Learnings from Technological Interventions in a Low Resource Language: A Case-Study on Gondi

The primary obstacle to developing technologies for low-resource languages is the lack of usable data. In this paper, we report the adoption and deployment of 4 technology-driven methods of data collection for Gondi, a low-resource vulnerable language spoken by around 2.3 million tribal people in south and central India. In the process of data collection, we also help in its revival by expanding access to information in Gondi through the creation of linguistic resources that can be used by the community, such as a dictionary, children's stories, an app with Gondi content from multiple sources and an Interactive Voice Response (IVR) based mass awareness platform. At the end of these interventions, we collected a little less than 12,000 translated words and/or sentences and identified more than 650 community members whose help can be solicited for future translation efforts. The larger goal of the project is collecting enough data in Gondi to build and deploy viable language technologies like machine translation and speech to text systems that can help take the language onto the internet.

Introduction
Around 40% of all the languages in the world face the danger of extinction in the near future. Languages are not only a means of communication but also a carrier of tradition and cultures like verbal art, songs, narratives, rituals etc. When a language spoken in a particular community dies out, future generations lose a vital part of the culture that is necessary to completely understand it. This makes language a vulnerable aspect of cultural heritage and hence calls for their preservation. When it comes to saving such endangered languages, there are two aspects: Preservation and Revitalization (also referred to as 'revival linguistics') (Zuckermann, 2013). The former is concerned with how languages can be archived using different linguistic techniques so that it can serve as a lookup for future generations, while the latter focuses on ensuring that the language is resurrected into the daily fabric of people's lives. The biggest success story of a language getting revitalized is Hebrew (Fellman, 1973), which went from few native speakers to several million. Initiatives like SOAS' Endangered Languages Documentation Programme (ELDP) 1 and The Language Conservancy (TLC) project 2 contribute mostly towards the documentation of endangered languages. However, language evolves with culture, and focusing solely on archival efforts misses out on how societies might have evolved differently had their language continued to be in use. In the present day and age of globalization and the integration of technology into almost every aspect of life, native speakers are turning to dominant languages at a faster rate than ever before to provide greater economic and social opportunities to future generations. Any revitalization effort undertaken to-Figure 1: UNESCO 2017 World Atlas day needs to include technological interventions that can comprehensively reverse this degradation. At a bare minimum, these languages need to be integrated with the Internet, which is becoming an ever dominant part of our lives, to ensure their survival and continued usage. We focus our efforts on Gondi, a South-Central Dravidian tribal language spoken by the Gond tribe in Central India. Gondi provides a unique outlook of how a language can be in danger even after having all the ingredients of a sustainable language like (1) long historical continuity (2) a population of 3 million people speaking it and, (3) is widely spoken in around 6 states of India with various dialects and forms. The complexities arise as Gondi is a predominantly spoken language with no single standard variety but a number of dialects, some mutually unintelligible. (Beine, 1994). Deploying technology is a non-trivial task and there are legitimate concerns surrounding how language technologies should be implemented for low-resource languages (Joshi et al., 2019). It is difficult to simply transfer technologies prevalent in high resource language communities to minority communities for many reasons, the chief among them being the lack of data in low-resource languages. Our focus when working with the Gond community is thus centered more around devising novel approaches for data collection, unlike well-resourced languages where the focus is more on engineering. There also needs to be groundwork and identification of the real problems that can be solved by deployment of language technologies in minority communities. (Dearden and Tucker, 2015). Technical systems working in isolation from social contexts can be very dangerous to the ecosystem of these minority language communities and hence aren't ethically neutral exchanges of information. As far as possible, we have ensured that the technology interventions described in this study were led by the Gond community and non-profit organizations with a long history of working with the community. We have a deep appreciation of the fact that the problem we are trying to tackle is different from solving an engineering problem, since the expected outcomes have social rather than technical consequences. In this paper, we deploy 4 technological interventions to help revitalize Gondi. The interventions are designed to achieve two objectives: (1) create a repository of linguistic resources in Gondi, with the intention of eventually using them to build language technologies like machine translation or speech to text systems that are essential for taking Gondi onto the internet; and (2) expand the information available to the Gond community in their language. The first linguistic resource created is a Gondi dictionary that is accessible to the community as an Android app. The second is 230 children's books that were translated by the Gond community in a 10 day workshop. The third is an Android app that serves as a one-stop shop for Gondi content on the internet and also crowdsources translations from the community. The final intervention is a phone number that community members could call to gain awareness about a local election in their area, upon completion of which they earn mobile credits. These interventions respectively resulted in identifying 80-100 community members that participated in creating the 3,500 word dictionary; 20 community members that translated about 8000 sentences from Hindi to Gondi; 7 community members that translated 601 words; and 557 native speakers of Gondi that can be called for future workshops. The goal of the project is working with the Gond community members to collect enough data to build machine translation and speech to text systems that can help take Gondi onto the internet.

Context
According to the 2011 census (Chandramouli and General, 2011), the total population of the Gond tribe is approximately 11.3 million. However, the total Gondi speaking population is only around 2.7 million. That is, only about 25 percent of the entire tribe now speaks it as a first language. UNESCO's Atlas of the Worlds Languages in Danger (Moseley, 2010) lists Gondi as belonging to the vulnerable category. There is an added difficulty of creating resources for Gondi due to the linguistic heterogeneity within As a predominantly oral language, the proportion of Gondi speakers is expected to go down further as opportunities are shrinking to hear the language spoken outside of their everyday surroundings. For example, All India Radio, the only radio station in India allowed to broadcast news, does not have a single Gondi news bulletin in their broadcasts. There is no TV station or channel catering to Gondi speakers. There is also a severe dearth of online content in Gondi, resulting in members of the tribe having to learn a mainstream language in order to enjoy the benefits of internet connectivity. One of the few exceptions to this is "The Wire" 3 , an Indian news outlet that has a news bulletin in Gondi that is published on Youtube. Views of their Gondi news broadcast range from 2,500 to 7,500, although it should be kept in mind that the Gondi spoken in the broadcast caters to the Gond Adivasis from the Central states of India and it is difficult for Gonds from the Southern states to understand the content. Gondi is also not included in the 8 th Schedule of the Indian Constitution, with the result that education and exams for government jobs cannot be administered in the language. The deleterious effects of this on their society are manifold. Gondi is considered the lingua franca of the local insurgents, who use the knowledge of the language and the perceived neglect by the government to recruit candidates from the tribe to join them (Kumar, 2019). Further, there are high dropout rates among children that speak Gondi as a first language. A 2008 UNESCO study found that children whose mother tongue is not the medium of instruction at primary school are more likely to fail in early grades or drop out, which in turn increases the chances of them joining the insurgency (Bühmann and Trudell, 2008). Working with the Gond tribes on reviving their language is thus important not just for cultural reasons, but may also serve as an instrument for bringing peace to their society. Reports from workshop participants attest to the younger generation in the Gond tribe attaching less importance to developing their mother tongue. However, we have also found committed community members determined to revive their language and it proved easy to recruit participants for the 8 workshops we held with the community.

Technological Intervention
There are relatively few cases that provide a holistic view of technology being used to help revive usage of an endangered or vulnerable language. The larger framework our interventions fall under is that language resource creation feeds into building language technologies, which in turn enhances access to information in that language. To give an example of how this framework might operate, ensuring that Gondi is usable and accessible online greatly enhances the access to information. However, building the necessary language technology to take it online requires copious amounts of language data -by one estimate, a minimum of 100,000 translated sentences are required to build a machine translation tool (Koehn and Knowles, 2017), while at least 500 hours of transcribed and translated Gondi audio content is needed for a speech to text interface. (Huang et al., 2014) Our efforts at collecting Gondi language resource creation and enhancing access to information in Gondi can be placed under broadly four buckets:

Gondi Dictionary Development
The Gondi speaking community is spread over 6 states in India. The dominant language in each state has crept into the dialect spoken by the Gond tribe residing there, with the result that it has become difficult for speakers from different parts to understand one another easily. In order to facilitate a democratized process of mutual intelligibility between the Gond groups, CGNet Swara organized seven workshops with Gondi speaking representatives from 6 states to develop a Gondi thesaurus containing all the different words used by speakers from various Gond regions. Some words, such as water, had as many as 8 different words for it. At the 8 th workshop in 2018, which saw more than 80 people in attendance, the thesaurus was developed into a dictionary containing 3,500 words that were understandable by all groups, in essence 'purifying' the language of words that had entered their dialect due to the influence of the dominant state language. This dictionary not only enables translation of key words between Hindi and Gondi, but also understanding between the Gond tribes themselves. 4 To enhance reach, the dictionary was made into an Android app, Gondi Manak Shabdkosh 5 , that allows users to enter a Hindi or Gondi word and immediately hear or read its equivalent translation. This app is in many ways similar to the Ma! Iwaidja dictionary app 6 , except that there is no wheel based interface for conjugation and sentence formation. One of the use cases being explored with this app is in primary education, where tribal students and teachers are sometimes unable to communicate as the teacher does not know Gondi while the student does not know any other language. The hope is that the dictionary app will allow some basic communication and learning to take place. 4 aka.ms/indian-express-gondi-dictionary 5 aka.ms/gondi-dictionary 6 ma-iwaidja-dictionary.soft112.com/

Creating children's books in Gondi
One of the most effective ways of reviving a language is introducing it as a medium of instruction in schools, or at least as a subject. However, creating textbooks in that language is an important first step to achieving this goal. Pratham Books is a non-profit publisher with a motto "Book in every child's hand". Storyweaver 7 is an initative of Pratham Books that hosts more than 15,000 children's stories in various languages and dialects. A 10-day workshop was organized where 20 bilingual Gond tribals from three states of India came together and translated children's books from Hindi to Gondi on the Storyweaver platform. These books were published on Storyweaver's website 8 , resulting in the first ever online repository of children's stories in Gondi. 9 At the end of the workshop, 230 books and about 8000 sentences were translated from Hindi to Gondi. These stories, many of which introduced Gondi children to climate change for the first time, were printed out and distributed in primary schools in the Central Gondi speaking belt of Chhattisgarh. Efforts are now ongoing to convince the state government to include them as part of the school curriculum across the tribal belts of the state. 10

Crowdsourcing Gondi translations
At the Pratham Books translation workshop, it was found that many participants wanted to continue the translation work from home, but there was no avenue for them do so. Taking inspiration from Aikuma (Bird et al., 2014), we developed Adivasi Radio, an Android application that presents users with Hindi words or sentences for which they need to provide the Gondi translation.

Figure 4: Adivasi Radio
In the one month since its launch, there have been a total of 601 appearances translated through the app from 7 unique users. However, 5 of these users are either paid staff or volunteers hoping to become paid staff, indicating that soliciting translations from the community without monetary compensation may be a challenge. Moreover, the bulk of the translations, 493, have come from one superuser. Future translation workshops will include a component on continuing the translation work through the app, with the hope that attendees continue translating even after they return to their village. In addition to the translation role, Adivasi Radio also serves as a one-stop shop for Gondi content on the internet. The translated books from Pratham are accessible through the app, as are the Gondi stories from CGnet Swara. The information on The Wire's Gondi news bulletin are also available here. To ensure these are comprehensible to populations that cannot read or write, a bootstrapped Devanagari text-to-speech system is integrated within the app to read out the written reports in Gondi. As more Gondi content proliferates online, we envisage Adivasi Radio as not only becoming the go-to place for native speakers to find outlets and sites publishing Gondi content, but also the primary medium for collecting the 100,000 sentences needed to build a machine translation tool between Gondi and other mainstream languages.

Disseminating Gondi content
Many recent studies on information dissemination in lowresource settings have relied on technologies, such as Interactive Voice Response (IVR), that could be used with internet-less mobile phones to connect to people and deliver information (Swaminathan et al., 2019;Chakraborty et al., 2019;Marathe et al., 2015;Moitra et al., 2016;Patel et   2013; Vashistha et al., 2015). As an example, Learn2Earn (Swaminathan et al., 2019) is an IVR based system that was used as an awareness campaign tool to spread farmers' land rights in rural India. Learn2Earn awards mobile talktime to users who call a toll-free number and listen to an awareness message, and answer all multiple-choice questions on the message correctly. Further, it has a peerto-peer referral component where an additional recharge is provided for every new user successfully referred to the system. Learn2Earn was successful in spreading land rights awareness to 17,000 farmers in 45 days, starting from an initial set of just 17 farmers (Swaminathan et al., 2019).
In this intervention, we adapted the Learn2Earn technology to spread voter awareness among Gondi speakers in Dantewada (a rural district in the state of Chhattisgarh in India), during the time that a bypoll election was held. We chose to disseminate voter rights messages in Gondi, as the bypoll was crucial for Gondi speakers to establish representative and effective governance in their area. Further, prior work has shown that larger the contexts, identities and communicative functions associated with the language use, the more likely the language is expected to survive. (Walsh, 2005) We believe voter rights content in local language during elections has the potential to encourage conversations on topics of wider contexts and functions. Learn2Earn was previously deployed in Hindi to spread awareness for voting awareness (Kommiya Mothilal et al., 2019). We extrapolated these experiments to Gondi to do that same in preparation for an upcoming bypoll in a Gondi speaking district. Similar to the original Learn2Earn implementation, the experiment started with a few 'seed' users and is intended to spread voluntarily through word of mouth or through peer-referrals thereon, both increasing the chances of language and content spread. Figure 5 shows the number of unique calls that were made to our system and the number of users who passed the awareness quiz over time. Further, the figure shows that a majority of quiz passers came to know about our system organically through word of mouth, though people knew that additional credits can be earned through referrals. Only a very few users continued to use the system even after the elections in The blue and orange bars represent those users who came to know about the system through word of mouth and through referrals, respectively.
September and after the seeding was stopped, probably to earn additional mobile talktime. Table 1 describes important descriptive statistics of our experiment. We were able to spread voter awareness in Gondi to 557 speakers of which a majority (86%) were reached when we actively seeded. Nearly 60% of the users correctly answered all questions, either in their first attempt or in successive attempts, indicating the effectiveness of the system for content dissemination. Further, many users called the system more than once, with one user calling 64 times (to refer someone, users had to place another call to the system). A follow-up survey revealed that 22 of 113 users surveyed could not vote as they did not have a voter ID card, potentially useful information for authorities to increase voter turnout. One disappointing finding was that only about 8.3 percent of users were women, indicating that a focus on outreach towards this community is needed. We see three clear benefits from conducting Learn2Earn pilots in endangered or vulnerable languages. First, since it is entirely in the spoken form, only speakers of the endangered or vulnerable language can comprehend the content and earn the reward. Second, the phone numbers of the 557 users collected are an important dataset of speakers of that language and can be used for future translation workshops and related programs that help their economic and linguistic development. Finally, an oral language has a tendency to die out unless there is an opportunity for that language to be used outside of everyday surroundings, which periodic Learn2Earn campaigns on important issues help achieve.

Preservation Programs
The Endangered Languages Documentation Programme (ELDP) engages in documentation of endangered languages by creating a repository of resources for linguistics, the social sciences, and the language communities themselves. The Language Conservancy is a non-profit organization that strives towards revitalization of the world's endangered languages, restoring them to health and stability, and safeguarding them for future generations. They intend to implement this by introducing it as medium of instruction in schools by developing appropriate teaching methodologies and promoting and supporting the use of such languages beyond this setting -in homes and communities.

Language Revitalization Efforts and Successes
Hebrew is one of the languages which has shown the most promise in revitalization. Not being used since the second century, the usage of language in common conversations was kick-started by some Jewish communities in the 19 th century (Fellman, 1973). It has now risen to become the official language for the state of Israel and is spoken fluently by 7 million people. However, such organic growth is almost impossible when the usage of language at this time is reinforced by many more factors. Ojibwe is an interesting example, where computer-based language learning technology was used and studies were conducted on how a particular multimedia tool might jumpstart communication in the Ojibwe language at home. (Hermes and King, 2013) Additionally, there were efforts where twitter was seeded with many Ojibwe tweets and hashtags to motivate individuals to converse in Ojibwe on twitter.

Deployed Applications and their Effects
Documentation and easy access to it is the first step in reviving a language. The Ma! Iwaidja is a mobile phone app which runs a dictionary of 1500 word and 450 English-Iwaidja translations along with audio for each. In addition, it provides a functionality to add words to the dictionary by the lay user. Due to their ubiquitous nature, crowdsourcing translations through apps are ideal due to their convenience and ease of use. Steven Bird's Aikuma app has leveraged its intuitive design to crowdsource 10 hours of audio or 100,000 words from indigenous communities in Brazil, Nepal and Papua New Guinea. (Bird et al., 2014)

Conclusion
While working with well-resourced languages, the main problem in designing language technologies is engineering.
For low-resource languages, however, the main problem is one of designing methods for data collection upon which the language technology can be built.
To keep community members motivated through the process of collecting the large amounts of translations needed, our team strived to achieve 2 simultaneous goals in each of the four technology interventions: the collection of data upon which language technologies such as speech to text or machine translation can be built, and expanding the access to information in that language, which the community members could point to as a demonstrable success. For example, the Learn2Earn pilot in Gondi not only provided Gond tribals with an opportunity to earn money for answering a quiz in their language and referring others to it, but it also provided a dataset of native Gondi speakers that can be called for future translation workshops. Similarly, translating children's stories and creating a standardized dictionary resulted in both data upon which machine translation tools can be built, and also tangible language resources that can be used by their community. The Chhattisgarh government recently allowed primary education in 10 tribal languages, including Gondi 11 . Our plan is to work with the government in creating new resources in Gondi that can be used in schools and distributing the translated childrens stories through the government apparatus. The larger goal of our research project is integrating Gondi with the internet, which requires at least 100,000 translated sentences; and building a speech to text platform, requiring at least 100 hours of transcribed and translated transcripts. Our most immediate goal is getting more users on the Adivasi Radio app and crowdsourcing translations through it. We plan to make all the data collected openly available and invite other researchers to participate in building language technologies that can benefit the Gond community.

Acknowledgements
We would like to thank Shubhranshu Choudhury from CGnet Swara, William Thies from Microsoft Research New England, Amna Singh from Pratham Books, and the director of IIIT Naya Raipur, Pradeep Kumar Sinha, for their invaluable assistance and advice. A word of thanks to all participants and workshop attendees from the Gond community, without whom this would not have been possible or meaningful. We are also grateful for the financial contributions made by the National Mineral Development Corporation (NMDC), South Eastern Coalfields Limited (SECL), Indira Gandhi National Center for Arts (IGNCA) and Microsoft Research India (MSR) towards supporting this research.


Vibration Analysis of Shaft Misalignment Using Machine Learning Approach under Variable Load Conditions

)e Industry 4.0 revolution is insisting strongly for use of machine learning-based processes and condition monitoring. In this paper, emphasis is given on machine learning-based approach for condition monitoring of shaft misalignment. )is work highlights combined approach of artificial neural network and support vector machine for identification and measure of shaft misalignment. )e measure of misalignment requires more features to be extracted under variable load conditions. Hence, primary objective is to measure misalignment with a minimum number of extracted features. )is is achieved through normalization of vibration signal. An experimental setup is prepared to collect the required vibration signals. )e normalized time domain nonstationary signals are given to discrete wavelet transform for features extraction. )e extracted features such as detailed coefficient is considered for feature selection viz. Skewness, Kurtosis, Max, Min, Root mean square, and Entropy. )e ReliefF algorithm is used to decide best feature on rank basis. )e ratio of maximum energy to Shannon entropy is used in wavelet selection. )e best feature is used to train machine learning algorithm. )e rank-based feature selection has improved classification accuracy of support vector machine. )e result obtained with the combined approach are discussed for different misalignment conditions.

Introduction
All production and processing industries have been using rotary machines on a major scale. In order to ensure hasslefree operating conditions and fewer maintenance costs, it is essential to monitor machine health condition effectively. Eventually, machines get to adhere to the faulty conditions in due course of time due to various inherent causes. It is seen that out of many listed causes, misalignment is one of the prominent causes of fault set up. Hence, to avoid such faults, continuous monitoring is essential. Vishwakarma et al. [1] have discussed different modes of condition monitoring techniques. It emphasizes the importance of both time and frequency domain analysis for nonstationary signals. Tang et al. [2] have proposed an adaptive waveform decomposition method of the waveform to extract timefrequency features of nonstationary signals. e feature extraction for vibration signal of rolling bearing is carried out with the Adaptive Waveform Decomposition (AWD) algorithm and local frequency concept. e Adaptive Neuro Fuzzy Inference System (ANFIS) architecture has been implemented effectively for simulation of nonlinear components in online control systems. e effective implementation of ANFIS has reduced nondimensional errorindex and minimized adjustable parameters very less than other methods such as cascade correlation neural network and backpropagation neural network [3]. Li et al. have explained [4] the importance of online condition monitoring and diagnosis of power equipment. A brief review of a transformer, gas-insulated switchgear, cable, generator, and capacitor are described with the help of big data, Internet of things, and cloud computing techniques. e wavelet gray moment vector approach is claimed as an effective tool in fault diagnosis of rotating machinery [5]. e detailed fault classification method [6] is based on the wavelet packet energy ratio of resampled vibration signals. In comparison of wavelet transform with other methods such as variational mode decomposition and empirical mode decomposition, the evaluation of the upper as well as lower envelops is one of the main steps in calculations. For that reason, the error developed in envelop estimation will spread in the recursive decomposition results [7]. e analysis is carried out at a multilevel energy ratio to extract fault features of the vibration signal. Sohn and Farrar [8] have presented time series analysis for fault source in mechanical systems. A twostage model combined with autoregression and exogenous input technique is used for damage location. Dhumale and Lokhande [9] have presented fault diagnosis of voltage source inverter. e author has used extracted features from normalized current signals effectively to train Artificial Neural Network (ANN). e fault diagnosis system under variable load condition is developed for diagnosis of the voltage source inverter. Wilson Wang has proposed an extended Neuro Fuzzy system for real-time machinery condition monitoring. e developed monitoring system has been validated with experimental results and confirmed adaptability for different fault conditions [10]. Liu and Wang have explained fault diagnosis analysis for low-speed and heavy load slewing bearing. Different options viz. vibration, temperature, oil, stress, etc. are discussed and compared with innovative current analysis [11]. Shao et al. [12] have adopted deep wavelet autoencoder to handle unsupervised feature learning and developed an intelligent fault diagnosis system for rolling bearing. A multiple wavelet autoencoder is used to improve unsupervised feature learning ability. Tonks and Wang [13] have presented a combined approach of Artificial Neural Network (ANN) and Support Vector Machine (SVM) for fault identification in radial distribution systems. e principal component analysis technique is used for data analysis and faults are classified in combination with support vector classifiers. e change in thermometric condition in combination with SCADA system have been effectively used by Tonks and Wang [13] for detection of angular and offset misalignment in wind turbine shaft. e change in a condition of misalignment has been mapped with the changing temperature of the system. In this case, fault isolation is very essential to correlate misalignment with a change in temperature. e effect of torsional longitudinal vibration on aligned condition [14] has been studied through the simple lumped mass model and results are verified experimentally. A required coupling stiffness coefficient for reducing torsional vibration has been discussed. Acoustic emission technique [15] is used over conventional vibration analysis to detect angular misalignment of the shaft. e change in sound condition at support bearing is considered as a source of input. Especially at remote locations, the misalignment present is detected accurately with a combined approach of thermograph, i.e., thermal imaging and vibration analysis.
is is claimed as an effective technique in which elevated positions are considered for measurement such as windmill gearbox [16]. A theoretical analysis of the combined effect of shaft misalignment and unbalance is presented in the first part of the paper. Experimental validation is carried out to support the claims in conclusion [17]. e fuzzy-based controlling of current to avoid nonlinear load drawbacks has been explained. e compensating currents are injected with the help of static current distribution compensator [18]. Singh et al. have explained helical gearbox fault diagnosis using wavelet theory and J48 algorithm. e maximum accuracy in feature extraction is claimed by using SYM8 wavelet [19]. Patra and Bruzzone [20] have explored combined advantage of self-organizing map neural network and support vector machine to select uncertain and diverse samples in image classification. e effective combination of feature selection and feature extraction technique with SVM [21] is used for the prediction of defective software modules. e correlation-based feature selection technique with SVM has been compared with other available techniques to prove accuracy claimed in results. e vibration signal obtained is normalized [22] for effective feature selection. e discrete wavelet transform is applied for suitable feature extraction. e discrete wavelet transform and fuzzy logic have been used in combination to predict shaft misalignment. In the review paper, Hsu and Lin [23] presented compared several methods of SVM and showed sample cases which are one-against-one (OAO) as a best suitable for practical use. e mathematical analysis part of binary and multiclass SVM with an example of disease classification is explained [24].
An integrated approach of data mining and machine learning method is proposed for classification of type of damage condition in wood poles [25]. e advantage of nonlinear mapping of SVM along with enhanced cat swarn optimization is used to predict compressive strength of high performance concrete [26]. e nonlinear behavior of magnetorheological elastomer base isolator is optimized based on artificial neural network and ant colony algorithm [27]. e artificial neural network is proposed for accurate estimation of modulus of elasticity by considering effect of Alkali-Silica reaction in concrete [28].
e statistical methods such as the fuzzy system are much better by formulating rules for handling ambiguity and defining the relationship between input and output. If there is no ambiguity in the information collected and since the data is labeled, there is no need to use fuzzy systems or unsupervised machine learning algorithm such as K-NN [29]. ANN is a nonlinear model that is easy to use and understand as a simple statistical method [30]. Most of the statistical methods are parametric models that require a high background of statistics; ANN is a nonparametric model. It cannot define the relationship between input and output and cannot deal with uncertainty. To overcome this, a number of approaches have been combined with ANN to select features, and so on [31]. Deep learning requires a large amount of data and needs to be trained in complex data models, which can be very expensive. It requires huge datasets to train.
In an overview of the literature study, the feature extraction-based condition monitoring technique is discussed for various faults other than misalignment [1][2][3][4][5][6][7][8]. e various fault analysis technique based on vibration, temperature, stress analysis, and some of these in combination with ANN are considered for fault identification. In many cases of mechanical fault analysis, measurement of fault is essential to understand severity of fault generated. e major of faulty severity is not focused cases such as unbalance, misalignment, and crack analysis [9][10][11][12][13][14][15][16].
ere are different artificial intelligence algorithms for fault classification. e selection depends on the type of problem and size of data available [28][29][30][31]33]. e fault prediction and measure of fault severity, both are essential parts of run time condition monitoring. e present work focuses on the classification and measure of shaft misalignment under variable load conditions using combined approach of ANN and SVM. e normalized vibration signals are used for feature extraction. e suitable mother wavelet is selected on the basis of maximum Energy to Shannon Entropy (ESE) ratio. e ReliefF algorithm is used for best feature selection. e selected best features are used to train SVM for classification of misalignment as well as an input for ANN for measure of misalignment. e suitable structure for ANN is selected out of several trained structures based on the accuracy of prediction. e novelty of proposed Classification and Prediction of Shaft Misalignment (CPSM) is to classify the type of misalignment and to measure misalignment under variable speed conditions with minimum number of features and least data size for training. is is achieved by normalization of vibration signals before feature extraction. e results obtained show that accuracy of SVM and ANN classifier has been improved due to rank-based feature selection.

Methodology
e proposed CPSM is implemented to output signals obtained for healthy and faulty condition, and observations are recorded for all conditions. e outline of test rig used is shown in Figure 1. An accelerometer is placed at the casing of second bearing to sense vibration in all three directions viz. Longitudinal (V g ), Lateral (V t ), and Vertical (V r ). e misalignment is generated artificially in set up to visualize a proportional change in Overall Vibration Level (OVL). e wide range of vibration levels is observed for a different range of misalignment and speed conditions. ese output signals obtained are normalized in the range of 0 to 1. e normalization of the signal maintains distinctive values of extracted features under varying load conditions without loss of information. e normalized signals viz. V gNn , V tNn , and V rNn are obtained from [22] where j is a direction vector which represents g, randt three direction. e output vibration signals are recorded in these directions. e vibration signals are normalized and features such as Detailed coefficient (DC) and Average coefficient (AC) are extracted. Normalization reduces data size in the training of classifier and helps to improve accuracy. e selection of appropriate mother wavelet is carried out on the basis of DC.
e DC and AC are obtained from From equations (2) and (3), h and g are filtered coefficients, p is the number of samples, and u is shifting parameter. e extracted features are used for feature selection viz. Maximum (Max), Minimum (Min), Skewness, Kurtosis, Rms, and Entropy. e selected DC feature is revealed better with change in OVL for different conditions of misalignment. Hence, in CPSM, selection of correct mother wavelet is carried out on the basis of DC.

Experiment Facilities and Instrumentation
In the training of ANN and SVM, a large amount of realtime data with the actual misaligned condition is the foremost important part. It is obtained from the experimental setup. Figure 2 shows a pictorial view of the experimental setup. It comprises a motor, coupling, base plate, and two bearings. e vibration isolation pads at the base of a heavy foundation plate are used to isolate vibration from other sources. In the setup preparation, a major focus is projected on the actual induction of parallel and angular misalignment. e proper directional slot at the base of motor and base plate interface facilitates an easy induction of offset and parallel misalignment for experimental purpose on the artificial mode. It is very important to ensure zero misaligned states of an experimental setup in static conditions before carrying out the experiments. A fixture with special consideration has been prepared to verify zero misalignments. is fixture facilitates the use of the Face and Rim method to serve the purpose of checking alignment conditions. In this, the fixture is clamped on motor side coupling and the dial is simultaneously mounted on the face and rim part of rotor side coupling. e face dial calibrates angular alignment deviation and rim dial calibrates offset alignment deviation simultaneously in reference to motor side coupling. A variable frequency drive (VFD) is used to run setup at different operating speeds. e range of motor speed is closely considered with a standard rated speed of industrial motor selection.
In the implementation of CPSM, two sets of observations are recorded. One with varying speeds and constant misalignment and others with varying misalignment and constant speed. e few samples collected at 1200 rpm for different misalignment conditions are presented in . e variation of OVL with respect to change in misalignment and speed is shown in Figure 6. In order to prevent any unbalance or runout problem, a shaft along with a rotor was tested on a dynamic balancing machine before its assembly. e vibration signals are collected at bearing. An accelerometer (PCB make, Model: 352B70, measurement range: ±49000 m/s 2 , frequency: 0.4 to 20 kHz) is used for sensing vibration signals in three directions. e directional slots are provided at the base plate, which enables to introduce offset and angular misalignment in the setup on artificial mode. e misalignment is introduced with a step of 0.02 mm, i.e., 7.88 mils for the entire range of experiments.
e digital storage oscilloscope (DSO) (Tektronix make TBS 1064, 60 MHz, 4 channels, measurement accuracy: vertical ±3%, from 10 mV/div to 5 V/div) is used to record and store vibration signals obtained from an accelerometer. ese signals are analyzed with Discrete Wavelet Transform (DWT) and further considered as input for processing data with SVM-ANN. e input referred for experimentation is shown in Table 1.

Implementation
In the experimental setup, misalignment is introduced externally to obtain the vibration signal required for analysis. e output vibration signals are recorded in all three directions viz. Longitudinal (V g ), Lateral (V t ), and Vertical   (V r ). For detailed discussion and comparison, a sample vibration signal at 1200 rpm and variation of misalignment in the range 0 to 0.2 mm is considered, as shown in Figure 7.
It is observed that the overall vibration level (OVL) is increased with an increase in the value of misalignment, as compared in Figure 6. e fault which may occur in the rotary machine is confirmed with the particular fault frequency. It clear that the misalignment of the shaft is observed at 1X and 2X frequency harmonics [16,22]. For detailed discussion and comparison, a sample vibration signal at 1200 rpm and variation of misalignment in range 0 to 0.2 mm is considered, as shown in Figure 7. It is essential to understand fault information associated with nonstationary signals. is is possible with multilevel analysis using DWT. DWT is a widely used technique to obtain information in time and frequency domain. e DC feature extracted is compared for various sample condition mentioned in Figure 7. e change in OVL for different misaligned condition has been reflected with corresponding change in DC values. It is compared and depicted in Figure 8. It is observed that few faults are registered at same common frequency as shown in the mechanical fault diagnostic chart [32]. In such cases, DWT assists to identify and isolate uncommon feature of fault.  Shannon entropy are commonly selected features that can be obtained from extracted feature of vibration signals. e required feature extraction of vibration signal is carried out using wavelet transform. Dwt is useful in time and frequency domain, which shows fault existing impulse effectively. Different mother wavelets are examined at different levels to select most suitable wavelet and suitable level based on maximum Energy to Shannon Entropy ratio (ESE), as shown in Table 2.
All mother wavelet considered are compared at different levels of decomposition based on ESE ratio, as shown in Figure 9. It is clearly observed for all considered mother wavelet that energy contained in signal is reduced as the level of signal decomposition increased. erefore, level one is considered, as it contains maximum information for wavelet and feature selection. Different types of mother wavelet viz. Daubechies (DB), Coiflet, Symlet, HARR, DMEY, Biorthogonal, and Reverse Biorthogonal are considered during the analysis while using DWT. e correct level of mother wavelet is decided on the basis of maximum Energy to Shannon Entropy (ESE) ratio. is ratio is maximum at level 1 for all considered wavelet. e average of ESE for each class of fault and for each mother wavelet is plotted and compared in Figure 10. It is clear from Figure 10 that DB2 and SYM2 has higher ESE ratio. As mathematical function of these two wavelets are the same, so any one can be selected. Hence, DB2 mother wavelet at level 1 is selected for analysis.

Multiclass SVM Theory
e SVM is used as a classifier in the present work. e SVM refers to category of supervised learning algorithm in which set of output values are given to learning machine. Let us consider two classes of misalignment to be identified as Q 1 and Q 2 . M is an unknown feature vector to be classified into classes. e classification rule is applied, as shown in equation (4). In this equation, 'i' is the unknown input to be classified: where W T is the orientation of hyperplane and 'a' is position of hyperplane. e classifier is implemented to train the data by finding out the values of W T and a. During training, ensure that the value of W T and a is modified in such a way that P(M 1 ) will come to the positive side of hyperplane. Similarly, modify the value of W T and "a" in such way that P(M 2 ) will come to the negative side of hyperplane. Support Vector Machine (SVM) finds the best position of line. SVM tries to keep the maximum distance between these classes and separating boundaries so that a small noise cannot misclassify the given feature of unknown input.
For every M i , assign class belonging to it. M i , belonging to class Y i , where Y i � ±1, can be written as e generalized equation can be written as equation (6), irrespective of class:  Shock and Vibration Once W and "a" are determined, the unknown vector P can be classified into two classes using equation (4). In SVM, representing maximum margin can be written as where β is margin. e distance of M from the hyperplane is given by By proper scaling, the β parameter can be set to unity. Hence, equation (8) can be written as if M i is not Support Vector.

Shock and Vibration
From equation (8), it can be observed that the margin β can be maximized by minimizing ||W|| and maximizing the bias 'a'. erefore, a function to minimize the weight can be written as Similarly, for support vector, the constraint is obtained by the following equation to minimize the term (1/2Wt · nW). e above constraint optimization problem can be converted into unconstraint optimization using the "Lagrangian Multiplier": where α i is the Lagrangian Multiplier Optimization of equation (11), which can be carried out by taking derivative with respect to 'a' and equating it to zero and equation (12) is obtained: Similarly, Lagrangian Multiplier Optimization can be carried out by differentiating equation (11) w.r.t W, and equation (13) is obtained: e above binary classification is applicable if class labels have only two values (k-class, k < 2). In some cases, it is required to deal with more than two classes in the actual fault diagnosis of the machine. In such a case (k-class, k > 2), Multiclass SVM classifier is used. It can be obtained by combining several binary classifiers. e various methods of obtaining Multiclass SVM are viz. One-against-all (OAA), One-against-one (OAO), and Direct acyclic graph (DAG). e OAO is observed most commonly as the considered method [24]. is method constructs k * (k − 1)/2 classifier, where each one is trained on data from two classes. Let, ith and jth be two classes for training, which can be explained as follows: Minimize: e decision is based on the following rule. If ((w ij ) T ϕ(x t ) + b ij ) says that x is in ith class, then one vote will be added to ith class. If this is not true, then a vote will be added to the jth class. Accordingly largest vote count will decide class for x.  Table 3. For training, the Levenberg-Marquardt algorithm method is used with tan sigmoid activation function. e selection of the best structure depends on the size training data, neurons in input, hidden, and output layer, and the initial weight is assigned to the input signals.

Training of ANN
In the range of 0 to 0.2 mm, 10 conditions of misalignment are considered for different operating speeds up to 2100 rpm, respectively. In the proposed work, for ANN training, 6000 samples are considered, which includes 4500 samples of the misaligned condition and 1500 samples of aligned (healthy) conditions. e samples are considered as 50% of the total for the training of ANN, 25% of the total sample for testing of ANN, and the remaining 25% for crossvalidation of ANN. e Machine Learning Models (MLMs) can guarantee the optimal performance, as it test several models, first with the fundamental ones. Crossvalidation is a method for assessing MLMs by training numerous MLMs on subsets of the accessible input data and assessing them on the complementary subset of the data. Use crossvalidation to detect overfitting, failing to generalize a MLM.
An input layer, hidden layer, and output layer are considered as the main part of the ANN structure. For the proposed ANN structure, it has three inputs. e attainment of accuracy controls the number of hidden layers. Hence, the number of hidden layers is considered a trial and error basis such as 5, 10, 15, 20, and 25. e learning rate during the training of ANN is varied in the range of 0.01 to 0.04. e number of epochs considered is 1800. e different structures considered for training and testing are shown in Table 3. e ANN structure 3-20-11 with learning rate 0.03 is good for MoM in offset misalignment and angular misalignment. e performance of ANN during training is shown in Figure 11. e MSE, is 0.05 which is obtained at 1300 epochs. e MATLAB software is used for training, testing, and validation of ANN. e output error observed in the testing of trained ANN is calculated as below: where E o is expected output and A o is actual output.

Results and Discussion
In the present study of shaft misalignment, the output vibration signals are obtained from the experimental setup. e output signals are normalized to achieve reduction in data size required for training as explained earlier.
e average ESE is more for DB2 and SYM2. e DB2 wavelet is selected as the suitable mother wavelet as explained earlier.
e eighteen statistical features are obtained to analyze information in output signal. e ReliefF algorithm is used to optimize feature selection on rank basis. e sample vibration signal at 1200 rpm for misalignment is considered for presenting key points of analysis. It is clearly seen that all mother wavelet reflect good ESE ratio at level 1.
e explanation in support with fact that disorder, i.e., 8 Shock and Vibration entropy is minimum and information is maximum at the first level of signal decomposition. is is the basis for selection of level 1 for comparison. e rank basis feature optimization is carried out by using ReliefF algorithm. e kurtosis feature is observed as rank 1 feature. erefore, kurtosis features of all   Shock and Vibration 9 signals are obtained using DB2 at level 1.
e kurtosis feature of normalized vibration signals is considered as an input to train ANN and SVM. In the rank-based feature selection, the Kurtosis as a single feature shows efficiency 19.8 %. is efficiency has been improved upto 89.7 % by adopting combination of top eight ranked features, as depicted in Table 4. It is clear that eight topranked features are sufficient to obtain highest efficiency for fine Gaussian SVM classifier referred in this implementation.
In the CPSM approach, SVM and ANN are used for misalignment analysis. SVM classifier is applied to identify the class of misalignment. e misalignment condition which is to be classified has assigned a number as 0, 1, and −1 for healthy condition, offset misalignment, and angular misalignment, respectively. e few samples of output vibration signals are tested with SVM to confirm the output of fault classification, as shown in Table 5. It contains classification results obtained for three conditions related to healthy and misalignment. e sample cases of parallel and angular misalignment for varying load conditions are considered, as shown in Table 6. e output of Multiclass SVM has obtained with good accuracy, as shown in Table 6. e selected kurtosis feature of DC of all normalized vibration signals is taken as input to SVM. e points which has significant effect on improving the accuracy of CPSM are explained. e best part of the CPSM is the normalization of the vibration signal. e correct selection of mother wavelet is on the basis of the ESE ratio. e selection of the correct ANN structure has also contributed to minimizing MSE. e application of ReliefF algorithm for deciding rank of features and selecting top-ranked feature combination in training has also influenced in improving classification accuracy of misalignment.

Conclusion
A combined approach of Support Vector Machine and Artificial Neural Network is implemented successfully to obtain classification and prediction of shaft misalignment. e main contribution of study lies in implementing normalization of signals and ranking of features which is uncommon in problem of misalignment analysis. e selection of proper mother wavelet on the basis of maximum ESE has contributed well in feature selection. e implementation of the classification and prediction of the shaft misalignment method is seen with the least error in output results in misalignment fault classification and MoM. e accuracy of Support Vector Machine is seen to a good level for all conditions viz. healthy, parallel, and angular misalignment. In tested results of trained artificial neural network, a 3-20-11 structure is observed as the best artificial neural network structure for offset and angular measure of misalignment. e use of first eight ranked features has improved classification accuracy. It is observed that the selection of epochs and learning rate has also an effect on minimizing the error. e different samples tested for parallel and angular misalignment have classified successfully with the implementation of support vector machine. e average error observed in the output of the trained artificial neural network is 2.28%. It is concluded that the error in output of classification and prediction of shaft misalignment is within limit due to normalization, correct wavelet selection on the basis of maximum energy to Shannon entropy ratio, and rankbased feature selection using ReliefF algorithm. is approach is helpful in effective real-time condition monitoring of machines. e future scope of this work can be extended for fault prognosis of other faults related with bearing, gears, insufficient lubrication, and unbalance combined with misalignment to ensure effective condition-based maintenance.

Data Availability
Data used in this work can be made available on request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.


extfieldsofstudy: Mathematics Economics

text:
Generalized distance to a simplex and a new geometrical method for portfolio optimization

Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization we determine the portfolio that possesses the minimal risk by using a new geometrical method. For this purpose, we elaborate an algorithm that enables us to compute any generalized Euclidean distance to a standard simplex. With this new approach, we are able to treat the case of portfolio optimization without short-selling in its entirety, and we also recover in geometrical terms the well-known results on portfolio optimization with allowed short-selling. Then, we apply our results in order to determine which convex combination of the CAC 40 stocks possesses the lowest risk: not only we get a very low risk compared to the index, but we also get a return rate that is almost three times better than the one of the index.

1 Introduction and aims of the article

Framework
The paper [M52] published by Harry Markowitz in 1952 completely changed the methods of portfolio management and gave birth to the so-called "Modern Portfolio Theory", thanks to which its author earned the Nobel Prize in Economics in 1990. Since his works and the paper [S63] of Sharpe, this theme centralizes a lot of interest and many developments have been written in this domain. Let us recall some recent and important works to which our article is linked.
In [DJDY08], Jón Daníelsson, Bjørn N. Jorgensen, Casper G. de Vries and Xiaoguang Yang study the portfolio allocation under the probabilistic VaR constraint and obtain remarkable topological results: the set of feasible portfolios is not always connected nor convex, and the number of local optima increases in an exponential way with the number of states. They propose a solution to reduce computational complexity due to this exponential increase.
In [FS12], Claudio Fontana and Martin Schweizer give a simple approach to mean-variance portfolio problems: they change the problems' parametrisation from trading strategies to final positions. In this way they are able to solve many quadratic optimisation problems by using orthogonality techniques in Hilbert spaces and providing explicit formulas.
In their important article [BCGD18], Hanene Ben Salah, Mohamed Chaouch, Ali Gannoun and Christian De Peretti (see also the thesis [B15]) define a new portfolio optimization model in which the risks are measured thanks to conditional variance or semivariance. They use returns prediction obtained by nonparametric univariate methods to make a dynamical portfolio selection and get better performance.
In [PR19], Sarah Perrin and Thierry Roncalli show how four algorithms of optimization (the coordinate descent, the alternating direction method of multipliers, the proximal gradient method and the Dykstra's algorithm) can be used to solve problems of portfolio allocation.
In [BIPS20], Taras Bodnar, Dmytro Ivasiuk, Nestor Parolya and Wolfgang Schmid make an interesting work about the portfolio choice problem for power and logarithmic utilities: they compute the portfolio weights for these utility functions assuming that the portfolio returns follow an approximate log-normal distribution, as suggested in [B00]. It is also noticeable that their optimal portfolios belong to the set of mean-variance feasible portfolios.

Aims and organization of the paper
The three aims of this article are the following: -give a new geometrical algorithm (Algorithm 1) to compute any generalized distance to a simplex, -determine, by making use of this algorithm, a portfolio with minimal variance, -apply this technique to the CAC 40 stocks, and get a portfolio with return rate that is almost three times better than the one of the index.
After having briefly explained the notations in Section 1, we expose in Section 2 the portfolio optimization problem and prove by compactness and con-vexity arguments that it possesses a unique solution. Then, in Section 3, we solve the problem in the case where short-selling is allowed. For this, we recall the classical method, and we give our very simple geometrical method. Section 4 is the heart of the article: in this section, we solve the portfolio optimization problem in the case where short-selling is not allowed. For this purpose, we give a new geometrical algorithm to compute the distance from a point to a standard simplex, which can be used for every Euclidean distance. We can eventually apply this algorithm to the example of the CAC 40 stocks and determine the portfolio with the lowest risk. This portfolio also has the property of being almost three times more efficient than the underlying index. This is done in Section 5.

Notations
We consider n stocks S 1 , S 2 , . . . , S n and denote by X 1 , X 2 , . . . , X n the random variables that represent their return rate (for example, daily, monthly or yearly).
Matrix C is the covariance matrix of X 1 , X 2 , . . . , X n , and X is a random vector.
Definition 1. We call portfolio (with allowed short-selling) every linear com- The return rate of the portfolio is the linear combination R If we don't allow short-selling, then every x i must be nonnegative, and in that case the linear combination is a convex combination. Moreover, The following proposition is immediate.
Proposition 2. The matrix C has the two following properties. In all the following, we assume that C is symmetric definite positive: this is always true in practise.
Let us denote by H the affine hyperplane of R n with equation n j=1 x j = 1, and by K the standard (n − 1)−simplex (also called standard simplex of dimension n − 1), i.e.
The simplex K is a Haussdorff compact subset of R n that is contained in the hyperplane H. For example, if n = 2, H is the line of equation x + y = 1 in the usual plane, and the 1−standard simplex K is the segment [(0, 1), (1, 0)] of this line.

Existence and uniqueness of the solution
Minimizing the variance of the portfolio is equivalent to finding the minimum on K of the quadratic form Let us consider the scalar product (x, y) → x, y := t xCy and the Euclidean norm The aim is to determine the point of K that realizes the minimal distance to K from the origin point in the sense of · . As K is a Haussdorff compact subset, and as f is continuous, we know that this minimum does exist. We will prove that it is also unique. For this, the convexity plays a central role (see for example [R17]).
Proposition 3. The map f is strictly convex.
Proof. For every x, y ∈ R n and for every λ ∈ [0, 1], we have which is nonnegative, as C is positive. Moreover, if x = y, this quantity is positive as C is definite positive.
Proposition 4. Let K be a convex domain and f : K → R a convex map. Then, (ii) if f is strictly convex, then f possesses at most one minimum.
Proof. (i) Let x 0 be a local minimum of f in K. Let us assume by contradiction that it is not global: there exists y ∈ K such that f (y) < f (x 0 ). For every t ∈]0, 1[, let us set y t = ty + (1 − t)x 0 . Then y t belongs to K, and for t small enough, (ii) Let us assume by contradiction that f possesses a least two distinct minima , which is a contradiction to the fact that x 1 is a minimum.
As a consequence of Proposition 4, the quadratic form f possesses exactly one minimum on f , and his minimum is global.

Minimisation of f on H
In this section, we give two methods to compute the portfolio that possesses the lowest risk: the classical one, and our geometrical approach.
Let us denote by E = (e 1 , . . . , e n ) the canonical basis of R n . A basis of the vector hyperplane that directs H is B = (e 1 − e 2 , e 1 − e 3 , . . . , e 1 − e n ). Moreover, x j e j ∈ R n , x belongs to H if and only if n j=1 x j = 1.
Let is denote by u the vector u = n j=1 e j , which is orthogonal to the hyperplane H, and let us set

Minimisation of f on H by the classical method
Here we briefly recall the classical method to compute the portfolio that possesses the lowest risk. Several sources, such as [N09], [M10] and [PP14], provide a clear presentation of these well-known tools.
Proposition 5. The unique solution x 0 that minimises the map f on H is the Proof. According to Lagrange's multipliers theorem, there exists λ ∈ R such that ∇f (x 0 ) = λ∇h(x 0 ). Here we have ∇f (x) = 2Cx and ∇h(x) = u, thus 2Cx 0 = λu, i.e. x 0 = λ 2 C −1 u. As t x 0 u = 1, we get Example 1. For n = 2, the formula is very simple: by setting and

Minimisation of f on H by the geometrical approach
Here we recover the classical results on the portfolio with minimal variance with allowed short-selling by making use of an Euclidean interpretation. This portfolio is P x0 , where x 0 is the orthogonal projection onto H of the origin point.
Let us define the (n, n)−matrix Proposition 6. The unique solution x 0 that minimises f on H is the vector whose coordinates in E are given by the last column of the inverse of matrix A.
Proof. For every x in H, x is the orthogonal projection onto H of the origin point if and only if x is orthogonal to H, that is to say, for every 4 Distance to K from a point of R n In this section, we will solve the problem of portfolio optimization without shortselling, by giving an explicit and calculable solution that doesn't seem to appear in the literature. Let us set Proposition 7. The orthogonal projection of a onto H is the vector whose nonzero coordinates in E are given by Proof. For every x = n j=1 x j e j ∈ R n , x is the orthogonal projection of a onto H if and only if the three following conditions hold (i) for every j ∈ J, x j = 0, n j=1 x j = 1,

4.2
The algorithm for computing the generalized distance to K from a point of R n We now propose a recursive algorithm to compute the point x 0 realizing the distance to K from a point a ∈ R n . In his article [C16], L. Condat gave a new and fast algorithm to project a vector onto a simplex. However, his algorithm was made only for the usual Euclidean distance. Our algorithm can be used for every Euclidean distance. The reader can also have a look at the paper [CY11] about the projection onto a simplex. If K is a 1−simplex (i.e. K has exactly 2 vertices) Return the vertex that is the closest to x Else Determine the hyperface K of K that is the closest to x Compute y the orthogonal projection of x onto H (the affine subspace defined by K ) Apply recursively the algorithm to (y,K ) Proposition 8. Algorithm 1 ends.
Proof. This is straightforward since at each step of the algorithm the dimension of the simplex decreases of one unit.
Lemma 1. If x belongs to H \ K, then the distance from x to K is realized in a point of the frontier of K.
Proof. Let us proceed by contradiction by assuming that the distance from x to K is realized in a point z in • K. Let us denote by y the intersection of the line (x, z) with an hyperface of K crossed by this line. Then, by Minkowski, we get x − z = x − y + y − z > x − y , which is absurd since z realizes the minimal distance from x to K.
As a consequence, if x belongs to H \ K, then the distance from x to K is the distance from x to the hyperface of K that is the closest to x.
Proof. Let us prove by induction on the dimension of K that the algorithm provides us x 0 ∈ K such that d(a, K) = − − → ax 0 . • If K has dimension 1, the result is clear.
• Now assume that the algorithm is correct for every (n − 1)−simplex. Let us consider K a n−simplex (with n ≥ 2), and prove that the algorithm is correct for K. Let x be the orthogonal projection of a onto H.
-If x belongs to K, then x is the solution, and the algorithm is correct.
-If x does not belong to K, as n ≥ 2, we consider the simplex K defined above, the affine subspace H and y the orthogonal projection of x onto H . By induction hypothesis applied to y and the (n − 1)−simplex K , the algorithm provides us x 0 ∈ K such that d(y, K ) = − − → yx 0 . In particular, x 0 belongs to K. Let us now prove that d(a, K) = − − → ax 0 . According to the Pythagorean theorem, as − → ax is orthogonal to H, we have thanks to Lemma 1. Moreover, as − → xy is orthogonal to H , we have ax 0 and the algorithm is correct for K.
Remark 1. Let x be in H \ K. Then the hyperface of K that is the closest to x is not necessarily the hyperface of K obtained by suppressing the (or one) vertex of K that is the furthest of x.
Proof. Let us consider the following example: let K be the 2−simplex in the hyperplane {x + y + z = 1} of R 3 . Let us set   , and the distances from x to these edges are δ 1 0.039, δ 2 0.048, δ 3 0.0002. So we have d 2 < d 3 < d 1 but δ 3 < δ 1 < δ 2 . Here, the vertex of K that is the furthest of x is e 1 , but the distance from x to K is realized in a point of the edge defined by {e 1 , e 2 }.

Minimisation of f on K
Now that we have the algorithm to compute the generalized distance to a standard simplex, it is easy to find the solution that minimises f on K: the portfolio that possesses the lowest risk is P x0 , where x 0 is the point of K that realizes the distance from the origin point to K, i.e. d(0, K) = x 0 .

Application to portfolio optimization
Here we determine the portfolio with lowest risk: we determine the convex combination of CAC 40 stocks 1 for which the variance is minimal 2 . We use the mean and the standard deviation of monthly 3 variation.

Portfolio optimization from 2007-04-23 to 2020-07-21
Here we consider the period from 2007-04-23 to 2020-07-21, that is to say we start from the highest point of CAC 40 index. Table 1 gives the mean and the standard deviation of stocks' return rates that appear in the results. By using Algorithm 1, we determine the portfolio with allowed short-selling that possesses the lowest risk: this linear combination is given by Table 2. The mean of its monthly variation is 0.44% and its standard-deviation 4.35%. We observe here that the linear combination obtained is a convex combination, which means that this portfolio is also the portfolio without short-selling that possesses the lowest risk. In geometrical terms, this means that the orthogonal projection of the origin point onto the hyperplane H already belongs to the simplex K.    Table 3 and Figure 2 give the yearly return rate of this portfolio. We notice that the portfolio is more profitable and more regular than the index: indeed, its mean is 7.41% and its standard deviation 11.93%, whereas for the index, the mean is 1.12% and the standard deviation 19.61%. Moreover, the return rate of the portfolio is almost never negative.  Table 4 and Figure 3 give the final value of the portfolio compared with the CAC 40 index and show the monthly variations of their value.  Here we consider the period from 2009-01-19 to 2020-07-21, that is to say we start from the lowest point of CAC 40 index. As in previous section, Table 5 gives the mean and the standard deviation of stocks' return rates that appear in the results.
The portfolio with allowed short-selling that possesses the lowest risk is given by the following linear combination in Table 6. The mean of its monthly variation is 0.76% and its standard-deviation 4.17%.
Now, according to Algorithm 1, the portfolio without short-selling that possesses the lowest risk is given by the following convex combination in Table 7. The mean of its monthly variation is 0.87% and its standard-deviation 4.22%.
Let us note that some stocks that were in the linear combination of the portfolio with allowed short-selling now disappear: the geometric explanation of this fact immediately comes from Lemma 1. The yearly return rate is given by Table 8. Here again, as shown by Table 8 and Figure 4, the portfolio is more profitable and more regular than the index: its mean is 13.27% and its standard deviation 11.99%, whereas for the index, the mean is 5.94% and the standard deviation 16.78%. Moreover, the return rate of the portfolio is negative for only two years, and the absolute value of these negative return rates very small.

Appendix -Python programs
Here we give a possible way to program Algorithm 1 in Python as well as the subroutine used to compute an orthogonal projection.
The function orth_proj(c,a,J) computes an orthogonal projection, where c is the covariance matrix, a is the point of which we want to compute the orthogonal projection, -J is the list of indices of p vectors of E that define the affine subspace onto which we want to project a. def orth_proj(c,a,J): p=len(J); n=len(c); i0=J[0]; L=list(set(range(n))-set(J)) #L is the complementary of J #Matrix The function mini_dist_fct(c,a) finds the point that realizes the minimal distance from a to the standard (n − 1)−simplex and also returns the square of this distance: it is a possible version of Algorithm 1. def mini_dist_fct(c,a): ]-a)] #Case 3: the orthogonal projection does not belong to the #simplex and the simplex has dimension greater than 1 else: #Looking for the hyperface that is the closest to x delta=mini_dist(c,x,J) dico[str(set(J))+str(x)]=delta x=delta [0] return [x,phi(x-a,x-a)] #Computing the point realizing the minimal distance return mini_dist(c,a,list(range(n)))


A new web map for the MeinGrün app

The starting point for developing a new map was defined by the requirements of the “MeinGrün” project1 (can be translated as ‘my green’ project). The aim is the development of a mobile app, which enables routing to urban areas, including suggestions for attractive places for different activities. A specific map style was designed to communicate information related to green spaces effectively and to make users excited about the topic of the project. Among other reasons, we also want to apply our knowledge on vector tile generation and use it in teaching. For the demonstration of our research on generalization, it is beneficial to offer a web map service because such a service allows illustrating developed methods and results. Finally, the experience enables us to train students in the design and development of customized styles for zoomable web maps. The aim is to build a map service with several zoom levels up to small scales using data from OpenStreetMap and NaturalEarth. For better adaptivity, it is aimed to offer the map as vector and raster tiles with the same style. Besides, making high-resolution raster tiles available for retina displays is considered as well. The rationale is that everyone can choose the appropriate method of delivery for different contexts of application. These requirements result in some technological challenges: provide vector and raster tiles at the same time and style, keep the computation time for an update, and generation low. For providing and delivering up to date data, on-the-fly map generalization has been implemented, e.g., scale-dependent selection, simplification, and aggregation of various features. Figure 1: Example screenshot from our map style for the city of Glashütte in Germany. 1 https://meingruen.org/ Abstracts of the International Cartographic Association, 2, 2020. Central European Cartographic Conference and 68th German Cartography Congress – EuroCarto 2020, 21–25 September 2020, Vienna, Austria (online) | https://doi.org/10.5194/ica-abs-2-8-2020 | © Authors 2020. CC BY 4.0 License.s of the International Cartographic Association, 2, 2020. Central European Cartographic Conference and 68th German Cartography Congress – EuroCarto 2020, 21–25 September 2020, Vienna, Austria (online) | https://doi.org/10.5194/ica-abs-2-8-2020 | © Authors 2020. CC BY 4.0 License.

The starting point for developing a new map was defined by the requirements of the "MeinGrün" project 1 (can be translated as 'my green' project). The aim is the development of a mobile app, which enables routing to urban areas, including suggestions for attractive places for different activities. A specific map style was designed to communicate information related to green spaces effectively and to make users excited about the topic of the project.
Among other reasons, we also want to apply our knowledge on vector tile generation and use it in teaching. For the demonstration of our research on generalization, it is beneficial to offer a web map service because such a service allows illustrating developed methods and results. Finally, the experience enables us to train students in the design and development of customized styles for zoomable web maps.
The aim is to build a map service with several zoom levels up to small scales using data from OpenStreetMap and NaturalEarth. For better adaptivity, it is aimed to offer the map as vector and raster tiles with the same style. Besides, making high-resolution raster tiles available for retina displays is considered as well. The rationale is that everyone can choose the appropriate method of delivery for different contexts of application. These requirements result in some technological challenges: provide vector and raster tiles at the same time and style, keep the computation time for an update, and generation low. For providing and delivering up to date data, on-the-fly map generalization has been implemented, e.g., scale-dependent selection, simplification, and aggregation of various features.  Figure 1 shows our result, a map in warm colors, and a reduced information load for serving a reference map. The visualization of roads with a simple line is unique, but this was also the intension of the applied research project: the production of something unique and easy rememberable for the "MeinGrün" project. The hill-shading uses raster tiles while all other map features work with vector tiles.
The data transformation from the OpenStreetMap format to the spatial PostgreSQL/PostGIS database has been applied with IMPOSM, a well-documented and efficient tool. GDAL is used to import the NaturalEarth data and doing some processing steps. PostgreSQL and its spatial extension PostGIS serve in many web-mapping projects as a data store and offer a wide range of options for processing data. After specified queries are applied, the t_rex software generates the vector tiles from the database, which are then packed as MBtiles using mbutil. Finally, Tileserver GL is used to serve vector and raster tiles, including further necessary additions such as style, sprites, and glyphs.
To sum up, we already have a working service, which is available on our server 2 with an ongoing blog about the project. Still, it is a work on progress project that needs further research and development. For example, the integration of Wikipedia/Wikidata information for selecting place by their importance, transliteration of no-Latin place names for a world-wide coverage, and more and better labeling of features. Now the map extent is scale depended and covers at low zoom levels the whole world. In contrast, the higher zoom levels are only available in Dresden and Heidelberg to match the requirements of the "MeinGrün" project but will be extended in the future.


extfieldsofstudy:
Physics
Computer Science

text:
Design and User Satisfaction Digital Learning Through Kelana Peribahasa

Kelana Peribahasa is a digital learning approach that includes e-learning, teaching aids, teaching and learning strategies, and assessment tools. The approach used is online learning proverbs through digital devices of smartphones, tablets, and laptops. Module Designs are available in Jom Mengenal, Jom Baca, Jom Main, and Jom Nilai. Jom Kenal is a module that is an introduction to Proverbs. Jom Baca is a module that contains a story proverbs produced by Digital Book Book. Digital Storybook which contains a proverbs story that covers Bloom’s Taxonomy Cognitive Domain (Review). Jom Main is comprised of five activities that include activities through the use of QR Code Reader and Google Cloud technology applications. Activities performed based on Bloom’s Taxonomy Cognitive Domain (Revised) level using the i-THINK thought map. The teaching and learning strategies used are the 21st-century learning approaches of 4C (Communication, Collaboration, Creative & Innovative, and Critical Thinking). It is digitally accessible and online. Assessment of activities (Jom Nilai) also through the use of online digital assessment tools. The testability of the Kelana Peribahasa is measured in terms of user satisfaction. The mean value of 4.81 for user satisfaction indicates that Permanent Discretion is desirable for digital learning. This innovation is a new change to teachers and students to realize the shift to Seven in Malaysia’s Education Development Plan [1].

Introduction
The proverb is a Malay heritage that has special privileges in the language. This is because the Malay heritage of proverbs should be introduced to each generation so that this proverb is not forgotten and is not extinct in the ages. However, the role of proverbs in speech and writing is less often used. This phenomenon has shown that proverb is not used by the younger generation in conversations and writing.
In the school curriculum, the teaching is taught in the syllabus. It encompasses six types of proverbs that are proverbial, bidalan, comparisons, idioms, parables and words of wisdom. This is because the proficiency of the proverb should be applied from primary school because when the pupils learn the lesson from the lower level, the students will understand the usage of the proverbs. However, teaching techniques that use textbooks cause students to be bored and less attentive when teachers teach. There are other approaches that can be used to increase the attention of students to the teaching of proverbs. Among the approaches is the teaching of multimedia applications through digital and online learning. The Proverb is created to generate students' thinking towards high-level thinking skills. Indirectly the realization of the Malaysian Education Development Plan [1] which emphasizes ICT in learning.

Research Objectives
The objective of this study is to: i. Identify the basic design of the Kelana Peribahasa ii.Identify the usefulness of the Proverbial Linguistics from the aspect of digital learning. ii. Consumer Vulnerability (Satisfaction) Assessment on Probate Width Probability Testing methodology through questionnaire instrument. Instrument questionnaire was used to test the attributes of Kelana Peribahasa attributes to the students studied;

Research Questions
• Satisfaction attributes Satisfaction is the level of comfort when using a system [5] Consumers are delighted and contented [6] using Proverbs.
• Satisfaction is a subjective assessment of the system by consumers regarding the user-friendly level. Satisfaction as the last feature of usability measures the extent to which the user likes the system before actual use. This means that the system needs to be user-friendly so that users feel satisfied when using it.
This study uses a questionnaire adapted from the questionnaire in [7] The sample questionnaire consisted of 17 students in a high school in the Besut district. A sample of five persons was sufficient to identify 85% of usability problems [6].

Analysis and Findings
The findings are divided into two: i

ii. Assessment of Kelana Peribahasa
The testability of Kelana Peribahasa is measured in terms of user satisfactory. Table 1 is the result of the findings of consumer satisfaction on Kelana Peribahasa. Form one student of a secondary school in the Besut District is tested for the findings.  The overall mean findings for consumer satisfaction on Kelana Peribahasa Lectures are 4.81 (Table 1). Based on the mean score interpreted it shows the satisfaction attributes are high where the student agrees the Kelana Peribahasa based on Cognitive Domain Bloom Taxonomy (Review) and deserves to be used as a digital learning tool. Figure 6 is a percentage of consumer satisfaction charts on the Kelana Peribahasa. The percentage of finding for scale is very agreeable is as much as 83.5. This shows a high insight and gives users satisfaction and enjoyment. Table 2 is a summary of the comments and suggestions that users have provided.