text:
# Gino Fano

### Quick Info

Born
5 January 1871
Mantua, Italy
Died
8 November 1952
Verona, Italy

Summary
Gino Fano was an Italian mathematician whose work was mainly on projective and algebraic geometry. He is best known as the founder of the finite geometry.

### Biography

Gino Fano's father was Ugo Fano and his mother was Angelica Fano. Ugo Fano came from a wealthy family and he had no need for employment. Ugo Fano was a follower of Giuseppe Garibaldi and strongly in favour of Italian unification. In fact on 17 March 1861, ten years before Gino's birth, the Kingdom of Italy was formally created but it was only just before Gino was born that Italian troops captured Rome. Gino grew up in the newly created country which suffered many problems but also had a new confidence in education.

Fano studied at the University of Turin which he entered in 1888. His studies there were directed by Corrado Segre and he was also influenced by Castelnuovo. In fact Castelnuovo had been appointed as D'Ovidio's assistant in Turin the year before Fano began his studies and Corrado Segre had been appointed to the chair of higher geometry in Turin the year that Fano entered the University of Turin. This was an exciting place for research in geometry and it is not surprising that Fano was led to specialise in this area.

In 1892 Fano graduated from Turin and then, in 1893, he went to Göttingen to undertake research and of course to study under Felix Klein. Twenty years earlier, in 1872, Klein had produced his synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm (1872). The Erlanger Programm gave the unified approach to geometry that is now the standard accepted view. Corrado Segre corresponded regularly with Klein and in this way Fano had been brought to Klein's attention. In fact this had led to Fano translating the Erlanger Programm into Italian while he was an undergraduate at Turin and it had been published in the Annali di matematica in 1890. Of course Fano did indeed study with Klein in Göttingen where he attended his lectures.

Fano became Castelnuovo's assistant in Rome in 1894, a position he held for four years. Following this assistantship, Fano went to Messina in the extreme northeastern Sicily where he worked from 1899 to 1901. He had left that city well before an earthquake struck Messina on 28 December 1908, almost totally destroying the city and killing 78000. By this time Fano was far away in Turin where he had been appointed as professor at the University in 1901. In 1911 Fano married Rosetta Cassin and their two children, both of the sons, became professors in the United States.

He taught at Turin from 1901 until 1938 when he was deprived of his chair by the Fascist Regime. After this Fano went to Switzerland where he taught Italian students at an international camp near Lausanne. After the end of World War II Fano, who was seventy-four years old by this time, continued to travel and lecture on mathematics. In particular he visited the United States where he lectured and he also lectured in his native Italy during the remaining six years of his life.

Fano's work was mainly on projective and algebraic geometry. Fano was a pioneer in finite geometry and one of the first people to try to set geometry on an abstract footing. Before Hilbert was to make such abstract statements Fano said:-
As a basis for our study we assume an arbitrary collection of entities of an arbitrary nature, entities which, for brevity, we shall call points, but this is quite independent of their nature.
Struik, in [1], describes Fano's contribution:-
Early studies deal with line geometry and linear differential equations with algebraic coefficients ... . Later work is on algebraic and especially cubic surfaces, as well as on manifolds with a continuous group of Cremona transformations. He showed the existence of irrational involutions in three-space $S_{3}$, i.e., of "unirational" manifolds not birationally representable on $S_{3}$. He also studied birational contact transformations and non-euclidean and non-archimedean geometries.
Fano wrote many textbooks, examples of which are his famous geometry texts Lezioni di geometria descrittiva (1914) and Lezioni di geometria analitica e proiettiva (1930). This last text was written jointly with Alessandro Terracini who wrote the obituaries [5] and [6] of Fano.

### References (show)

1. D J Struik, Biography in Dictionary of Scientific Biography (New York 1970-1990). See THIS LINK.
2. L Boi, The influence of the Erlangen Program on Italian geometry, 1880-1890 : n-dimensional geometry in the works of D'Ovidio, Veronese, Segre and Fano, Arch. Internat. Hist. Sci. 40 (124) (1990), 30-75.
3. Elenco delle pubblicazioni del prof. Gino Fano fino al luglio 1950, Univ. e Politecnico Torino. Rend. Sem. Mat. 9 (1950), 33-45.
4. J P Murre, On the work of Gino Fano on three-dimensional algebraic varieties, Algebra and geometry (1860-1940) : the Italian contribution, Rend. Circ. Mat. Palermo (2) Suppl. 36 (1994), 219-229.
5. A Terracini, Obituary : Gino Fano, Bollettino dell'Unione matematica italiana 7 (1952), 485-490.
6. A Terracini, Gino Fano, 1871-1952. Cenni commemorativi, Atti Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. 87 (1953), 350-360.
7. H Umemura, Gino Fano (Japanese), Sugaku 37 (2) (1985), 169-178.


text:
# Permanents -- Computes the permanent of a square matrix.

## Description

Permanents is a package of functions for computing the permanent of a square matrix.

Computing the permanent is believed to be computationally intractable. In Valiant's theory of algebraic complexity the permanent polynomial is complete for the class VNP. Even computing the permanent of 0-1 matrices is #P-complete. See Valiant, Leslie G. (1979), "The Complexity of Computing the Permanent," Theoretical Computer Science (Elsevier) 8 (2): 189-201.

The permanent of a $n\times n$ matrix $(x_{i,j})$ is defined in analogy to the determinant as $\sum_{\sigma \in S_n} \prod x_{i,\sigma(i)}$. There are two other formulas for the permanent polynomial, Ryser's formula and Glynn's formula, both of which have the asymptotically smaller formula size of $O(2^n n^2)$. This can be improved further to {$O(2^n n)$} arithmetic operations with the use of Gray codes, and we do so in this package. The connection between the two formulae and the possibility of others is discussed in Glynn, David G. (2013), "Permanent Formulae from the Veronesean." Designs Codes and Cryptography, 68(1-3) pp. 39-47.

It is conjectured that the permanent polynomial does not have a polynomial size formula. By Valiant's theory, a possible strategy for proving this is to show that the permanent of the $n\times n$ generic matrix $N$ cannot be the determinant of a $p(n) \times p(n)$ matrix $M$ with entries affine linear entries of the variables of $M$ where $p(n)$ is a polynomial. The best lower bound is quadratic, i.e. the permanent of the $nxn$ generic matrix is not the affine projection of the determinant of a $n^2/2xn^2/2$ matrix. See T. Mignon, N. Ressayre. "A Quadratic Bound for the Determinant and Permanent Problem." (2004).

The best known upper bound is $2^n-1$ due to Grenet. More specifically, Grenet constructs a $2^n-1x2^n-1$ matrix $M$ with entries $0,1,-1$ and individual variables of the $nxn$ generic matrix $N$, such that the determinant of $M$ is equal to the permanent of $N$. See B. Grenet, "An Upper Bound for the Permanent versus Determinant Problem" (2012).

## Caveat

Computationally intensive

## Version

This documentation describes version 0.9 of Permanents.

## Source code

The source code from which this documentation is derived is in the file Permanents.m2.

## Exports

• Functions and commands
• glynn -- compute permanent using Glynn's formula
• grenet -- Construct 2^n-1 by 2^n-1 matrix with determinant equal to the permanent of the input matrix
• pminors -- Return ideal generated by pminors of a specified size
• ryser -- compute permanent using Ryser's formula
• Methods
• "glynn(Matrix)" -- see glynn -- compute permanent using Glynn's formula
• "grenet(Matrix)" -- see grenet -- Construct 2^n-1 by 2^n-1 matrix with determinant equal to the permanent of the input matrix
• "pminors(ZZ,Matrix)" -- see pminors -- Return ideal generated by pminors of a specified size
• "ryser(Matrix)" -- see ryser -- compute permanent using Ryser's formula

## For the programmer

The object Permanents is .

format: plain


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# Digital Signage System Based on Intelligent Recommendation Model in Edge Environment: The Case of Unmanned Store

Kihoon Lee* and Nammee Moon*

## Abstract

Abstract: This paper proposes a digital signage system based on an intelligent recommendation model. The proposed system consists of a server and an edge. The server manages the data, learns the advertisement recommendation model, and uses the trained advertisement recommendation model to determine the advertisements to be promoted in real time. The advertisement recommendation model provides predictions for various products and probabilities. The purchase index between the product and weather data was extracted and reflected using correlation analysis to improve the accuracy of predicting the probability of purchasing a product. First, the user information and product information are input to a deep neural network as a vector through an embedding process. With this information, the product candidate group generation model reduces the product candidates that can be purchased by a certain user. The advertisement recommendation model uses a wide and deep recommendation model to derive the recommendation list by predicting the probability of purchase for the selected products. Finally, the most suitable advertisements are selected using the predicted probability of purchase for all the users within the advertisement range. The proposed system does not communicate with the server. Therefore, it determines the advertisements using a model trained at the edge. It can also be applied to digital signage that requires immediate response from several users.

Keywords: Correlation Analysis , Deep Learning , Digital Signage , Edge Computing , Recommended System

## 1. Introduction

Signage, a simple outdoor billboard, has evolved into a digitized and interactive platform. It is being integrated with the latest IT technologies, such as artificial intelligence and virtual reality.

This paper proposes an intelligent digital signage platform using an intelligent content determination system based on edge computing. The proposed system consists of a server and an edge. The server manages the data, learns the recommendation model used as the content determination system, and uses the learned content determination system to determine the products to be advertised in real time. As a content decision system, a recommendation list was derived by predicting the probability of purchase for selected products using a wide-and-deep learning-based recommendation model.

The wide and deep recommendation model combines individual wide and deep models, each of which learns different types of input values. The wide model is a product probability prediction model that uses logistic regression functions. The deep model expresses the product purchase status of each user in binary, adds an embedded product matrix and user features as input, and learns a dependent variable expressing the product purchase status of each user in binary. If several users exist in the advertisement range, a matrix is created by using a list recommended to the users in the advertisement range to select the product with the highest probability of purchase. The selected product is displayed to the user through signage. The system proposed in this paper determines the content using the model trained at the edge without communicating with the server. It is well suited for digital signage that requires immediate response to multiple users. This paper suggests a direction toward achieving a custom signage system suitable for several people, rather than a conventional one-to-one or one-way signage system.

## 2. Related Research

Digital signage involves the use of digital technology to provide various types of services to various displays or billboards for advertising in public or commercial spaces [1-3]. Digital signage functions by displaying various media content both indoors and outdoors. In other words, information is provided through outdoor advertisements in real time, allowing interaction with consumers [2-5]. In addition, digital signage uses a display combined with a camera to identify basic information such as the gender and age of a person within the advertising range and to display customized advertisements [4-6]. The display not only conveys one-sided information of a person, but also aims to provide a customized view of the content that the user wants to see.

Artificial intelligence technology is at the core of intelligent digital signage. It is being developed rapidly for predicting consumer behavior, and several types of daily data are used to predict consumer activity. An artificial neural network is used for extracting meaningful information from the data, and the types of learning data and layers constituting the artificial neural network vary depending on the purpose [7]. Advances in semiconductor technology have shown that the accuracy of neural networks can be considerably improved by enabling the rapid learning of large amounts of data [8].

In the past, artificial intelligence was used to transfer all the data to the data center or cloud for processing [9,10]. However, recently, edge computing has attracted considerable attention [11,12]. Edge computing processes data directly at the edge where they are generated, rather than processing them centrally. This allows us to analyze and utilize data in real time by reducing the amount of time required to transmit data to and from the cloud [10]. Recently, signage systems have evolved into digital signage systems that can communicate with users beyond simple outdoor billboards [4]. As such, digital signage systems aim to provide customized content to several users in real time, which needs to be studied further.

##### 2.1 Digital Signage

Digital signage is a mixture of similar concepts according to display type, network type, etc. However, it can be defined as “fused media that deliver various contents and messages through a digital display in a specific space” [1-4]. Digital signage is mainly composed of hardware (display), software (content determination system), content, and network, and it is classified according to the type of display and installation location (indoor or outdoor). The concept and scope of digital signage have been expanding due to IT convergence and display diversification. Digital signage includes telescreens (an evolution of converged media and network), smart signage (which combines smart devices and various contents), media facades (which utilize the entire building as a display), and projection of the screen (rear projection). Humanoid digital signage and narrowcasting, which broadcasts to viewers who are clustered locally and hierarchically through displays, are also being developed [2,3].

In recent years, Indian signage has been considerably developed and used in various fields such as recognizing the gender and age of a user through face recognition technology to display customized advertisements or issue discount coupons [13]. Such digital signage has a significant influence on a society that is close to digital, and previous studies have investigated factors that influence signage [14].

Table 1 compares the edge-based digital signage proposed in this paper with existing research cases. First, a study using emotion recognition technology proposed a meaningful content determination system by collecting the emotion data of users, scoring them, and using them as weights when scheduling advertisements [5]. In another study, we proposed a content determination system based on gender classification by collecting user gender data through image processing technology. In addition, we provided a direction for real-time recommendation using edge computing by collecting and transmitting the gender data to a Raspberry Pi environment [15].

Digital signage research cases
##### 2.2 Intelligent Recommendation Model

A recommendation system or recommendation model finds a list that might be of interest to a specific user at a given time. It collects user information, information on the list to be recommended, and information outside the system in some cases, and reflects it to provide a list desired by a specific user at a specific time [16-18]. Three types of recommendation systems exist: collaborative-filtering-based recommendation model, content-based recommendation model, and a hybrid model that combines them. Various techniques have been proposed to implement them.

First, collaborative filtering predicts the items to be selected by a user in the future based on the taste information collected from several users [16]. It is classified into user-based filtering, which groups users who have similar preferences and recommends the group preference products, and item-based filtering, which recommends other items with high preference association with the items purchased in the past [17].

The content-based recommendation method is based on information search technology. It analyzes the similarity between item-item or item-user preferences and recommends the item to the user. The collaborative-filtering-based and content-based recommendation methods have their respective advantages and disadvantages. The content-based recommendation method can recommend items whose evaluation is unclear, but there is a tendency toward excessive specialization. The collaborative-filteringbased recommendation method shows high serendipity, but the user is not recommended items whose evaluation is unclear. Recently, a hybrid recommendation system that can effectively utilize various types of information, maximize the advantages of the two aforementioned methods, and compensate for their disadvantages has been proposed [18-21]. Hybrid recommendations are categorized into four broad categories [22]. The first category involves combining the results of several recommendation techniques into various forms. It may be a method of combining the results of several recommendation techniques into a single result using a weighted average sum or a method of selecting and using a recommendation technique suitable for a situation or mixing various variables of each recommendation technique. The second category is a model in which a user profile that uses the attributes of items rather than the evaluation information is constructed to use the same information simultaneously for content-based recommendation and collaborative filtering. The third category involves using the features of collaborative filtering for content-based recommendations. A representative example is the use of a topic model, a technique for reducing content-based information [23]. The final model is a single model that uses collaborative filtering and content-based recommendation simultaneously [24].

In this study, the content decision system to be applied to the signage system uses a recommendation system that combines the results of two recommendation models with different data as inputs. To the best of our knowledge, this is the first study to propose a hybrid recommendation system.

Similar to the wide and deep recommendation model used for content decision in this study, the recommendation system using machine learning has been studied extensively [25-28]. A previous study investigated the characteristic that affects the behavior, which is derived from deep matrix factorization under the assumption that there is a potential characteristic that the developer or user does not recognize [19]. This was used to improve the accuracy of the recommended model. As computing power improves and data are diversified, the types of data available for recommendation systems are increasing. The content decision system used in this study is one such recommendation model. Similar studies have suggested a recommendation algorithm using appreciation environment data, such as weather, season, and time, for achieving performance improvement. This study assumes various characteristics as factors of music listening. Each feature was set to multidimensional weights, and the effects of the factors of music listening were analyzed using multiple regression analysis [20]. Another study proposed a recommendation system using long short-term memory (LSTM) and embedding technology [21]. This study embedded movie genres as a product category. The LSTM_WT model was applied to the LSTM model by employing a weight combining method that combines the embedding matrix and the projection matrix of the film.

As listed in Table 2, the recommendation system is used in different fields with various algorithms and types of data. Among them, the recommendation system using deep learning is attracting attention. The recommendation performance of deep learning is proportional to the complexity of data quality and network structure.

Comparison of learning models

In other words, the amount of computation is proportional to performance, which is closely related to real-time operation. The wide and deep recommendation model used in this study consists of a simple three-layer deep neural network (DNN) and multiple regression equations. We used a wide and deep recommendation model that can recommend a minimum amount of computation for application to the real-time recommendation pursued in this study [29-31].

##### 2.3 Edge Computing

As data originate from several smart devices, it is not efficient to send all the data from the device to the cloud for processing or analysis. Approaches began to appear at or near where the data were generated [32,33]. The attempt to process important data in real time by computing at the edge where data is generated is called edge computing [33]. IDC defines edge computing as “a mesh network consisting of micro data centers of about 10 square meters or less, which processes or stores critical data locally and sends all received data to a central data center or cloud storage repository” [32].

In addition, prominent IT companies or experts on edge computing predicted that half of all the data generated by 2020 would be stored, processed, analyzed, and utilized at the edge [33]. In addition, several market forecasting agencies and economic journals, such as the Forbes magazine and Gartner, have suggested that edge computing is already a major trend or a change that should be noted [34,35].

## 3. Digital Signage based on Intelligent Predictive Model

##### 3.1 Introduction to Data

Fig. 1 shows the data used for the deep learning model for correlation prediction and prediction. The table on the left shows the amount of Social Network Service buzz collected by daily income amount, payment number, and consumption-related keywords. The table on the right lists the public data showing the daily dust concentration (PM2.5) in the Cheonan region [36].

In fact, studies have been conducted on the effect of fine dust concentration on off-line consumption [37-39]. Based on these studies, fine dust was selected from the weather data [40]. The study analyzed the effect of fine dust on domestic retail sales, which were measured by the sales volume of large retailers. Consequently, it was shown that an increase in fine dust (PM2.5) by 10 μg/m3 reduces the sales of large retailers by approximately 2%. In the present study, we used the calculation of the correlation coefficient and basic regression analysis.

Data sample.
##### 3.2 Correlation Analysis

Fig. 2 shows the process of analyzing the correlation between unstructured data, SNS data, consumption data, and climate data. Normalization was used to analyze the collected data and to organize the data on duplicate dates. Pearson correlation was used to analyze the correlation between the consumption, SNS, and fine dust data.

Correlation analysis process.

The correlation between fine dust concentration data and consumption data using Pearson correlation coefficient is expressed as:

##### (1)
[TeX:] $$\rho(X, Y)=\frac{\operatorname{Cov}(X, Y)}{\sigma_{X} \sigma_{Y}}$$

A list of defined variables is shown in Table 3.

The correlation analysis using Pearson correlation coefficient with 2017 data shows that the consumption rate can be lowered as Max PM2.5 is increased, and the maximum value of PM2.5 has a greater influence on consumption than the average value does (Fig. 3).

Variable definition
Proposed partition-based device discovery.
##### 3.3 Intelligent Recommendation Model

Fig. 4 shows a schematic of the intelligent digital signature system from the user’s point of view. A user such as a camera is used to identify a user near a space where a digital signage is installed, that is, a user who has entered the advertisement coverage. The advertisements will be sent to the edge device whose advertisement range contains the user.

User data such as the age, gender, and location of the user, and category data about products within the advertising range are sent to the recommendation model at the edge to predict the probability of purchase and consider all the users within the advertising range. This is the process of advertising through signage for products with high sales probability.

The system consists of a two-level DNN model. As shown in Fig. 5, it consists of a product candidate group generation model for predicting the products to be purchased by existing users and a DNN-based recommendation model for predicting the purchase probability of the candidate products. First, the product candidate group generation model embeds the basic information and product information of the user and uses them as input to the DNN. Using this information, the model extracts several products for the user to purchase. In the product candidate selection step, the amount of calculation in the recommendation step, which is the next step, is reduced by filtering the users within the corresponding advertisement range by using the user information and the location information of the user.

System from the user's point of view.
Prediction model.

In the recommendation stage, the final selected product is derived by using the wide and deep recommendation model (Fig. 6), which learns the user’s previous purchase history, product metadata, and basic user information.

The wide and deep recommendation model has been chosen because the recommendation using a logistic regression model lacks serendipity, a phenomenon in which only the top products are continuously displayed. In addition, when using the DNN to solve this phenomenon, various products are displayed, but a product not suitable for the user at all may also be shown. We used the wide and deep recommendation model to avoid the two disadvantages of recommendation: over-consolidation and underfitting. The wide model uses a logistic regression model to create recommendation algorithms and returns detailed prediction results through training. However, this model always makes the same recommendation to the user, resulting in the a for mentioned lack of serendipity. Hence, the deep model is used together with the wide model to overcome the above issue. The deep model is a neural network model that generalizes specific products into higher categories (e.g., coffee, instant food, snacks) and recommends them. In this study, we used a deep model consisting of a simple DNN and a wide and deep recommendation model using a wide model as a content decision system for minimizing computation.

Wide and deep model.
##### 3.4 Probability and Method of Predicting Purchase Probability

The wide and deep model differs from other models in that it has two types of input data as shown in Fig. 7. In other words, it analyzes the result of inputting different types of data. Accordingly, discontinuous data such as category (classification) are suitable for learning. For predicting user-specific purchase history using Doc2Vec, user characteristics such as region, age, and gender were used as input values for the deep model through embedding.

In this study, we selected the most recent purchase history as test data for each user and selected the purchase history up to that point as learning data. If the user made less than one purchase, it was excluded from learning.

Referral process using the wide and deep recommendation model.

## 4. Implementation of Intelligent Digital Signage System

##### 4.1 Recommendation System Construction

In this study, the products for the advertisement are selected using the wide and deep recommendation model. This model considers the merits of using both wide and deep recommendation models and overcomes their limitations. First, in the wide model, logistic regression is used to predict the products that can be purchased by a user. In the deep model, we recommend a DNN using embedded vectors.

Embedding results.

First, the purchase history data were vectorized to learn the wide and deep recommendation model. If the purchase history data are changed to one-hot encoding during the vectorization process, the column will have as many labels as the number of traded items (N). This indicates that N products were traded. It is a classic deep learning approach to use this data simply as input, and as it is a one-hot method, the features purchased for the “apple” data cannot be utilized [41].

In this study, we perform embedding of the data with Gensim’s Doc2Vec technology to determine the distributed expression in deep learning [42] (Fig. 8). Item2Vec is an embedding technology that applies Doc2Vec used in NLP series to products.

Fig. 9 shows the vector product for 56 products and 17 categories and data consisting of [Item Name, Category] to create the input data of the wide model. Here, 896 columns are created for entering the data in the wide category, which is a combination of 56 item types and 17 upper category types. As there are four categories of 896 degrees (T, T), (T, F), (F, T), and (F, F), up to 3,584 columns are produced after stacking.

Wide model.
Deep model.

In the case of the neural network model, that is, the deep model, Fig. 10 is generalized and classified as a non-alcoholic beverage, thereby increasing the width of the recommendable product. The inputs of the deep model combine and dummy user feature data. In the dummy process, embedding technique is embedded using TensorFlow’s embedding_lookup function. In this case, categorical to num is used because the categorical variable must be entered as a factor rather than one-hot encoding.

## 5. Experiment and Result

Fig. 11 shows a table illustrating the experimental procedures and experimental environments to demonstrate the necessity of edge computing in digital signage. The learning speed comparison based on the same dataset in each environment is presented in Fig. 11.

To evaluate the performance of the wide and deep recommendation model used as a content determination system, we recommend the top 10 products having a score of 0.5 or higher and determine the precision of the top 10 recommendation list. In other words, we consider the hit rate: (number of hits/number of recommendations) by comparing the recommendation list with the actual purchase history of the user. Then, the precision is calculated as shown in Eq. (2) and Table 4 to determine the performance of the recommender system.

##### (2)
[TeX:] $$\text { Precision }=\frac{T P}{T P+F P}$$

Experimental environment.
Recommended precision

For example, the purchase history of the actual user (ID: 14674) is compared with the list of items recommended by the above recommendation model and the actual purchased items.

From Table 5, it can be observed that, although there are no products that lead to actual purchases in the recommendation list, the recommendation list is related to the actual purchased products and does not contain irrelevant products. The recommendation of chocolate to users who bought candy can be observed.

In addition, several prior experiments showed the highest precision for the top 10 recommendations near epoch 10 (Fig. 12). In addition, after experimenting by changing the number of items included in the recommendation list, it was observed that 25.94% of three recommendations and 16.28% of 10 recommendation led to actual purchases from the recommended list.

Table 6 compares the time it takes to display the same intelligent digital signage service at the edge and server. The service at the edge did not require video data transmission; hence, it was approximately twice as fast as the service in the cloud environment with a better performance.

Recommended list
Recommended result.
Service rate comparison (unit: second)

## 6. Conclusion

In this paper, we proposed an intelligent digital signage system based on edge computing and a trained intelligent advertisement recommendation model. The proposed system consists of a server and an edge. The server manages the data, trains the advertising recommendation model, and uses the learned advertising recommendation model to determine the product to be advertised in real time. The advertisement recommendation model consisted of selecting products and predicting purchase probability. In the product candidate generation stage, the size of the candidate set was reduced by filtering out users within the advertising range using user information and user location information. We used the wide and deep recommendation model to derive the recommendation list by predicting the purchase probability of the selected products. Finally, the most suitable advertisement was selected using the predicted probability of purchase of the cluster within the advertisement range. The proposed system does not communicate with the server and determines the advertisement using the model trained at the edge. It is well suited for digital signage that requires immediate response to multiple users. In this study, we constructed a digital signage system in edge and cloud environments. Consequently, it was demonstrated that the service based on edge computing should be used in the proposed signage system because it was approximately twice as fast as the service in the cloud. In future studies, we will investigate ways to reduce various network delay times and propose systems suitable for digital signage that needs to provide real-time processing and service to multiple users by using parallel computing.

## Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2021R1A2C2011966).

## Biography

##### Kihoon Lee
https://orcid.org/0000-0001-7445-832X

He received B.S. and M.S. degrees in School of Computer Science and Engineering from Hoseo University in 2018. His current research interests include machine learning, big data processing and analysis.

## Biography

##### Nammee Moon
https://orcid.org/0000-0003-2229-4217

She received B.S., M.S., and Ph.D. degree in School of Computer Science and Engineering from Ewha Womans University in 1985, 1987, and 1998, respectively. She served as an assistant professor at Ewha Womans University from 1999 to 2003. From 2003 to 2008, she is a Professor of Digital Media, Graduate School of Seoul Venture Information. Since 2008, she is currently a professor of computer science at Hoseo University. She is current research interests include social learning, HCI and user centric data, big data processing and analysis.

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Table 1.

Digital signage research cases
Emotion-recognitionbased signage [5] Gender perception signage [15] Suggestion system
Development environment Intel i5-6660 Raspberry Pi Jetson
Service target 1 person Several Specific community
Computing environment Local Edge Edge
Content determination system Bipartite graph matching X Deep-learning-based recommendation system
Requirement data Image data Image data Image data Behavioral data
User awareness Emotion recognition Gender recognition Face recognition
Interaction Possible Possible Possible
Signage form Indoor Indoor Indoor
Feature Recognize and score human emotions through image processing using deep learning + OpenCv. The use of bipartite graph matching algorithm to schedule user-advertised advertisements weighted by this emotional score. This paper classifies the genders of multiple users through image processing using deep learning + OpenCv. In Raspberry Pi, the video is processed using gender classification and the classified gender data are sent to the server. Recommended models based on deep learning that require multiple computations based on edge computing. It is possible to recommend specific clusters using this model.

Table 2.

Comparison of learning models
Element Deep matrix factorization based [19] Multi profile based [20] Cyclic neural network based [21] Wide and deep based
Recommended range Individual Association Individual All
Types Collaborative filtering Hybrid Hybrid Hybrid
Utilized learning model Deep matrix factorization Multiple regression LSTM_WT Multiple regression & DNN model
Result Grade (movie), category (music) Category (music genre) Viewing probability (movie) Probability o
Troubleshooting excessive specialization Possible Partially possible Partially possible Partially possible
Customization degree Good Good Usually Usually
Required operation Slow (high-dimensional learning model) Fast (location estimation, topic operation) Usually (embedding vector acquired) Fast (location estimation, probability of purchase)

Table 3.

Variable definition
Variable Means
X Daily fine dust concentration
Y Daily Consumption Index (SNS Buzz + Consumption Frequency)
[TeX:] $$\rho(X, Y)$$ [TeX:] $$X, Y \text { Pearson's correlation coefficient }$$
[TeX:] $$\operatorname{Cov}(X, Y)$$ Covariance (variation between two variables)
[TeX:] $$\sigma_{X}$$ [TeX:] $$\text { Standard deviation of } X$$
[TeX:] $$\sigma_{Y}$$ [TeX:] $$\text { Standard deviation of } Y$$

Table 4.

Recommended precision
Recommended Not recommended Total
Bought TP FN TP+FN
Not bought FP TN FP+TN

Table 5.

Recommended list
Recommended list Real purchase list
C11_00001, INSTANT RICE C16_00002, NOODLE
C13_00002, SAUSAGE C14_00001, MILK
C15_00003, JUICE C17_00002, CANDY
C12_00003, LAUNCH BOX
C15_00007, BOTTLED WATER
C17_00001, CHOCOLATE
C13_00001, MILK
C13_00001, TUNA CAN
C16_00001, RAMEN

Table 6.

Service rate comparison (unit: second)
Edge Server
Video data transmission - 8
User awareness 3 1.8
Recommendation 2 0.8
Total 5 10.6
Data sample.
Correlation analysis process.
Proposed partition-based device discovery.
System from the user's point of view.
Prediction model.
Wide and deep model.
Referral process using the wide and deep recommendation model.
Embedding results.
Wide model.
Deep model.
Experimental environment.
Recommended result.


text:
# CAT Quant Practice Problems

Question: Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still

$\frac{9}{{20}}$ of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

 12 hr and 8 hr 8 hr and 5.6 hr 10 hr and 8 hr 5 hr and 4 hr

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text:
# Prediction of sales based on previous data

A bit scared to post a question here (math fear syndrome I bet). I was looking for a way to predict (rough estimation) a next value based on series of previous values. These values are a sales totals for several previous years.

I found few websites i.e. The Online Excyclopedia of Integer Sequences but cannot understand formulas that are given there and how to modify them.

I know that the problem is not easy but was wondering if there is some way to do at least rough estimation of next few values.

An example. Lets say I have previous years sales: 200, 280, 370, 450, 530. Now I am looking to predict next few value(s).

Regards

• You could run a linear regression on your points. – uniquesolution Sep 10 '15 at 9:43
• Plot the data and see how they look like. – Claude Leibovici Sep 10 '15 at 10:12

Your example data seems to be linear:

You could fit a linear function to the data.

You would get $$f(x)=83x+117$$.

EDIT: To do that, you need to find the values of $$a$$ and $$b$$ such that $$f(x)=a x + b$$ minimices the square of the distance to your data points. You can find more information and the formula for $$a$$ and $$b$$ in https://en.wikipedia.org/wiki/Simple_linear_regression

If you just want to do a quick calculation, you can use wolfram alpha.

If your data seems non linear data, it can be a difficult problem. You can try to fit other simple functions, such as polynomials or exponentials (you can do that with wolfram alpha too). Predicting the behavior of a function based on some data points is studied by statistical learning theory.

If you have more data or you want to try more complex fits, you should use a programming language such as Mathematica, Matlab, Python or R (the last two are free and open source).

• Not really, to be honest. I have to admit I was looking for an example I can run against the array of values that would return - let's say - few next predictions. Not sure where 83x and 117 came from. – Mariusz Sep 10 '15 at 12:21
• I understand so far that I'd need to look for which function could represent my data. So, I can imagine when data would look different than something that can be a linear function other function would need to be used. What if I have values like: 200,300,400,300,400. This wouldn't work? If that's the case I would need to first calculate which function to use. That seems like not a trivial task. – Mariusz Sep 10 '15 at 12:35
• Seems like a bummer then. I cannot guarantee that sales will always raise in linear fashion. I've got at least general idea now. Thanks again @mlainz – Mariusz Sep 10 '15 at 15:08

I found something called Microsoft Time Series Algorithm which is part of Sql Server Analyses Services.

https://msdn.microsoft.com/en-GB/library/ms174923.aspx

This seems to be the route to take as I am not familiar with higher matt and Sql Server seems to cover exactly what I need.

Thanks for trying to help me.

Chart example from the page:


text:
#### On the Convergence of SARAH and Beyond

##### Bingcong Li, Meng Ma, Georgios B. Giannakis

The main theme of this work is a unifying algorithm, \textbf{L}oop\textbf{L}ess \textbf{S}ARAH (L2S) for problems formulated as summation of $n$ individual loss functions. L2S broadens a recently developed variance reduction method known as SARAH. To find an $\epsilon$-accurate solution, L2S enjoys a complexity of ${\cal O}\big( (n+\kappa) \ln (1/\epsilon)\big)$ for strongly convex problems. For convex problems, when adopting an $n$-dependent step size, the complexity of L2S is ${\cal O}(n+ \sqrt{n}/\epsilon)$; while for more frequently adopted $n$-independent step size, the complexity is ${\cal O}(n+ n/\epsilon)$. Distinct from SARAH, our theoretical findings support an $n$-independent step size in convex problems without extra assumptions. For nonconvex problems, the complexity of L2S is ${\cal O}(n+ \sqrt{n}/\epsilon)$. Our numerical tests on neural networks suggest that L2S can have better generalization properties than SARAH. Along with L2S, our side results include the linear convergence of the last iteration for SARAH in strongly convex problems.

arrow_drop_up


text:
# Recursive formula for joint moments in free probability

Suppose $\mathfrak{A}$ is an algebra (over $\mathbb{C}$, let's say), $\phi$ a linear functional on $\mathfrak{A}$, and $A_1, A_2 \subset \mathfrak{A}$ subalgebras which are $\phi$-freely independent. Then one can calculate the value of any "moment" $\phi(x_1 \dots x_n)$, where (WLOG) the $x_i$ are alternately in $A_1$ and $A_2$, even when the $x_i$ are not centered: Define the centered elements $\mathring{x}_i = x_i - \phi(x_i) \mathbf{1}$, and then write $$x_1 \dots x_n = \big( \mathring{x}_1 + \phi(x_1) \mathbf{1} \big) \dots \big( \mathring{x}_n + \phi(x_n) \mathbf{1} \big).$$ The right-hand side can be expanded into $2^n$ terms, constants pulled out, and neighboring terms from the same subalgebra "collapsed"; when the dust settles, all remaining terms are shorter than $n$ in length, except for the term $\mathring{x}_1 \dots \mathring{x}_n$, on which $\phi$ vanishes by the free independence hypothesis. This technique is mentioned in Remark 1.5.6 of Free Random Variables, and an example of such a calculation appears on page 70 of Lectures on the Combinatorics of Free Probability.

The above description of how to calculate moments makes good enough sense, but it would be useful to me to have an actual recursive formula, for assistance in things like (i) writing some code (for Mathematica, say), or (ii) proving assorted properties of the moments.

My initial stab at how to formalize this:

• Let $[n]$ denote the set $\{1, \dots, n\}$, or sometimes the ordered tuple $(1, \dots, n)$; I'll blur that distinction a little.
• Distinguish two kinds of moments, "general moments" and "alternating moments". Given an $n$-tuple $\vec{i} = (i_1, \dots, i_n) \in \{1,2\}^n$, and an $n$-tuple $\vec{x} = (x_1, \dots, x_n) \in (A_1 \cup A_2)^n$, let $GM(\vec{i}; \vec{x})$ denote the value of $\phi(x_1 \dots x_n)$ when, for each $j \in [n]$, $x_j \in A_{i_j}$. (By "value" here I mean some formal expression in the $\phi(x_i)$.) Note that we do not require neighboring entries of $\vec{i}$ to be distinct.
• The alternating moment $AM(x_1, \dots, x_n)$ is the value of $\phi(x_1 \dots x_n)$ if the $x_i$ alternate between $A_1$ and $A_2$.
• Given a tuple $\vec{i} \in \{1,2\}^n$, define the consecutivity tuples of $\vec{i}$ to be the maximal consecutive sub-tuples of $[n]$ such that, for all $j$ in such a tuple, $i_j$ is the same. For instance, if $\vec{i} = (1,2,2,1,1,2,1)$ then the consecutivity tuples of $\vec{i}$ are $\vec{c}_1 = (1)$, $\vec{c}_2 = (2,3)$, $\vec{c}_3 = (4,5)$, $\vec{c}_4 = (6)$, and $\vec{c}_5 = (7)$.
• Given $\vec{i}$ with consecutivity tuples $\vec{c}_1, \dots, \vec{c}_\ell$, one has

$$GM(\vec{i}; \vec{x}) = AM \left( \prod_{i \in \vec{c}_1} x_i, \dots, \prod_{i \in \vec{c}_\ell} x_i \right),$$

so that one can reduce any general moment to an alternating moment of at most the same length.

• The center-and-expand strategy referenced above yields

$$AM(x_1, \dots x_n) = \sum_{\vec{i} \subset [n]} GM(\mathring{x}_{i_1}, \dots, \mathring{x}_{i_k}) \prod_{j \in [n] \setminus \vec{i}} \phi(x_j)$$

where $k$ denotes the (variable) length of $\vec{i}$. The term with $\vec{i} = [n]$ vanishes by free independence, while the other terms involve moments of shorter tuples.

This seems a bit of a mess. Any suggestions for a cleaner approach? My apologies if something of this sort is already out there in the free probability literature, which I'm not as familiar with as I'd like to be.

-


text:
## Teichmuller Theory And Applications To Geometry Topology And Dynamics Teichmuller Theory

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Description : Read Now Teichmuller Theory And Applications To Geometry Topology And Dynamics by John H. Hubbard and you can download with pub, pdf, txt, doc, and more file format with free account. complete self-contained treatment of teichmuller theory, providing the background needed for proving the theorems by williamthurston discussed in volume 2: the classification of homeomorphisms of surfaces, the topological characterization of rational maps, the hyperbolization theorem for 3-manifolds that fiber over the circle, and the hyperbolization theorem for haken 3-manifolds.

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Author by : John H. Hubbard
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Publisher by : American Mathematical Soc.
Category : Mathematics
Description : Read Now Function Theory Of Several Complex Variables by Steven George Krantz and you can download with pub, pdf, txt, doc, and more file format with free account. the theory of several complex variables can be studied from several different perspectives. in this book, steven krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. he has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. in the spirit of a student-oriented text, krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. the main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. while due attention is paid to algebraic aspects of several complex variables (sheaves, cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. this book is suitable for a first graduate course in several complex variables.

## Pangeometry

Download Pangeometry Book or Ebook File with PDF Epub Audio and Full format File

Author by : Nikolaĭ Ivanovich Lobachevskiĭ
Languange Used : English, France, Spanish, Italia and chinese
Page : 310
Isbn : 9783037190876
Identifier : 3037190876
Release : 2010-01-01
Publisher by : European Mathematical Society
Category : Mathematics

## Geometry, Topology, and Dynamics

Download Geometry Topology And Dynamics Book or Ebook File with PDF Epub Audio and Full format File

Author by : François Lalonde
Languange Used : English, France, Spanish, Italia and chinese
Page : 148
Isbn : 082180877X
Identifier : 9780821808771
Release : 1998
Publisher by : American Mathematical Soc.
Category : Mathematics
Description : Read Now Geometry Topology And Dynamics by François Lalonde and you can download with pub, pdf, txt, doc, and more file format with free account. this volume contains the proceedings from the workshop on geometry, topology and dynamics'' held at crm at the university of montreal. the event took place at a crucial time with respect to symplectic developments. during the previous year, seiberg and witten had just introduced the famous gauge equations. taubes then extracted new invariants that were shown to be equivalent in some sense to a particular form of gromov invariants for symplectic manifolds in dimension 4. with gromov's deformation theory, this constitutes an important advance in symplectic geometry by furnishing existence criteria. meanwhile, contact geometry was rapidly developing. using both holomorphic arguments in symplectizations of contact manifolds and ad hoc topological arguments--or even gauge theoretic methods--several results were obtained on 3-dimensional contact manifolds and new surprising facts were derived about the bennequin-thurston invariant. furthermore, a fascinating relation exists between hofer's geometry, pseudoholomorphic curves and the $k$-area recently introduced by gromov. finally, longstanding conjectures on the flux were resolved in a substantial number of specific cases by comparing various aspects of floer-novikov homology with morse homology. the papers in this volume are written by leading experts and are all clear, comprehensive, and original. the work covers a complete range of exciting new developments in symplectic and contact geometries.

## Geometry, Topology and Dynamics of Character Varieties

Download Geometry Topology And Dynamics Of Character Varieties Book or Ebook File with PDF Epub Audio and Full format File

Author by : William Goldman
Languange Used : English, France, Spanish, Italia and chinese
Page : 349
Isbn : 9814401366
Identifier : 9789814401364
Release : 2012
Publisher by : World Scientific
Category : Mathematics
Description : Read Now Geometry Topology And Dynamics Of Character Varieties by William Goldman and you can download with pub, pdf, txt, doc, and more file format with free account. this book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the western world - as the most reliable way of knowing. the book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the vikings and the chinese, and of the unknown interiors of the american and african continents by foot and horseback. after the invention of the telescope, visual exploration of the surfaces of the moon and mars were made possible, and finally a visit to the moon. the book then turns to our legacy from the ancient greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. for concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.

## Problems on Mapping Class Groups and Related Topics

Download Problems On Mapping Class Groups And Related Topics Book or Ebook File with PDF Epub Audio and Full format File

Author by : Benson Farb
Languange Used : English, France, Spanish, Italia and chinese
Page : 371
Isbn : 0821838385
Identifier : 9780821838389
Release : 2006-09-12
Publisher by : American Mathematical Soc.
Category : Mathematics


text:
Permutation Calculator

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 4. nCr n= C r= {::}^(3)C_(2){::}^(4)C_(4){::}^(5)C_(3){::}^(6)C_(4){::}^(7)C_(5){::}^(8)C_(6)
 5. How many words can be formed by using all letters of the word . and daughtersistermotherfatherbrother
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 8. Permutation, Combination List n = , r = Is order important?   Yes No Is repetition allowed?   Yes No List variables : A,B,C,D,E,...,Z 1,2,3,4,5,...,10 n=3, r=2n=4, r=4n=5, r=3n=6, r=4n=7, r=5n=8, r=6
SolutionHelp


text:
1.16

## The University of Waikato

Skip to 0 minutes and 11 secondsHi! My name is Geoff Holmes, and today’s lesson, is infrared data from soil samples. Before starting to talk about the actual application we’ll develop, I thought I’d just mention something about application development in general. The top academic conference in machine learning is called ICML, International Conference on Machine Learning. This is where all the top people in the field present their work. In 2012, a paper was published at this conference which was something of a wake-up call to the machine learning community. The author was Kiri Wagstaff from the Jet Propulsion Lab in Pasadena, CA, and the paper, which is accessible to anyone with an interest in machine learning, is called Machine Learning that Matters.

Skip to 0 minutes and 50 secondsThe URL there on the slide will enable you to download it and read it. What the paper does is it points out that the field is focusing too much on new methods and on the accuracy of those methods and less on the kind of application that will really make a difference. What Kiri did was to suggest six challenges for machine learning applications. I’m not going to go through all the six that are listed there on the slide. I just

Skip to 1 minute and 21 secondswant to talk about the highlighted one: $100M saved through improved decision making provided by an ML system. Now, believe it or not, you can develop an ML system using near-infrared data on soil samples that will be something that could save$100 million. This lesson is a starting point for such a system, but it is possible. Before we do that, let’s just take a moment to think about what machine learning requires in order for us to develop an application of any kind. Well, it needs input and output in its training phase.

Skip to 2 minutes and 1 secondIn our case, we need a set of samples – those are going to be soil samples in some form, and you’ll see that in a while – and an output target value. In our case, this is going to be a real valued number, and will represent a property of interest of the soil. That could be organic carbon, organic nitrogen, available nitrogen, potassium. Something that we’re interested in predicting from the input. Our problem, of course, is to learn a mapping that describes the relationship between the input and the output. We refer to this mapping as a “model”.

Skip to 2 minutes and 37 secondsWe build the model on our training data, and then we use that model on unseen observations – new soil, if you like – in order to apply the model to the new soil in order for it to predict the target soil property of that soil that we’re interested in, such as the organic carbon. Now we need to think about where we’re going to get X and Y from for this particular application. Traditionally, soil samples are processed using techniques called “wet chemistry” techniques, and what those wet chemistry techniques are trying to do is determine the properties of the soil, such as available nitrogen, organic carbon and so forth. They will result in the Y values that we’re interested in.

Skip to 3 minutes and 35 secondsWhat we need for this application is for a number of samples to have been processed using wet chemistry to determine these Y values for us. Let’s say we’re interested in available nitrogen. We need, let’s say 50 or 100 different soil samples to have been processed using wet chemistry to produce 50 to 100 Y values. We need to take a portion of each of those samples from, let’s say, a thing called a “soil bank”. Suppose we’ve got a soil bank. We divide our soil sample into half. We send half off to the wet chemistry lab to get the property determined, and with the other half, we put that through a near-infrared device. That will produce the X values for our input.

Skip to 4 minutes and 25 secondsNow, the near-infrared device produces a signature, if you like, for the soil sample. I’ve got an example of one there below on the slide. These values will form the input. In the sense of an ARFF file, they represent the values or reflectance values for a given wavelength band. You’ll see in the ARFF file produced for the [quiz] that that starts at around 350 nanometers – that’s the first attribute. The next one might be 370 nanometers, 390 – or 80, 90, 400, 410, and so on.

Skip to 5 minutes and 3 secondsThe number of attributes we have, as you’ll see in the example, is something like 200 for each of those spectral wavelength bands, and then the values are numeric values, which are the amplitudes, if you like, of the spectrum, just the reflectance values that you get from the device. So as I said, you need a few hundred samples, so it’s not cheap, because you’ve got to send off – whatever number of samples you’ve got, it’s very cheap to get the X, but it’s expensive to get the Y, because you’ve got to send those off for wet chemistry analysis. So to put together a decent training set is expensive.

Skip to 5 minutes and 42 secondsGiven that, why would you bother doing that for the soil in this particular application? Well, once you’ve, let’s say, got your 50–100 samples and you’ve built your model, and if a farmer comes in with a new soil sample and says “I want to know what the available nitrogen is”, we just get out our available nitrogen model that we built and we get the NIR spectra for that new sample – that represents new X, if you like – we run it through the model, and it will produce an estimate of Y for that soil signature. We’ll be able to tell the farmer “for your soil sample, the available nitrogen is 4.3” (or whatever that estimated Y value is).

Skip to 6 minutes and 27 secondsInstead of days for the wet chemistry to take place, we’re talking about milliseconds for the NIR device to produce the signature for us to run through the model and get the estimate of Y. That’s the first thing that makes it useful. It’s very fast. Second thing that makes it useful is that we can produce, for the same input, if we’ve got enough models, an estimate for a number of soil properties, not just one. If we’ve got, for example, wet chemistry which has determined the potassium, available nitrogen, the organic carbon, the organic nitrogen, and so on, then we can build models for each of those and for the same X value, we can produce predictions for each of those soil properties.

Skip to 7 minutes and 15 secondsSo we can tell the farmer with the soil sample in very short order – of the order of milliseconds – what the values are for each of those soil properties. All right, so that’s the value of it. How do we actually go about doing the modeling? Well, the training set, remember, let’s imagine it’s an ARFF file. The right-most column, or the class column, would be a set of numeric values, so we’re talking about a regression problem. Then the attributes are all these reflectance values at various wavelengths. They’re all numeric values, as well. We’ve got X numeric values, and so is Y.

Skip to 7 minutes and 56 secondsThe classifiers of interest are things such as LinearRegression, RepTree, model tree M5 prime, RandomForest, support vector machine regression, GaussianProcesses, and so on. What I’ve done there is lined up the algorithms in terms of their processing speed. What you’ll do in the [Quiz] activity is you’ll process the data using the first four, because you’ll see that it’s quite a large dataset, and the other two take too long really to be useful. We’ll be saying more about that later. The big thing – message – though is that pre-processing can make a big difference to a classifier’s performance. What you’ll do is process the data raw, and then you’ll see what happens to the results when you start applying the pre-processing techniques.

Skip to 8 minutes and 39 secondsThe classifiers respond in different ways to the different pre-processing techniques. Some get better, some get worse, some stay the same. One thing that’s worth bearing in mind is that you’re about to enter experimental machine learning, where you’re going to have lots of results, because the [Quiz] activity takes you through the first four classifiers on the previous slide, but all in default mode. Now, each of them has parameters that can be tweaked, and so can each form the basis for a separate experiment. You’ll be using four pre-processing methods, one of which is to do nothing, just use the raw spectrum. Now, some of those methods themselves have parameters, as well. Of course, you can combine the pre-processing methods, as well.

Skip to 9 minutes and 27 secondsSo the space of experiments is extremely large. From all of that, you’ll be able to produce some pretty good results. Now, what you’ll be looking at is particularly the correlation coefficient. So how well does the predicted value match the known value from the training data using cross-validation? That will give you some idea of how close you are, and what want, of course, is to produce models that get you close to 1.0, the perfect correlation with what you’ve seen in training data previously. Now, you’ll see that that’s not possible, because there’s too much error in the data typically. But it will be a starting point.

Skip to 10 minutes and 15 secondsYou’ll mainly see the improvement you can get from that baseline or benchmarking that you do with the raw data to what happens when you apply various pre-processing techniques. I hope you enjoy that. I hope it wets your appetite for machine learning application development.

# Analyzing infrared data from soil samples

Some feel that data miners focus too much on new methods and tiny improvements in accuracy, instead of on applications that will make a real difference in practice. Geoff Holmes discusses six major challenges that have been proposed for data mining applications: one is to save \$100M through improved decision making. Inferring properties of soil samples from infrared data can save significant sums of money, because it can enable expensive wet chemistry to be replaced by an automatic process. However, achieving sufficient accuracy is a real challenge.


text:
# Answer the Following About 200 to 250 Words Explain Various Methods to Measure Price Elasticity of Supply. - Economics

Explain various methods to measure Price Elasticity of Supply.

#### Solution

The price elasticity of supply can be measured by the following two methods namely:

1. Proportionate Method

2. Geometric Method

Proportionate or percentage method

According to this method, the price elasticity of supply is given, by the ratio of percentage change in the quantity supplied and percentage change in the price of commodity.

Algebraically, it can be expressed as:

Es = "Percentage Change in Quantity Supplied"/"Percentage Change in Price"

Geometric method

The geometric method is a graphical presentation of the elasticity of the supply. This method does not involve any calculation. Just by looking at the shape of the supply curve, we can infer the degree of the elasticity of the supply. The degree of the price elasticity of supply depends on the slope and origin position of the supply curve.

There are following possible situations.

a. Unitary Elasticity of Supply (Es=1 )- If the straight line supply curve originates from the origin, then irrespective of the angle of inclination of the supply curve, the elasticity of supply will always be equal to one i.e. (Es=1 ). Such a supply curve is called unitary elastic supply curve.

b. Less Elastic Supply (Es < 1)- If the supply curve originates from the horizontal intercept of quantity-axis, then irrespective of the angle of inclination of the supply curve, the elasticity of the supply curve will be less than one i.e. (Es < 1)

c. More Elastic Supply (Es > 1)- Unlike the less elastic supply curve, the relatively more elastic supply curve originates from the vertical intercept of price-axis. The value of elasticity of supply originating from the vertical intercept is greater than one, i.e. (Es > 1)

Is there an error in this question or solution?

#### APPEARS IN

Micheal Vaz Economics HSC 12th Standard Maharashtra State Board
Chapter 5 Producer's Behaviour
Exercise | Q 4 | Page 45


text:
Carnegie Mellon University

# Projects

► Exploring Origami Generated Structures in ${C}$, Yu Xuan Hong (download paper)

Abstract:  The origami generator problem can be described as follows: given a set $U$ of angles, and a set $S$ of points containing 0 and 1, construct lines at angles in $U$ from each point in $S$ and from all possible intersection points of constructed lines, the set $R(U)$ is the closure of all possible points (including initial points) generated by such action. Previous research has shown many properties regarding the algebraic and geometric structures of $R(U)$, given $U$ and $S$ satisfying certain conditions. In particular, results have been proven for cases where $1 \in U$ and $S=\{0,1\}$.

In this paper, we venture beyond these restrictions to explore results for more general cases of $U$ and $S$. Our main results hold for cases where $U$ does not contain 1, and when $|S| \geq 2$. We will state and prove the conditions in those cases for $R(U)$ to be a lattice or a ring.

► Fractal Behavior of the Fibonomial Triangle Modulo Prime $p$, where the Rank of Apparition of $p$ is $p+1$, Michael DeBellevue, Ekaterina Kryuchkova (download paper)

Abstract:  Pascal's triangle is known to exhibit fractal behavior modulo prime numbers. We tackle the analogous notion in the fibonomial triangle modulo prime $p$ with the rank of apparition $p^*=p+1$, proving that these objects form a structure similar to the Sierpinski Gasket. Within a large triangle of $p^* p^{m+1}$ many rows, in the $i^{th}$ triangle from the top and the $j^{th}$ triangle from the left, $\binom{n+ip^*p^m}{k+jp^*p^m}_F$ is divisible by $p$ if and only if $\binom{n}{k}_F$ is divisible by $p$. This proves the existence of the recurring triangles of zeroes which are the principal component of the Sierpinski Gasket.

The exact congruence classes follow the relationship $\binom{n+ip^*p^m}{k+jp^*p^m}_F\equiv_p(-1)^{ik-nj}\binom{i}{j}\binom{n}{k}_F$, where $0\leq n,k$ < $p^*p^m$. It is a known result that the Fibonacci sequence modulo an integer is periodic. Denote the period modulo $p$ $\pi(p)$.

Fibonnaci Quarterly: Volume 56, Number 2, May 2018

► Turán numbers of vertex-disjoint cliques in $r$-partite graphs, Adam Kapilow, Anna Schenfisch (download paper)

Abstract: The Turán number of a pair of graphs $G$ and $H$ is denoted $ex(G,H)$, and is the maximum number of edges a subgraph of $G$ may have and still contain no copy of $H$.

In this paper, we determine $ex(K_{a_1,a_2,...,a_r}, mK_r)$, where $K_{a_1,a_2,...,a_r}$ denotes a complete $r$-partite graph with part sizes $a_1,...,a_r$ and $mK_r$ denotes $m$ vertex-disjoint copies of $K_r$, the complete graph on $r$ vertices. We prove that for any integers $1 \leq m \leq a_1 \leq a_2 \leq ... \leq a_r$ we have $ex(K_{a_1,a_2, ... , a_r}, mK_r) = \sum \limits_{1\leq i < j \leq r}a_ia_j - a_1a_2 + a_2(m-1).$

Discrete Mathematics: to appear

► Change in State: using Markov chains to explore national economic mobility and the evolving American Dream, Daniel Ayasse, Emily Myers, Christian Schmidt, Allison Schwam (download paper)

Abstract:  By classifying the economic status of children and their parents into equal quintiles, it is possible to use Markov chains to provide general statements about intergenerational economic mobility. Using income tax records from over 40 million children and their parents, we examine the evolution of the probability of achieving the "American Dream" over three generations.

We then explore areas found to have greater upward mobility and attempt to identify contributing factors and trends. Our findings show a moderately high, negative correlation between attainability of the American Dream and race.

► $\tau$-Norm-Perfect and $\tau$-Perfect Eisenstein Integers for $\tau=\omega+2$ and $2$, Carlos Rojas Mena (download paper)

Abstract: Using Robert Spira's [4] definitions of complex Mersenne numbers and the complex sum-of-divisors function, we characterize $(\omega+2)$-norm-perfect and $(\omega+2)$-perfect numbers that are divisble by $\omega+2$ and prove the nonexistence of $2$-norm-perfect numbers that are divisible by $2$ in the Eisenstein integers.

## Students

• Daniel Ayasse, Missouri State University
• Michael DeBellevue, University of Texas, Arlington
• Emily Myers, Smith College
• Carlos Rojas Mena, University of Rochester
• Christian Schmid, Carnegie Mellon University
• Anna Schenfisch, University of Wyoming
• Alison Schwam, University of Maryland, College Park
• Yu Xuan Hong, Pomona College
• Ekaterina Kryuchkova, Brown University

# Faculty

Dave Handron, Associate Teaching Professor
Course: Symbolic Programming in Mathematics

Project Director

E-mail:  handron@andrew.cmu.edu
Wean Hall 6214
412-268-5583

Gregory Johnson, Assistant Teaching Professor

Project Director

E-mail:  greggo@andrew.cmu.edu
Wean Hall 8122
412-268-1504

David E. Offner, Associate Professor, Westminster College
Course: Cryptography

E-mail:  offnerde@westminster.edu

Aris Winger, Assistant Professor, Georgia Gwinnett College

Project Director

E-mail:  awinger@ggc.edu

Michael Young, Assistant Professor, Iowa State University

Project Director

E-mail:  myoung@iastate.edu


text:
# Linear Image Denoising¶

This numerical tour introduces basic image denoising methods.

In [1]:
from __future__ import division
from nt_toolbox.general import *
from nt_toolbox.signal import *
%pylab inline
%matplotlib inline

/Users/gpeyre/anaconda/lib/python3.5/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.
warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')
/Users/gpeyre/anaconda/lib/python3.5/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.
warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')

Populating the interactive namespace from numpy and matplotlib

/Users/gpeyre/anaconda/lib/python3.5/site-packages/IPython/core/magics/pylab.py:161: UserWarning: pylab import has clobbered these variables: ['pylab']
%matplotlib prevents importing * from pylab and numpy
"\n%matplotlib prevents importing * from pylab and numpy"

## Noisy Image Formation¶

In these numerical tour, we simulate noisy acquisition by adding some white noise (each pixel is corrupted by adding an independant Gaussian variable).

This is useful to test in an oracle maner the performance of our methods.

Size $N = n \times n$ of the image.

In [2]:
n = 256
N = n**2

We load a clean image $x_0 \in \RR^N$.

In [3]:
name = 'nt_toolbox/data/flowers.png'

Display the clean image.

In [4]:
imageplot(x0)

Variance of the noise.

In [5]:
sigma = .08

We add some noise to it to obtain the noisy signal $y = x_0 + w$. Here $w$ is a realization of a Gaussian white noise of variance $\si^2$.

In [6]:
y = x0 + sigma*random.standard_normal(x0.shape)

Display the noisy image.

In [7]:
imageplot(clamp(y))

## Linear Image Denoising¶

We consider a noising estimator $x \in \RR^N$ of $x_0$ that only depends on the observation $y$. Mathematically speaking, it is thus a random vector that depends on the noise $w$.

A translation invariant linear denoising is necessarely a convolution with a kernel $h$ $$x = x_0 \star h$$ where the periodic convolution between two 2-D arrays is defined as $$(a \star b)_i = \sum_j a(j) b(i-j).$$

It can be computed over the Fourier domain as $$\forall \om, \quad \hat x(\om) = \hat x_0(\om) \hat h(\om).$$

In [8]:
cconv = lambda a,b : real(ifft2(fft2(a)*fft2(b)))

We use here a Gaussian fitler $h$ parameterized by the bandwith $\mu$.

In [9]:
normalize = lambda h : h/sum(h.flatten())
t = transpose( concatenate( (arange(0,n/2), arange(-n/2,0) ) ) )
[Y,X] = meshgrid(t, t)
h = lambda mu: normalize(exp(-(X**2 + Y**2)/ (2*mu**2)))

Display the filter $h$ and its Fourier transform.

In [10]:
mu = 10
subplot(1,2, 1)
imageplot(fftshift(h(mu)))
title('h')
subplot(1,2, 2)
imageplot(fftshift(real(fft2(h(mu)))))
title('$\hat h$');

In [11]:
imageplot(h(mu))

Shortcut for the convolution with $h$.

In [12]:
denoise = lambda x,mu : cconv(h(mu), x)

Display a denoised signal.

In [13]:
imageplot(denoise(y, mu))

Exercise 1: Display a denoised signal for several values of $\mu$.

In [14]:
run -i nt_solutions/denoisingsimp_2b_linear_image/exo1

Exercise 2: Display the evolution of the oracle denoising error $\norm{y-x_0}$ as a function of $\mu$. Set $\mu$ to the value of the optimal parameter.

In [15]:
run -i nt_solutions/denoisingsimp_2b_linear_image/exo2

Display the results.

In [16]:
imageplot(denoise(y, mu))

## Wiener Filtering¶

We suppose here that $x_0$ is a realization of a random vector $x_0$, whose distribution is Gaussian with a stationary covariance $c$, and we denote $P_{X_0}(\om) = \hat c(\om)$ the power-spectrum of $x_0$.

Recall that $w$ is a realization of a random vector $W$ distributed according to $\Nn(0,\si^2 \text{Id})$.

The (oracle) optimal filter minimizes the risk $$R(h) = \EE_{W,X_0}( \norm{ X_0 - h \star (X_0 + W) }^2 ).$$

One can show that the solution of this problem, the so-called Wiener filter, is defined as $$\forall \om, \quad \hat h(\om) = \frac{ P_{X_0}(\om) }{ P_{X_0}(\om) + \si^2 }.$$

We estimate $P_{X_0}$ using the periodogram associated to the realization $x_0$, i.e. $$P_{X_0} \approx \frac{1}{N}\abs{\hat x_0}^2.$$

In [17]:
P = 1/N * ( abs(fft2(x0))**2 )

Compute the approximate Wiener filter.

In [18]:
h_w = real(ifft2(P / (P + sigma**2)))

Note that this is a theoretical filter, because in practice one does not have access to $x_0$. Display it.

In [19]:
u = fftshift(h_w)
imageplot( u[n/2-10:n/2+10,n/2-10:n/2+10] )

nt_solutions/denoisingsimp_2b_linear_image/exo2.py:2: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
# err = arrayfun(@(mu)norm(x0-denoise(y,mu), 'fro' ), mulist);

Display the denoising result.

In [20]:
imageplot( cconv(y,h_w) )

Note that this denoising is not very efficient, because the hypothesis of stationarity of $X_0$ is not realistic for such piecewise-regular signal.


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Search for Higgs boson production in trilepton and like-charge electron-muon final states with the D0 detector

We present a search for Higgs bosons in multilepton final states in pp-bar collisions at sqrt(s)=1.96 TeV recorded with the D0 detector at the Fermilab Tevatron Collider, using the full Run II data set with integrated luminosities of up to 9.7 fb-1. The multilepton states considered are two electron plus muon, electron with two muons, muon with two hadronic tau leptons, and like-charge electron-muon pairs. These channels directly probe the HVV (V=W,Z) coupling of the Higgs boson in production and decay. The muon with two hadronic tau lepton channel is also sensitive to H to tau lepton pair decays. Upper limits at the 95% C.L on the rate of standard model Higgs boson production are derived in the mass range 100 <= M_H <= 200 GeV. The expected and observed limits are a factor of 6.3 and 8.4 above the predicted standard model cross sectio...


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# Distinguishing between a Polynomial and a Laurent Polynomial

Let $$f(x) \in \mathbb{Z}_p[x]$$ (for a prime $$p \gg d$$) be a polynomial of degree $$d$$, and let $$g(x)$$ be a Laurent polynomial with the same degree and only the first negative exponent term ($$g(x) = \frac{a_{-1}}{x} + a_0 + a_1 x + \dots a_dx^d$$) over the same field.

Now, say we are given oracle access to both these functions with the additional condition that we can only $$< d$$ queries (Else we can just ask $$d+1$$ queries and interpolate the points to check if the function is a polynomial or not - this was the only way I could think of.)

Is this possible - if the test doesn't have to be perfect and can have some false positives or negatives?

Unless querying $$g(0)$$ gives you a distinguishable error for a Laurent polynomial, and assuming that the values $$a_0, …, a_d$$ are equidistributed (for both the Laurent and normal polynomial cases), it's not possible if you are limited to $$d$$ queries.
The question is equivalent to asking "you're given Oracle access to a Laurent polynomial $$g(x) = \frac{a_{-1}}{x} + a_0 + a_1 x + \dots a_dx^d$$, can you determine whether $$a_{-1} = 0$$?" [1]
Well, for any fixed value of $$a_{-1}$$, the $$d$$ queries can result in any of the $$p^d$$ possible sets of responses with equal probability (because there exists a unique polynomial $$a_0 + a_1 x + \dots a_dx^d$$ that results in the $$d$$ required $$g(x) - \frac{a_{-1}}{x}$$ values). Because this is true for any value of $$a_{-1}$$, we cannot gain any information on its value (including whether or not it is 0).
[1]: Along with the convention that $$\frac{0}{0} = 0$$
• Thanks, I forgot to include that for the case $g(0)$, the oracle simply returns a random value - so your answer would still hold. May 9, 2020 at 14:22