbert, who then replaced Fouquet as superintendent of finances, arrested him. Later, Voltaire was to sum up the famous fête: "On 17 August, at six in the evening Fouquet was the King of France: at two in the morning he was nobody." La Fontaine wrote describing the fête and shortly afterwards penned his Elégie aux nymphes de Vaux.

After Fouquet
After Fouquet was arrested and imprisoned for life and his wife exiled, Vaux-le-Vicomte was placed under sequestration. The king seized, confiscated or purchased 120 tapestries, the statues and all the orange trees from Vaux-le-Vicomte. He then sent the team of artists (Le Vau, Le Nôtre and Le Brun) to design what would be a much larger project than Vaux-le-Vicomte, the palace and gardens of Versailles.

Madame Fouquet recovered her property 10 years later and retired there with her eldest son. In 1705, after the death of her husband and son, she decided to put Vaux-le-Vicomte up for sale.

Recent history

Marshal Claude Louis Hector de Villars became the new owner without first seeing the château. In 1764, the Marshal's son sold the estate to the Duke of Praslin, whose descendants maintained the property for over a century. It is sometimes mistakenly reported that the château was the scene of a murder in 1847, when Charles de Choiseul-Praslin killed his wife in her bedroom. He did so at their Paris residence, rather than at Vaux-le-Vicomte.

In 1875, after thirty years of neglect, the estate was sold to in a public auction. "He came for the [Charles] Le Brun paintings, especially those on the ceiling of the Chambre des Muses – he loved art," according to descendant Alexandre de Vogüé. The château was empty, some of the outbuildings had fallen into ruin and the gardens were completely overgrown. Restoration and refurbishment began under the direction of the architect Gabriel-Hippolyte Destailleur, assisted by the landscape architect Elie Lainé. When Sommier died in 1908, the château and the gardens had recovered their original appearance. His son, Edme Sommier, and his daughter-in-law completed the task. His descendants continue to preserve the château, which remains privately owned.

Since 1967, the owner has been Patrice de Vogüé, Alfred Sommier's great-grandson, who received it as a wedding present, with his wife Cristina, the Count and Countess de Vogüé. By that time, the estate contained only a few pieces that had originally been owned by Fouquet. For some time, the family occupied the first floor, and then the refurbished stables, of this largest private château in France with its 1,235 acres of gardens.

In 1968, the property was opened for public tours. A major restoration was completed starting in 1976 and it was continuing in 2017; the roof repair alone took six years. The Baroque ceiling in the Chambre des Muses, "decorated by Charles Le Brun's workshop", was restored in 2016–2017 and was first shown to the public in March 2017. The business is now administered by their three sons: Alexandre, Jean-Charles and Ascanio de Vogüé. "We don’t care about the aristocratic part of this life," said Alexandre de Vogüé, but they are determined to continue the preservation. "We have a ten-year plan, detailing what to do and when; a plan that includes a project of infrastructure restoration, restoration of the garden, and smaller projects; all with anticipated costs next to it. We make this list public for our donors, and people can sponsor a special project, such as restoring a statue in the garden," Alexandre told a reporter in 2017.

Approximately 300,000 visitors arrive each year, 75% of them from France. Recognized by the state as a monument historique, the property is open most of the year, but closed for approximately two months in winter, 6 January to 22 March in 2019, for example. During the Christmas season, major decorations are installed: 150 trees, 10,000 items and 4,000 metres of garlands and lights, as well as a giant illuminated squirrel and angel, in 2018.

Architecture
The château is situated near the northern end of a 1.5-km long north–south axis with the entrance front facing north. Its elevations are perfectly symmetrical to either side of this axis. Somewhat surprisingly the interior plan is also nearly completely symmetrical with few differences between the eastern and western halves. The two rooms in the centre, the entrance vestibule to the north and the oval salon to the south, were originally an open-air loggia, dividing the château into two distinct sections. The interior decoration of these two rooms was therefore more typical of an outdoor setting. Three sets of three arches, those on the entrance front, three more between the vestibule and the salon, and the three leading from the salon to the garden are all aligned and permitted the arriving visitor to see through to the central axis of the garden even before entering the château. The exterior arches could be closed with iron gates and only later were filled in with glass doors and the interior arches with mirrored doors. Since the loggia divided the building into two-halves, there are two symmetrical staircases on either side of it, rather than a single staircase. The rooms in the eastern half of the house were intended for the use of the king, those in the western were for Fouquet. The provision of a suite of rooms for the king was normal practice in aristocratic houses of the time, since the king travelled frequently.

Another surprising feature of the plan is the thickness of the main body of the building (corps de logis), which consists of two rows of rooms running east and west. Traditionally, the middle of the corps de logis of French châteaux consisted of a single row of rooms. Double-thick corps de logis had already been used in hôtels particuliers in Paris, including Le Vau's Hôtel Tambonneau, but Vaux was the first château to incorporate this change. Even more unusual, the main rooms are all on the ground floor rather than the first floor (the traditional piano nobile). This accounts for the lack of a grand staircase or a gallery, standard elements of most contemporary châteaux. Also noteworthy are corridors in the basement and on the first floor, which run the length of house, providing privacy to the rooms they access. Up to the middle of the 17th century, corridors were essentially unknown. Another feature of the plan, the four pavilions, one at each corner of the building, is more conventional.

Vaux-le-Vicomte was originally planned to be constructed in brick and stone, but after the mid-century, as the middle classes began to imitate this style, aristocratic circles began using stone exclusively. Rather late in the design process, Fouquet and Le Vau switched to stone, a decision that may have been influenced by the use of stone at François Mansart's Château de Maisons. The service buildings flanking the large avant-cour to the north of the house remained in brick and stone, and other structures preceding them were in rubble-stone and plaster, a social ranking of building materials that would be common in France for a considerable length of time thereafter.

The main château is constructed entirely on a moated platform, reached via two bridges, both aligned with the central axis and placed on the north and south sides. The moat is a picturesque holdover from medieval fortified residences, and is again a feature that Le Vau may have borrowed from Maisons. The moat at Vaux may also have been inspired by the previous château on the site, which Le Vau's work replaced.

The bridge over the moat on the north side leads from the avant-cour to an ample forecourt, flanked by raised terraces on either side, a layout evoking the cour d'honneur of older aristocratic houses in which the entrance court was enclosed by anterior wings, typically housing kitchens and domestic quarters. Le Vau's terraces even terminate in larger squares suggesting former pavilions. In more modern residences, like Vaux, it had become the custom to put these facilities in the basement, so these structures were no longer needed. This U-shaped plan of the house with the terraces is a device that again recalls Maisons, where Mansart intended "to indicate that his château was conceived in a noble tradition of French design while at the same time emphasizing its modernity in comparison to predecessors."

The entrance front of the main château is characteristically French, with the two lateral pavilions flanking a central avant-corps, again reminiscent of Mansart's work at Maisons. Le Vau supplements these with two additional receding volumes between the pavilions and the central mass. All of these elements are further emphasized with steep pyramidal caps. Such steep roofs were inherited from medieval times and, like brick, were rapidly going out of fashion. Le Vau would never use them again. The overall effect at Vaux, according to Andrew Ayers, is "somewhat disparate and disorderly". Moreover, as David Hanser points out, Le Vau's elevation violates several rules of pure classical architecture. One of the most egregious is the use of two, rather than three, bays in the lateral pavilions, resulting in the uncomfortable placement of the pediments directly over the central pilaster. Ayers does concede however that, "although rather ungainly, the entrance facade at Vaux is nonetheless picturesque, in spite, or perhaps because, of its idiosyncrasies."

The garden front of the main château is considered more successful. The enormous, double-height Grand Salon that substantially protrudes from the corps de logis clearly dominates the southern elevation. The salon is covered by a huge slate dome surmounted with an imposing lantern and is fronted with a two-storey portico that is almost identical to one at the Hôtel Tambonneau. The use of a central oval salon is an innovation adopted by Le Vau from Italy. Although he himself had never been there, he undoubtedly knew from drawings and engravings of examples in buildings, such as the Palazzo Barberini in Rome, and had already used one to great effect at his Château du Raincy. At Le Raincy the salon spans the corps de logis and projects on both sides, but at Vaux, because of the double row of rooms, it is preceded by the vestibule on the entrance side, "thus delaying and dramatizing the visitor's discovery of this, the centrepiece of the house." The lateral pavilions of the garden facade project only slightly but are three bays wide with traditional tall slate roofs like those on the entrance front, effectively balancing the central domed salon.

Gardens

The château rises on an elevated platform in the middle of the woods and marks the border between unequal spaces, each treated in a different way. This effect is more distinctive today, as the woodlands are more mature, than it was in the seventeenth century when the site had been farmland, and the plantations were new.

Le Nôtre's garden was the dominant structure of the great complex, stretching nearly a mile and a half (3 km), with a balanced composition of water basins and canals contained in stone curbs, fountains, gravel walks, and patterned parterres that remains more coherent than the vast display Le Nôtre was to create at Versailles.

The site was naturally well-watered, with two small rivers that met in the park; the canalized bed of one forms the Grand Canal, which leads to a square basin.

Le Nôtre created a magnificent scene to be viewed from the house, using the laws of perspective. Le Nôtre used the natural terrain to his advantage. He placed the canal at the lowest part of the complex, thus hiding it from the main perspectival point of view. Past the canal, the garden ascends a large open lawn and ends with the Hercules column added in the 19th century. Shrubberies provided a picture frame to the garden that also served as a stage for royal fêtes.

Anamorphosis abscondita in the garden

Le Nôtre employed an optical illusion called anamorphosis abscondita (which might be roughly translated as 'hidden distortion') in his garden design in order to establish decelerated perspective. The most apparent change in this manner is of the reflecting pools. They are narrower at the closest point to the viewer (standing at the rear of the château) than at their farthest point; this makes them appear closer to the viewer. From a certain designed viewing point, the distortion designed into the landscape elements produces a particular forced perspective and the eye perceives the elements to be closer than they actually are. That point, for Vaux-le-Vicomte, is at the top of the stairs at the rear of the château. Standing atop the grand staircase, one begins to experience the garden with a magnificent perspectival view. The anamorphosis abscondita creates visual effects, which are not encountered in nature, making the spectacle of gardens designed in this way extremely unusual to the viewer (who experiences a tension between the natural perspective cues in his peripheral vision and the forced perspective of the formal garden). The perspective effects are not readily apparent in photographs, either, making viewing the gardens in person the only way of truly experiencing them.

From the top of the grand staircase, this gives the impression that the entire garden is revealed in one single glance. Initially, the view consists of symmetrical rows of shrubbery, avenues, fountains, statues, flowers and other pieces developed to imitate nature: the elements exemplify the Baroque desire to mold nature to fit its wishes, thus using nature to imitate nature. The centrepiece is a large reflecting pool flanked by grottos holding statues in their many niches. The grand sloping lawn is not visible until one begins to explore the garden, when the viewer is made aware of the optical elements involved and discovers that the garden is much larger than it looks. Next, a circular pool, previously seen as ovular due to foreshortening, is passed and a canal that bisects the site is revealed, as well as a lower level path. As the viewer continues on, the second pool shows itself to be square and the grottos and their niched statues become clearer. However, when one walks towards the grottos, the relationship between the pool and the grottos appears awry. The grottos are actually on a much lower level than the rest of the garden and separated by a wide canal that is over half a mile (almost a kilometre) long. According to Allen Weiss, in Mirrors of Infinity, this optical effect is a result of the use of the tenth theorem of Euclid's Optics, which asserts that "the most distant parts of planes situated below the eye appear to be the most elevated".

In Fouquet's time, interested parties could cross the canal in a boat, but walking around the canal provides a view of the woods that mark what is no longer the garden and shows the distortion of the grottos previously seen as sculptural. Once the canal and grottos have been passed, the large sloping lawn is reached and the garden is viewed from the initial viewpoint's vanishing point, thus completing the circuit as intended by Le Nôtre. From this point, the distortions create the illusion that the gardens are much longer than they actually are. The many discoveries made as one travels through the dynamic garden contrast with the static view of the garden from the château.

Use in film, television and popular culture
The château buildings and grounds have been used in at least 13 productions, a full 70, in fact, according to the owners. For example, the property was used as the California home of the main villain Hugo Drax (played by Michael Lonsdale) in the 1979 James Bond film Moonraker. It can also be seen in the background in the 1998 film The Man in the Iron Mask. In addition, the château appeared in several episodes of The Revolution, which is a documentary television series about the American Revolutionary War that was broadcast by History Channel in 2006. Australia's Next Top Model had a fashion shoot at the château for its 7th Cycle (Episode 02), televised in August 2011. A confused retelling of the Vaux-le-Vicomte story was given by character Little Carmine Lupertazzi in season 4 of HBOs The Sopranos. More recently, it featured as the Palace of Versailles for BBC/Canal+ production of the TV drama series Versailles.

The château is one of the settings of Alexandre Dumas' novel The Vicomte of Bragelonne: Ten Years Later.

The second most expensive wedding was held at the palace in 2004. Vanisha Mittal, daughter of British-Indian steel industrialist billionaire Lakshmi Mittal, held her wedding to Amit Bhatia, a British-Indian economist and businessman, at the château following their engagement ceremony at the Palace of Versailles. Kylie Minogue was paid $330,000 to sing at the wedding and the ceremony was followed by fireworks launched from the Eiffel Tower. According to a report in India Today,"over 35 craftsmen were flown in from Mumbai to erect a mandap on a pond in the sprawling gardens of the estate. Elephants made of fiberglass, minarets and a huge reception hall done up in pink were also put up. A lotus was designed in the pond and petals of all colour and shape scattered over it. Craftsmen were jetted in from India and florists from the Netherlands".

The Château de Vaux-le-Vicomte is the setting of Victoria's Secret first short film, Victoria’s Secret Holiday 2016: A Very Private Affair., featuring Stella Maxwell, Elsa Hosk, Taylor Hill, Romee Strijd, Sara Sampaio, Josephine Skriver and Jasmine Tookes.

title: Vaux-le-Vicomte


text:
Dassault Group

Dassault Group (also GIM Dassault or Groupe Industriel Marcel Dassault SAS) is a French corporate group established in 1929 with the creation of Société des Avions Marcel Bloch (now Dassault Aviation) by Marcel Dassault, later led by his son Serge Dassault, and led since 2018 by co-founder of Dassault Systèmes Charles Edelstenne.

According to Challenges, the Dassault family's combined net worth is estimated at around 23.5 billion euros.

Subsidiaries

 * Dassault Aviation
 * Dassault Falcon Jet
 * Dassault Falcon Service
 * Sogitec (simulation and integrated logistic support systems)
 * Dassault Systèmes (software and PLM development solutions)
 * Société de Véhicules Electriques (SVE), a joint venture between Dassault and Heuliez for the development of electric and plug-in electric hybrid vehicles (Cleanova II based on Renault Kangoo), its president and CEO is Gérard Thery. In 2010, Dow Kokam LLC acquired SVE, though Dassault Group still holds a minor share.
 * Groupe Figaro (media, including Le Figaro and L'Internaute)
 * Immobilière Dassault—an office and residential real estate firm focusing on properties in Paris, all revenues of which are generated in France
 * Artcurial (auctions)
 * Arqana (thoroughbred auctions) (30%)
 * Château Dassault (wine)
 * Veolia
 * SABCA

title: Dassault Group