Perry Rhodan

Perry Rhodan

Perry Rhodan is a German space opera franchise, named after its hero. It commenced in 1961 and has been ongoing for decades, written by an ever-changing team of authors. Having sold approximately two billion copies (in novella format) worldwide (including over one billion in Germany alone), it is the most successful science fiction book series ever written. The first billion of worldwide sales was celebrated in 1986. The series has spun off into comic books, audio dramas, video games and the like. A reboot, Perry Rhodan NEO, was launched in 2011 and began publication in English in April 2021. == Print publication == The series has spun off into many different forms of media, but originated as a serial novella published weekly since 8 September 1961 in the Romanheft (Meaning "Magazine novel") format. These are digest-sized booklets, usually containing 66 pages, the German equivalent of the now-defunct (and generally longer) American pulp magazine. They are published by Pabel-Moewig Verlag, a subsidiary of Bauer Media Group headquartered in Hamburg. As of February 2019, 3000 booklet novels of the original series, 850 spinoff novels of the sister series Atlan and over 400 paperbacks and 200 hardcover editions have been published, totalling over 300,000 pages. == English translation == The first 126 novels (plus five novels of the spinoff series Atlan) were translated into English and published by Ace Books between 1969 and 1978, with the same translations used for the British edition published by Futura Publications which issued only 39 novels. When Ace cancelled its translation of the series, translator Wendayne Ackerman self-published the following 19 novels (under the business name 'Master Publications') and made them available by subscription only. Financial disputes with the German publishers led to the cancellation of the American translation in 1979. An attempt to revive the series in English was made in 1997–1998 by Vector Publications of the US, which published translations of four issues (1800–1803) from the current storyline being published in Germany at the time. The series and its spin-offs have captured a substantial fraction of the original German science fiction output and exert influence on many German writers in the field. == Structure == The series is told in an arc storyline structure. An arc—called a "cycle"—would have anywhere from 25 to 100 issues devoted to it. Similar subsequent cycles are referred to as a "grand-cycle". == History == ‘Perry Rhodan, der Erbe des Universums’ (Eng: ‘The Heir to the Universe’, though the American/British editions instead used the subtitle 'Peacelord of the Universe') was created by German science fiction authors K. H. Scheer and Walter Ernsting and launched in 1961 by German publishing house Arthur Moewig Verlag (now Pabel-Moewig Verlag). Originally planned as a 30 to 50 volume series, it has been published continuously every week since, celebrating the 3000th issue in 2019. Written by an ever-changing team of authors, many of whom, however, remained with the series for decades or life, Perry Rhodan is issued in weekly novella-size installments in the traditional German Heftroman (pulp booklet) format. Unlike most German Heftromane, Perry Rhodan consists not of unconnected novels but is a series with a continuous, increasingly complex plotline, with frequent back references to events. In addition to its original Heftroman form, the series now also appears in hardcovers, paperbacks, e-books, comics and audiobooks. Over the decades there have also been comic strips, numerous collectibles, several encyclopedias, audio plays, inspired music, etc. The series has seen partial translations into several languages. It also spawned the German-Italian-Spanish 1967 movie Mission Stardust, which is widely considered so terrible that many fans of the series pretend it never existed. Coinciding with the 50th-anniversary World Con, on 30 September 2011, a new series named Perry Rhodan Neo began publication, attracting new readers with a reboot of the story, starting in the year 2036 instead of 1971, and a related but independent story-line. On 2 April 2021, light novel and manga publisher J-Novel Club announced Perry Rhodan NEO as a launch title for its new J-Novel Pulp imprint, making this the first ongoing English release of new Perry Rhodan serials in over 20 years. It has become the most popular science fiction book series of all time. == Overview == === Fictional history === The story begins in 1971. During the first human Moon landing by US Space Force Major Perry Rhodan and his crew, they discover a marooned extraterrestrial space ship from the fictional planet Arkon, located in the (real) M13 cluster. Appropriating the Arkonide technology, they proceed to unify Terra and carve out a place for humanity in the galaxy and the cosmos. Two of the accomplishments that enable them to do so are positronic brains and starship drives for near-instantaneous hyperspatial translation. These were directly borrowed from Isaac Asimov's science fiction. As the series progresses, major characters, including the title character, are granted relative immortality. They are immune to age and disease, but not to violent death. The story continues over the course of millennia and includes flashbacks thousands and even millions of years into the past. The scope widens to encompass other galaxies, even more remote regions of space, parallel universes and cosmic structures, time travel, paranormal powers, a variety of aliens ranging from threatening to endearing, and bodiless entities, some of which have godlike powers. === Multiverse === The universe in which the main plot generally takes place is called the Einstein Universe (or "Meekorah"). Its laws are for the most part identical to those of the real universe, as known by late 20th century science. Newer theories about dark matter and dark energy are currently not used in the series. The laws of nature follow old theories that have been disproven, in order to protect series continuity. There are many other universes, each to a greater or lesser extent different from the familiar one, in which, for example one in which time runs slower, an anti-matter universe, a shrinking universe, etc. Each universe possesses its owntimelines, which are for the most part unreachable from each other but may be accessed by special means, thereby itself creating many more parallel timelines. The Einstein Universe is embedded in a high-dimensional manifold, called Hyperspace. This hyperspace consists of several subspaces use for faster-than-light travel by technological means. The exact traits of those higher dimensions are got yhr mode pity unexplained. The border of the universe is a dimension called the deep, once used for construction of the gigantic disc-shaped world Deepland. === Psionic Web and Moral Code === The Psionic Web crosses the whole universe, constantly emitting "vital energy" and "psionic energy", guaranteeing normal (organic among others) life and the wellbeing of higher entities. The Moral Code crosses through all universes, and is linked to the Psionic Web. It is subdivided into the Cosmogenes, which are again subdivided into the Cosmonucleotids. The Cosmonucleotids determine reality and fate for their respective parts of a given universe, via messengers. Higher beings are trying to gain control of this Code to rule reality. The Moral Code itself was not installed by the higher beings, the higher powers by themselves have no clue why or by whom the Code was made. Once the Cosmocrats ordered Perry Rhodan to find the answer to the third ultimate question: "Who initiated the LAW and what does it accomplish?" Perry Rhodan had the chance to receive the answer at the mountain of creation, but refused, as he knew that the answer would destroy his mind. The negative Superintelligence Koltoroc had received the answer to the last ultimate question, 69 million years BC at Negane Mountain, but it is not known if it made any use of the information. === Onion-shell model === An evolutionary schema, similar to the Great Chain of Being, called the "onion-shell model" is employed in relationship to all life. Here, continuous evolution is from lower to higher lifeforms, culminating in bodiless entities. Later in the series, further lifeforms, representing stages between the known shells, were introduced. The main shells are: Lifeless matter Bacteria Higher animals Intelligent species Intelligent species that have contacted other species Superintelligences (SI) Matter sources/ Matter sinks Cosmocrats / Chaotarchs (High Powers) Powers close to the "Horizon of the LAW", the essence of the Multiverse The Superintelligences are the next step above normal minds. They can be born, for example, when a species collectively gives up its bodies and unites their spirits. Such Superintelligences may claim as their domain areas consisting of up to several galaxies (the entity known as "E

Escapex

Escapex, stylized as escapex, was a mobile app developer specializing in white-label fan engagement apps for celebrities. It was founded by Sephi Shapira in 2014 and has raised $18 million in funding. It allows celebrities to reach fans directly, as well as receiving revenue from fans through its freemium model. == Overview == Shapira is Israeli and previously founded Interchan and MassiveImpact. He graduated from Ben-Gurion University of the Negev. The company has raised $18 million in funding. Its 2018 revenue was $5.5 million. In 2016, the company had 57 employees split between Tel Aviv and New York City. The company's General Manager is Joe Cuello, formerly an executive at MTV, then Chief Creative Officer at TuneCore. Their director of social engagement is Rafe Lopresti-Oakes. A press release from the company described the service as having a "proprietary loyalty program" which allows "monetization of social engagement through e-commerce and in-app advertising". App launches typically offered a contest for one fan to meet the celebrity. The app also allows Escapex to collect and monetize user profiles for advertising. The New York Times described the concept of Escapex, musing, "If people love you, why not make money from them?". == Notable apps == The company has created over 350 applications, including: Enrique Iglesias, June 2016 or earlier Akon, June 2016 or earlier Ricky Martin, June 2016 or earlier Rohan Marley and the Bob Marley estate, February 2017 Marc Anthony, March 2017 Prince Royce, March 2017 Jeremy Renner, March 2017, making over $35,000 per month in April 2019 Galen Gering, June 2017 Yandel, June 2017 Greg Vaughan, June 2017 Jason Thompson, June 2017 Niecy Nash, September 2017 Tyler Posey, September 2017 Osric Chau, January 2018 Chris D'Elia Alessandra Ambrosio, making over $35,000 per month in April 2019 Abigail Ratchford, making over $35,000 per month in April 2019 Amber Rose, making over $35,000 per month in April 2019 Dita Von Teese Tommy Chong === Bollywood stars === Escapex has a large roster of Bollywood celebrities, including: Sunny Leone, December 2016 Remo D'Souza, January 2017 Amy Jackson, March 2017 Kajal Aggarwal, March 2017 Nargis Fakhri, April 2017 Disha Patani Sonam Kapoor Salman Khan == Jeremy Renner app == Renner released a mobile app called "Jeremy Renner" (Android) and "Jeremy Renner Official" (iOS) in March 2017. FastCompany wrote extensively about Renner's app in April 2019, calling it "a surprising new kind of social media". The Ringer's Kate Knibbs, explaining how self-referential the app is, summarized it stating "Jeremy Renner’s Jeremy Renner app is the Jeremy Renner of apps." The community developed to include memes, selfies, and a "Happy Rennsday" event on Wednesdays. As early as October 2017 there were claims of censorship, bullying, and "contest-rigging". In September 2019, comedian Stefan Heck wrote about discovering that any replies through the app would appear as if they were sent by Renner himself in push notifications. Heck wrote about notifications making it appear Renner was a big enthusiast of "porno"; other users made it appear Renner was a big fan of Casey Anthony. Renner had to ask Escapex to shut down the app the following day, stating "The app has jumped the shark. Literally." In September 2020, comedian/writer Caroline Goldfarb and actress Sarah Ramos launched The Renner Files podcast, a six-part series investigating the Jeremy Renner app.

Language identification

In natural language processing, language identification or language guessing is the problem of determining which natural language a given content is in. Computational approaches to this problem view it as a special case of text categorization, solved with various statistical methods. == Overview == === Logical approach === A common non-statistical intuitive approach (though highly uncertain) is to look for common letter combinations, or distinctive diacritics or punctuation. === Statistical approach === There are several statistical approaches to language identification. An older statistical method by Grefenstette was based on the frequency of short n-grams, which are often function morphemes. For example, "ing" is more common in English than in French, while the sequence "que" is more common in French. Given a new page found on the Web, one counts the number of occurrences of each such short sequence and picks the language whose frequency table it matches the most. One technique is to compare the compressibility of the text to the compressibility of texts in a set of known languages. This approach is known as mutual information based distance measure. The same technique can also be used to empirically construct family trees of languages which closely correspond to the trees constructed using historical methods. Mutual information based distance measure is essentially equivalent to more conventional model-based methods and is not generally considered to be either novel or better than simpler techniques. Another technique, as described by Cavnar and Trenkle (1994) and Dunning (1994) is to create a language n-gram model from a "training text" for each of the languages. These models can be based on characters (Cavnar and Trenkle) or encoded bytes (Dunning); in the latter, language identification and character encoding detection are integrated. Then, for any piece of text needing to be identified, a similar model is made, and that model is compared to each stored language model. The most likely language is the one with the model that is most similar to the model from the text needing to be identified. This approach can be problematic when the input text is in a language for which there is no model. In that case, the method may return another, "most similar" language as its result. Also problematic for any approach are pieces of input text that are composed of several languages, as is common on the Web. As of 2025, a commonly used baseline method is via the fastText library, which has comparable classification accuracy as deep learning techniques, but much faster. == Identifying similar languages == One of the great bottlenecks of language identification systems is to distinguish between closely related languages. Similar languages like Bulgarian and Macedonian or Indonesian and Malay present significant lexical and structural overlap, making it challenging for systems to discriminate between them. In 2014 the DSL shared task has been organized providing a dataset (Tan et al., 2014) containing 13 different languages (and language varieties) in six language groups: Group A (Bosnian, Croatian, Serbian), Group B (Indonesian, Malaysian), Group C (Czech, Slovak), Group D (Brazilian Portuguese, European Portuguese), Group E (Peninsular Spanish, Argentine Spanish), Group F (American English, British English). The best system reached performance of over 95% results (Goutte et al., 2014). Results of the DSL shared task are described in Zampieri et al. 2014. == Software == Apache OpenNLP includes char n-gram based statistical detector and comes with a model that can distinguish 103 languages Apache Tika contains a language detector for 18 languages

N-jet

An N-jet is the set of (partial) derivatives of a function f ( x ) {\displaystyle f(x)} up to order N. Specifically, in the area of computer vision, the N-jet is usually computed from a scale space representation L {\displaystyle L} of the input image f ( x , y ) {\displaystyle f(x,y)} , and the partial derivatives of L {\displaystyle L} are used as a basis for expressing various types of visual modules. For example, algorithms for tasks such as feature detection, feature classification, stereo matching, tracking and object recognition can be expressed in terms of N-jets computed at one or several scales in scale space.

Semantic interpretation

Semantic interpretation is an important component in dialog systems. It is related to natural language understanding, but mostly it refers to the last stage of understanding. The goal of interpretation is binding the user utterance to concept, or something the system can understand. Typically it is creating a database query based on user utterance.

Software construction

Software construction is the process of creating working software via coding and integration. The process includes unit and integration testing although does not include higher level testing such as system testing. Construction is an aspect of the software development lifecycle and is integrated in the various software development process models with varying focus on construction as an activity separate from other activities. In the waterfall model, a software development effort consists of sequential phases including requirements analysis, design, and planning which are prerequisites for starting construction. In an iterative model such as scrum, evolutionary prototyping, or extreme programming, construction as an activity that occurs concurrently or overlapping other activities. Construction planning may include defining the order in which components are created and integrated, the software quality management processes, and the allocation of tasks to teams and developers. To facilitate project management, numerous construction aspects can be measured; these include the amount of code developed, modified, reused, and destroyed, code complexity, code inspection statistics, faults-fixed and faults-found rates, and effort expended. These measurements can be useful for aspects such as ensuring quality and improving the process. == Activities == Construction includes many activities. === Coding === The following are a few of the key aspects of the coding activity: Naming Choice of name for each identifier. One study showed that the effort required to debug a program is minimized when variable names are between 10 and 16 characters. Logic Organization into statements and routines Highly cohesive routines proved to be less error prone than routines with lower cohesion. A study of 450 routines found that 50 percent of the highly cohesive routines were fault free compared to only 18 percent of routines with low cohesion. Another study of a different 450 routines found that routines with the highest coupling-to-cohesion ratios had 7 times as many errors as those with the lowest coupling-to-cohesion ratios and were 20 times as costly to fix. Although studies showed inconclusive results regarding the correlation between routine sizes and the rate of errors in them, but one study found that routines with fewer than 143 lines of code were 2.4 times less expensive to fix than larger routines. Another study showed that the code needed to be changed least when routines averaged 100 to 150 lines of code. Another study found that structural complexity and amount of data in a routine were correlated with errors regardless of its size. Interfaces between routines are some of the most error-prone areas of a program. One study showed that 39 percent of all errors were errors in communication between routines. Unused parameters are correlated with an increased error rate. In one study, only 17 to 29 percent of routines with more than one unreferenced variable had no errors, compared to 46 percent in routines with no unused variables. The number of parameters of a routine should be 7 at maximum as research has found that people generally cannot keep track of more than about seven chunks of information at once. One experiment showed that designs which access arrays sequentially, rather than randomly, result in fewer variables and fewer variable references. One experiment found that loops-with-exit are more comprehensible than other kinds of loops. Regarding the level of nesting in loops and conditionals, studies have shown that programmers have difficulty comprehending more than three levels of nesting. Control flow complexity has been shown to correlate with low reliability and frequent errors. Modularity Structuring and refactoring the code into classes, packages and other structures. When considering containment, the maximum number of data members in a class shouldn't exceed 7±2. Research has shown that this number is the number of discrete items a person can remember while performing other tasks. When considering inheritance, the number of levels in the inheritance tree should be limited. Deep inheritance trees have been found to be significantly associated with increased fault rates. When considering the number of routines in a class, it should be kept as small as possible. A study on C++ programs has found an association between the number of routines and the number of faults. A study by NASA showed that the putting the code into well-factored classes can double the code reusability compared to the code developed using functional design. Error handling Encoding logic to handle both planned and unplanned errors and exceptions. Resource management Managing computational resource use via exclusion mechanisms and discipline in accessing serially reusable resources, including threads or database locks. Security Prevention of code-level security breaches such as buffer overrun and array index overflow. Optimization Optimization while avoiding premature optimization. Documentation Both embedded in the code as comments and as external documents. === Integration === Integration is about combining separately constructed parts. Concerns include planning the sequence in which components will be integrated, creating scaffolding to support interim versions of the software, determining the degree of testing and quality work performed on components before they are integrated, and determining points in the project at which interim versions are tested. === Testing === Testing can reduce the time between when faulty logic is inserted in the code and when it is detected. In some cases, testing is performed after code has been written, but in test-first programming, test cases are created before code is written. Construction includes at least two forms of testing, often performed by the developer who wrote the code: unit testing and integration testing. === Reuse === Software reuse entails more than creating and using libraries. It requires formalizing the practice of reuse by integrating reuse processes and activities into the software life cycle. The tasks related to reuse in software construction during coding and testing may include: selection of the reusable code, evaluation of code or test re-usability, reporting reuse metrics. === Quality assurance === Techniques for ensuring quality as software is constructed include: Testing One study found that the average defect detection rates of Unit testing and integration testing are 30% and 35% respectively. Software inspection With respect to software inspection, one study found that the average defect detection rate of formal code inspections is 60%. Regarding the cost of finding defects, a study found that code reading detected 80% more faults per hour than testing. Another study shown that it costs six times more to detect design defects by using testing than by using inspections. A study by IBM showed that only 3.5 hours were needed to find a defect through code inspections versus 15–25 hours through testing. Microsoft has found that it takes 3 hours to find and fix a defect by using code inspections and 12 hours to find and fix a defect by using testing. In a 700 thousand lines program, it was reported that code reviews were several times as cost-effective as testing. Studies found that inspections result in 20% - 30% fewer defects per 1000 lines of code than less formal review practices and that they increase productivity by about 20%. Formal inspections will usually take 10% - 15% of the project budget and will reduce overall project cost. Researchers found that having more than 2 - 3 reviewers on a formal inspection doesn't increase the number of defects found, although the results seem to vary depending on the kind of material being inspected. Technical review With respect to technical review, one study found that the average defect detection rates of informal code reviews and desk checking are 25% and 40% respectively. Walkthroughs were found to have a defect detection rate of 20% - 40%, but were found also to be expensive especially when project pressures increase. Code reading was found by NASA to detect 3.3 defects per hour of effort versus 1.8 defects per hour for testing. It also finds 20% - 60% more errors over the life of the project than different kinds of testing. A study of 13 reviews about review meetings, found that 90% of the defects were found in preparation for the review meeting while only around 10% were found during the meeting. Static analysis With respect to Static analysis (IEEE1028), studies have shown that a combination of these techniques needs to be used to achieve a high defect detection rate. Other studies showed that different people tend to find different defects. One study found that the extreme programming practices of pair programming, desk checking, unit testing, integration testing, and regression testing can achieve a 90% defect detection rate. An experiment involving exper

Graph cut optimization

Graph cut optimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut in the theory of flow networks. Thanks to the max-flow min-cut theorem, determining the minimum cut over a graph representing a flow network is equivalent to computing the maximum flow over the network. Given a pseudo-Boolean function f {\displaystyle f} , if it is possible to construct a flow network with positive weights such that each cut C {\displaystyle C} of the network can be mapped to an assignment of variables x {\displaystyle \mathbf {x} } to f {\displaystyle f} (and vice versa), and the cost of C {\displaystyle C} equals f ( x ) {\displaystyle f(\mathbf {x} )} (up to an additive constant) then it is possible to find the global optimum of f {\displaystyle f} in polynomial time by computing a minimum cut of the graph. The mapping between cuts and variable assignments is done by representing each variable with one node in the graph and, given a cut, each variable will have a value of 0 if the corresponding node belongs to the component connected to the source, or 1 if it belong to the component connected to the sink. Not all pseudo-Boolean functions can be represented by a flow network, and in the general case the global optimization problem is NP-hard. There exist sufficient conditions to characterise families of functions that can be optimised through graph cuts, such as submodular quadratic functions. Graph cut optimization can be extended to functions of discrete variables with a finite number of values, that can be approached with iterative algorithms with strong optimality properties, computing one graph cut at each iteration. Graph cut optimization is an important tool for inference over graphical models such as Markov random fields or conditional random fields, and it has applications in computer vision problems such as image segmentation, denoising, registration and stereo matching. == Representability == A pseudo-Boolean function f : { 0 , 1 } n → R {\displaystyle f:\{0,1\}^{n}\to \mathbb {R} } is said to be representable if there exists a graph G = ( V , E ) {\displaystyle G=(V,E)} with non-negative weights and with source and sink nodes s {\displaystyle s} and t {\displaystyle t} respectively, and there exists a set of nodes V 0 = { v 1 , … , v n } ⊂ V − { s , t } {\displaystyle V_{0}=\{v_{1},\dots ,v_{n}\}\subset V-\{s,t\}} such that, for each tuple of values ( x 1 , … , x n ) ∈ { 0 , 1 } n {\displaystyle (x_{1},\dots ,x_{n})\in \{0,1\}^{n}} assigned to the variables, f ( x 1 , … , x n ) {\displaystyle f(x_{1},\dots ,x_{n})} equals (up to a constant) the value of the flow determined by a minimum cut C = ( S , T ) {\displaystyle C=(S,T)} of the graph G {\displaystyle G} such that v i ∈ S {\displaystyle v_{i}\in S} if x i = 0 {\displaystyle x_{i}=0} and v i ∈ T {\displaystyle v_{i}\in T} if x i = 1 {\displaystyle x_{i}=1} . It is possible to classify pseudo-Boolean functions according to their order, determined by the maximum number of variables contributing to each single term. All first order functions, where each term depends upon at most one variable, are always representable. Quadratic functions f ( x ) = w 0 + ∑ i w i ( x i ) + ∑ i < j w i j ( x i , x j ) . {\displaystyle f(\mathbf {x} )=w_{0}+\sum _{i}w_{i}(x_{i})+\sum _{i 0 {\displaystyle p>0} then w i j k ( x i , x j , x k ) = w i j k ( 0 , 0 , 0 ) + p 1 ( x i − 1 ) + p 2 ( x j − 1 ) + p 3 ( x k − 1 ) + p 23 ( x j − 1 ) x k + p 31 x i ( x k − 1 ) + p 12 ( x i − 1 ) x j − p x i x j x k {\displaystyle w_{ijk}(x_{i},x_{j},x_{k})=w_{ijk}(0,0,0)+p_{1}(x_{i}-1)+p_{2}(x_{j}-1)+p_{3}(x_{k}-1)+p_{23}(x_{j}-1)x_{k}+p_{31}x_{i}(x_{k}-1)+p_{12}(x_{i}-1)x_{j}-px_{i}x_{j}x_{k}} with p 1 = w i j k ( 1 , 0 , 1 ) − w i j k ( 0 , 0 , 1 ) p 2 = w i j k ( 1 , 1 , 0 ) − w i j k ( 1 , 0 , 1 ) p 3 = w i j k ( 0 , 1 , 1 ) − w i j k ( 0 , 1 , 0 ) p 23 = w i j k ( 0 , 0 , 1 ) + w i j k ( 0 , 1 , 0 ) − w i j k ( 0 , 0 , 0 ) − w i j k ( 0 , 1 , 1 ) p 31 = w i j k ( 0 , 0 , 1 ) + w i j k ( 1 , 0 , 0 ) − w i j k ( 0 , 0 , 0 ) − w i j k ( 1 , 0 , 1 ) p 12 = w i j k ( 0 , 1 , 0 ) + w i j k ( 1 , 0 , 0 ) − w i j k ( 0 , 0 , 0 ) − w i j k ( 1 , 1 , 0 ) . {\displaystyle {\begin{aligned}p_{1}&=w_{ijk}(1,0,1)-w_{ijk}(0,0,1)\\p_{2}&=w_{ijk}(1,1,0)-w_{ijk}(1,0,1)\\p_{3}&=w_{ijk}(0,1,1)-w_{ijk}(0,1,0)\\p_{23}&=w_{ijk}(0,0,1)+w_{ijk}(0,1,0)-w_{ijk}(0,0,0)-w_{ijk}(0,1,1)\\p_{31}&=w_{ijk}(0,0,1)+w_{ijk}(1,0,0)-w_{ijk}(0,0,0)-w_{ijk}(1,0,1)\\p_{12}&=w_{ijk}(0,1,0)+w_{ijk}(1,0,0)-w_{ijk}(0,0,0)-w_{ijk}(1,1