Deane Larkman

Masoud Mohammadian
email: masoud.mohammadian@canberra.edu.au

Bala Balachandran

Ric Jentzsch

Fuzzy Cognitive Map for Software Testing Using Artificial Intelligence Techniques

Keywords: Software testing, Fuzzy Cognitive Maps (FCMs), What-if Analysis

This paper discusses a framework to assist test managers to evaluate the use of AI techniques as a potential tool in software testing. Fuzzy Cognitive Maps (FCMs) are employed to evaluate the framework and make decision analysis easier. A what-if analysis is presented that explores the general application of the framework. Simulations are performed to show the effectiveness of the proposed method. The framework proposed is innovative and it assists managers in making efficient decisions.

Introduction

Software is a key element of systems and devices that support many of the activities that are an accepted part of our modern lifestyle. There is a consequent reliance on the correct behaviour of software, and an expectation that the software will not fail. However, software is an increasingly complex product that requires more and more testing a labour intensive and error prone activity [START_REF] Dick | Series in machine perception and artificial intelligence[END_REF]. The consequences of software failure range from the trivial (such as the need to restart a computer program), through the very inconvenient (such as the malfunction of traffic signals), to the catastrophic, where life and property may be affected. To minimise software failure, and its various impacts, high quality software must be created. Testing is a major quality assurance technique to evaluate the quality of software throughout the development cycle [START_REF] Dick | Series in machine perception and artificial intelligence[END_REF][START_REF] Hailpern | Software debugging, testing, and verification[END_REF].

Software Testing and Artificial Intelligence 2.1 Research on Software Testing using Artificial Intelligence

The application of AI techniques to testing software has moved beyond the speculative for many techniques, and now receives widespread attention from the research community. AI techniques have been used to explore different characteristics of a range of software, such as system software, real time software, embedded software, distributed software, and GUI software. The diverse investigations cover many areas. Various test approaches, at different test levels (such as unit, integration and system testing), have been used; for example, white box or structural testing, black box or functional testing, grey box testing, GUI testing and nonfunctional testing. Different programming paradigms have been examined, including procedural programs, object-oriented programs and aspect oriented programs. Distinct test aspects have been investigated, such as test data generation and test oracle generation [START_REF] Harman | A theoretical & empirical analysis of evolutionary testing and hill climbing for structural test data generation[END_REF][START_REF] Hermadi | Genetic algorithm based test data generator[END_REF][START_REF] Howe | Test case generation as an AI planning problem[END_REF][START_REF] Michael | Generating software test data by evolution[END_REF]. Software programs have been transformed to facilitate the application of AI techniques. AI techniques have been optimised, modified, hybridized with other AI techniques, and adapted.

Limitations using Artificial Intelligence in Software Testing

Although AI techniques are grounded in theory, these theoretical foundations have rarely been developed to address software testing problems. Investigations about the theoretical basis for using AI techniques to test software are limited. Consequently, AI techniques for testing software lack a firm scientific basis. A recent paper analysed the theories underpinning genetic algorithms, developed these theories for structural test data generation, and empirically validated the predictions of the theories against real world programs [START_REF] Harman | A theoretical & empirical analysis of evolutionary testing and hill climbing for structural test data generation[END_REF]. The reason for using an AI technique is commonly analytical. When cited, the reason for using an AI technique is usually because of the similarities between the characteristics of the AI technique, and those characteristics of the software testing problems.

Much of the empirical evidence for the use of AI techniques to test software stems from artificial laboratory programs, which are small and simple programs: real world programs are often not considered for validation. Real world programs are not merely scaled up versions of laboratory programs; but present complex test problems, which frequently require an intensive manual test effort to solve. Many researchers have voiced concern about the need to validate AI techniques against real world programs, rather than against simple laboratory programs [START_REF] Harman | A theoretical & empirical analysis of evolutionary testing and hill climbing for structural test data generation[END_REF][START_REF] Howe | Test case generation as an AI planning problem[END_REF][START_REF] Michael | Generating software test data by evolution[END_REF][START_REF] Kim | An empirical study of regression test application frequency[END_REF]. The limitations of laboratory programs have been observed, and it has been noted that toy (simple) programs fail to reveal the limitations of some test data generation techniques [START_REF] Michael | Generating software test data by evolution[END_REF].

Framework Software Testing Evaluating AI Techniques

A framework is at a high level generalised perspective of a domain of interest. It is a way to provide an initial understanding of some directed environment and its concepts or constructs. The framework described in this paper is a decision support framework, and was developed for use at an organisational environment level. It is aimed at test managers, or their equivalents -those people who, amongst other things, construct test plans, which encompass or are underpinned by test strategies.

Test managers are decision makers. The purpose of developing this framework is to support one aspect of that essential activity. Decision making is an increasingly complex activity with considerable potential for error. Decision makers need to have at their disposal tools to help reduce the risks inherent in their decisions. The complexity of the real world dictates the requirement to have tools that can be used to help lower the decision risk by selecting and analysing amongst multiple alternatives. Test managers need to have a way to help them decide which test technique will be the most beneficial. The selected technique must be consistent with the test strategy or with the test approach used to evaluate the software artefact, and must help reduce the risk of software defects, especially the critical ones, not being found before the software is released to users, customers, clients, or the public at large.

The components of the AI techniques decision support testing framework are Test Management, Test Information, Test Environment, and Technical Support The framework objective is the possible application of AI Techniques to the particular software to be tested. All the components relate to the objective.

Fuzzy Cognitive Maps -Application to the Framework

Fuzzy Cognitive Maps

Fuzzy Cognitive Maps (FCMs) [START_REF] Kosko | Fuzzy engineering[END_REF][START_REF] Kosko | Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence[END_REF] are graph structures that provide a method to capture and represent complex relationships within an environment (which defines a boundary), to improve understanding of that environment. FCMs have been used to model problems with no data [START_REF] Smith | Cognitive Fuzzy Modeling for Cognitive Fuzzy Modeling for a Health Care Institution[END_REF][START_REF] Kosko | Fuzzy engineering[END_REF][START_REF] Kosko | Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence[END_REF]. A FCM can be used for what-if analysis, where several alternative scenarios to a given situation are considered [START_REF] Kosko | Fuzzy engineering[END_REF][START_REF] Kosko | Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence[END_REF]. Concept nodes represent the environment behaviour within a FCM. The concepts are connected using arcs (arrows or edges) showing the relations between concepts. The framework's arcs are the influences between the concepts. The development of the FCM is based on the utilisation of domain experts' knowledge, forming a framework within that environment. Expert knowledge is used to identify concepts and the degree of influence between the concepts.

Use of a FCM to analyse the framework can only demonstrate general application of the framework. In contrast, validation of the framework involves specific, concrete applications of the framework. Concrete applications of the framework require case studies of different organisations in an industry environment. Validation of the framework is outside the scope of this paper.

FCM Construction

The FCM was constructed as follows. The events and the relationships defined by the proposed framework were used to build the graph structure of the FCM. Thus the FCM concepts are Test Management (C2) Test Information (C3), Test Environment (C4), Technical Support (C5) and the Application of AI Techniques to Software Testing (C1). Relationship weight values were assigned arbitrarily according to the authors' judgement, underpinned by industry experience in software testing of one of the authors. The FCM of the software testing framework is shown in Figure 1.

Static Analysis

If we consider the average effect of the influences from C2 + C3 + C4 (Figure 1) on C1 occurring, there is an estimated up to 75% chance that the software can be tested using an AI technique. Thus there is a 25% chance that some external influence will have an adverse, or even an advantageous effect, on the possibility of using an AI technique to test that particular software. Remember the 75% is based on the current knowledge of the domain expert. From C2 to C1 shows 0.75. This says that at most (upper boundary) if all the elements that make up Test Management of the software to be tested are positive, then at most there is a 75% chance that AI Techniques will be selected for testing the software.

From C3 to C1 shows 0.80. However, C2 influences C3 by 0.70 and C4 influences C3 by 0.40. If left by itself C3's upper boundary is 80%, but this could be diminished or enhanced by the 70% influence from C2 and the 40% influence from C4.

From C4 to C1 shows 0.70. C4 has two influences on its upper boundary of 0.70: C3 and C5. In this situation C4's upper boundary of 70% is dependent on C3's 70% and C5's 65%. Therefore the influences from the concepts C3 and C5 can potentially provide C4 with constraints that could either adversely or enhance the affect of C4 reaching its upper boundary.

The preceding static analysis shows that a decision maker, in this context, works in a very complex environment. Thus any assistance to reduce the complexity of the environment, or make that complex environment more understandable or easier to interpret, would be a plus for the decision maker. The decision maker needs a way to comprehend the consequences of the interacting concepts of the framework. They also need to be provided guidance for a better understanding of the elements within their decision, and for a better understanding of the consequences of the environment they are working with. The FCM inference mechanism is a technique that can be used to analyse the interacting knowledge captured by the framework.

What-If Analysis using the FCM Inference Mechanism

The dynamic dimension of a FCM is suitable for what-if analysis; where alternative scenarios (which involve what-if questions) are considered for a given situation. The solutions to the scenarios are obtained by using the FCM inference mechanism.

The FCM inference mechanism involves standard matrix multiplication. An initial state vector S 0 (a 1×n matrix) is multiplied by the FCM influence matrix, generating a new state vector S 1 as the next step. This process is repeated until the dynamical system reaches equilibrium. The influence matrix is an n x n matrix and each of its elements represents the influence values between the concept nodes. Values of concepts in new state vectors are calculated using the equation ( )

t j ji t i c W f c = +1 . The sigmoid function ( ) ( ) x e x f λ - + = 1 1
is used as the activation function. Large values of λ approximate the binary threshold or step function [START_REF] Kosko | Fuzzy engineering[END_REF][START_REF] Kosko | Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence[END_REF]. In the step function f(x) = 1if x > T and f(x) = 0 if x ≤ T, where T is the threshold value, taken from somewhere in the fuzzy interval [0,1]. Thus concepts are either on (1) or off (0). An approximate binary threshold was adopted and the threshold value used was 0.5 [START_REF] Kosko | Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence[END_REF]. The node to be tested is set to 1 in the input vector and in all the result vectors because it is a sustained input.

To develop a what-if analysis, scenarios are defined and the following process will be followed:

1) Create a connection or edge matrix E, which lists the values of the causal links between the nodes; 2) Define the scenario -select a node to test its effect or influence on the potential decision; 3) Create the initial state vector S 0 . Set the node to be tested to1 (on) and set all other nodes to 0 (off). This ensures independent analysis of the test node. The node to be tested is modelled as a sustained input, so the test node is set to1 in all the result vectors; 4) Multiply S 0 by E to obtain the result vector S 1; 5) Repeat step 4 with each result vector (S n * E) until equilibrium is reached -when a vector is repeated, ie the current iteration S n+1 = S n ; 6) Take the previous result vector S n for the analysis; and 7) Repeat steps 2 to 6 for each scenario. The influences among the concepts in Figure 1

=

The test manager and other domain experts are required to determine the weights of the different links between the concept nodes, and the initial activation level of each concept. Later research will identify a set of questions to assist the test manager to determine weightings. In this test of the framework the authors have carefully considered the system and provided the weights for the FCM shown in Figure 1. Now what-if analysis can proceed.

Let us first analyse the influence of C2; so C2 is set to 1. Thus C2 can be examined independently of the other nodes and their influences. This situation is represented by S 0 = [0, 1, 0, 0, 0]. The framework is flexible and the test manager can modify the concepts and relationships of the framework to match their organisational circumstances, and the characteristics of the software being tested. As indicated the influence weights are test manager dependent and may not represent specific organisational settings.

The FCM converges to a fixed point for each scenario -single vectors are the result when equilibrium is reached. All the equilibrium vectors are not null, so definite answers can be obtained for each scenario. The decision maker needs to be aware that effort into C4 can provide a more positive use of AI Techniques in testing of software. C3 and C5 have approximately the same degree of influence on the potential decision to use or not to use an AI technique on the software being tested. The influence of the Test Management node (C2) on the AI techniques decision is more difficult to determine, because its effect on the framework objective is both direct and indirect.

The information provided from what-if analysis of the framework can be used for decision analysis to support improved decision making by test managers. This approach provides a valuable tool for test managers to evaluate different scenarios for individual concepts, or combinations of concepts in the framework, and apply that evaluation in their organisation.

Temporal Analysis

FCM has introduced quantitative relationships between concepts to describe the strength of influence between elements. Miao in 2000 has shown that fuzzy cognitive maps generally do not provide a temporal mechanism to represent both the strength of influence and the temporal degree of the effect on the overall objective [START_REF] Miao | On causal inference in fuzzy cognitive map[END_REF]. The FCM within this framework includes a temporal degree as illustrated in Figure 1. The days are computed by the test manager based on their best estimates of the software to be tested and historical data. The temporal aspect conforms to critical path analysis for the FCM. Combined with strength of influence this provides a solid basis for compressing a software testing life cycle.

Conclusion and Future Work

A limitation of the AI testing framework is a potential inability to capture all the important concepts from the software testing domain. Therefore the proposed testing framework may be subject to external influences from concepts overlooked in the software testing domain.

Future work involves: 1) Applying increased granular of the AI testing framework, and analysing any differences in the results between representations of the framework; 2) Using an FCM inference method that is able to map or transform concept values of state vectors to any value of the fuzzy interval [0,1], and comparing the results with the less discriminating FCM inference method illustrated in this paper; 3) Extended temporal to include degree of dependency states; and 4) Constructing a set of questions to help test managers more easily determine the weight values for the relationships between the concepts in the AI testing framework.

Fig. 1 .

 1 Fig. 1. Fuzzy Cognitive Map with Influences and Temporal

  can be displayed using the following influence or edge matrix E.

  S0 = [0, 1, 0, 0, 0] S0 * E = [0.75, 0, 0.70, 0, 0] -this becomes S1 [1, 1, 1, 0, 0] S1 * E = [1.55, 0, 0.70, 0.70, 0] -this becomes S2 [1, 1, 1, 1, 0] S2 * E = [2.25, 0, 1.1, 0.70, 0] -this becomes S3 [1, 1, 1, 1, 0] S3 = S2: equilibrium has been reached. Let us next set C3 to 1. Thus C3 can be looked at independently of the other nodes and their influences. This situation is represented by S 0 = [0, 0, 1, 0, 0]. S0 = [0, 0, 1, 0, 0] S0 * E = [0.80, 0, 0, 0.70, 0] -this becomes S1 [1, 0, 1, 1, 0] S1 * E = [1.5, 0, 0.40, 0.70, 0] -this becomes S2 [1, 0, 1, 1, 0] S2 = S1: equilibrium has been reached. Let us next set C4 to 1. Thus C4 can be looked at independently of the other nodes and their influences. This situation is represented by S 0 = [0, 0, 0, 1, 0]. S0 = [0, 0, 0, 1, 0] S0 * E = [0.70, 0, 0.40, 0, 0] -this becomes S1 [1, 0, 0, 1, 0] S1 * E = [0.70, 0, 0.40, 0, 0] -this becomes S2 [1, 0, 0, 1, 0] S2 = S1: equilibrium has been reached. Let us next set C5 to 1. Thus C5 can be looked at independently of the other nodes and their influences. This situation is represented by S 0 = [0, 0, 0, 0, 1]. S0 = [0, 0, 0, 0, 1]. S0 * E = [0, 0, 0, 0.65, 0] -this becomes S1 [0, 0, 0, 1, 1] S1 * E = [0.70, 0, 0.40, 0.65, 0] -this becomes S2 [1, 0, 0, 1, 1] S2 * E =[0.70, 0, 0.40, 0.65, 0] -this becomes S3 [1, 0, 0, 1, 1] S3 = S2: equilibrium has been reached.


Dimitrios Mantzaris
email: dmantzar@med.duth.gr

George Anastassopoulos

Lazaros Iliadis
email: liliadis@fmenr.duth.gr

Konstantinos Kazakos
email: kazakosk@yahoo.gr

Harris Papadopoulos
email: h.papadopoulos@frederick.ac.cy

A Soft Computing Approach for Osteoporosis Risk Factor Estimation

Keywords: Artificial Neural Networks, Probabilistic Neural Networks, Learning Vector Quantization Neural Networks, ROC analysis, Osteoporosis

This research effort deals with the application of Artificial Neural Networks (ANNs) in order to help the diagnosis of cases with an orthopaedic disease, namely osteoporosis. Probabilistic Neural Networks (PNNs) and Learning Vector Quantization (LVQ) ANNs, were developed for the estimation of osteoporosis risk. PNNs and LVQ ANNs are both feed-forward networks; however they are diversified in terms of their architecture, structure and optimization approach. The obtained results of successful prognosis over pathological cases lead to the conclusion that in this case the PNNs (96.58%) outperform LVQ (96.03%) networks, thus they provide an effective potential soft computing technique for the evaluation of osteoporosis risk. The ANN with the best performance was used for the contribution assessment of each risk feature towards the prediction of this medical disease. Moreover, the available data underwent statistical processing using the Receiver Operating Characteristic (ROC) analysis in order to determine the most significant factors for the estimation of osteoporosis risk. The results of the PNN model are in accordance with the ROC analysis and identify age as the most significant factor.

Introduction

Artificial Neural Networks, Genetic Algorithms and Fuzzy Logic are modern subfields of the emerging field of Computational Intelligence and are used in order to solve problems without prior knowledge and symbolic representation of their rules. Methods and algorithms derived from these subfields exhibit certain advantages and drawbacks when applied to real-life problems.

The huge mass of applications, in which ANNs can be used with promising results [START_REF] Dayhoff | Artificial Neural Networks Opening the Black Box[END_REF] is the essential element of their growth. ANNs have been widely implemented over the last years in many scientific areas, like the industry [START_REF] Iliadis | An Intelligent Artificial Neural Network Evaluation System Using Fuzzy Set Hedges: Application in Wood Industry[END_REF], image processing [START_REF] Hisashi | Sigma-Delta Cellular Neural Network for 2D Modulation[END_REF], communications [START_REF] Haralambous | 24-hour Neural Network Congestion Models for Highfrequency Broadcast Users[END_REF] and medicine [START_REF] Mantzaris | Medical Disease Prediction Using Artificial Neural Networks[END_REF][START_REF] Papadopoulos | Confidence Predictions for the Diagnosis of Acute Abdominal Pain[END_REF][START_REF] Economou | FPGA Implementation of Artificial Neural Networks: An Application on Medical Expert Systems[END_REF].

Physicians use medical protocols in order to diagnose diseases. Medical diagnosis is the accurate decision of upon the nature of a patient's disease, the prediction of its likely evolution and the chances of recovery by a physician, based on a set of clinical and laboratorial criteria, applicable to a particular case.

ANNs are suitable for disease prognosis since there is no need to provide a diagnostic rule to identify the disease, but a set of examples that represent the variations of the disease. ANNs have been used in many medical areas successfully, such as cardiology [START_REF] Orr | Use of a Probabilistic Neural Network to Estimate the Risk of Mortality after Cardiac Surgery[END_REF], oncology [START_REF] Anagnostou | Artificial Neural Networks for Decision-Making in Urologic Oncology[END_REF], orthopaedics [START_REF] Mantzaris | Medical Disease Prediction Using Artificial Neural Networks[END_REF], urology [START_REF] Anagnostou | Artificial Neural Networks for Decision-Making in Urologic Oncology[END_REF], surgery [START_REF] Papadopoulos | Confidence Predictions for the Diagnosis of Acute Abdominal Pain[END_REF] etc.

The determination of the suitable ANN architecture is a critical point in some applications. An ANN with a small number of neurons involves deficient training, whereas a large number of processing elements limits its generalization ability. A typical approach for the proper design of an ANN is trial and error.

This study employees best-performance Probabilistic Neural Networks (PNN) [START_REF] Mantzaris | Medical Disease Prediction Using Artificial Neural Networks[END_REF] and also Learning Vector Quantization (LVQ) ones, which do not implemented in similar research efforts for osteoporosis estimation in the past [START_REF] Mantzaris | Medical Disease Prediction Using Artificial Neural Networks[END_REF], [START_REF] Lemineur | Efficient Estimation of Osteoporosis Using Artificial Neural Networks[END_REF][START_REF] Chiu | Applying an Artificial Neural Network to Predict Osteoporosis in the Elderly[END_REF][START_REF] Mohamed | Artificial Neural Network Analysis: A Novel Application For Predicting Site-Specific Bone Mineral Density[END_REF][START_REF] Rae | Artificial Neural Networks: A Potential Role in Osteoporosis[END_REF]. Moreover, the implemented ANNs are based on a vast data set comprising of 3426 records corresponding to an equal number of patients, whereas previous studies [START_REF] Lemineur | Efficient Estimation of Osteoporosis Using Artificial Neural Networks[END_REF][START_REF] Chiu | Applying an Artificial Neural Network to Predict Osteoporosis in the Elderly[END_REF][START_REF] Mohamed | Artificial Neural Network Analysis: A Novel Application For Predicting Site-Specific Bone Mineral Density[END_REF][START_REF] Rae | Artificial Neural Networks: A Potential Role in Osteoporosis[END_REF] were based on data sets with fewer cases.

The PNN with the best performance, as well as the Receiver Operating Characteristic (ROC) analysis were used for the investigation of the essential diagnostic factors of osteoporosis.

Osteoporosis and Data

Osteoporosis is a common bone disease that leads to an increased risk of fracture. In osteoporosis, the Bone Mineral Density (BMD) is reduced; the bone microarchitecture is disrupted whereas the concentration and the variety of proteins in bones are altered. Apart from the direct physical implications of a fracture, such as pain and inconvenience, osteoporotic fractures (involving the hip or the spine) are a major cause of morbidity and mortality.

Osteoporosis is a most frequent disease for women after menopause, when it is called postmenopausal osteoporosis, but it may also be developed in men. It may occur in anyone in the presence of particular hormonal disorders and other chronic diseases or as a result of medications, specifically glucocorticoids. In this case the disease is called steroid or glucocorticoid induced osteoporosis. It is a fact that a percentage as high as 75% of the women with osteoporosis disregards this disorder.

The diagnosis of osteoporosis is based on measuring the BMD of the patient. The most popular laboratorial method for doing this is the Dual Energy X-ray Absorptiometry (DEXA) scan. This examination, applied to specific bones, is costly and based on radiation absorption from the patient, so it is not recommended in all orthopedic cases.

The osteoporosis data, which were used for the design of the PNN and LVQ models, were obtained from the Orthopedic Clinical Information System of Alexandroupolis' University Hospital in Greece. This information system consists of a main database (MDB) where all medical records and statistical data is kept. For secure and real-time connection to the database, the information has been distributed, designing a replication scheme of the related database MDB. Although, the data belong to different instances, they seem to be included in a single database [START_REF] Anastassopoulos | A Spatial Distributed Approach for Electronic Medical Record Administration[END_REF].

The healthcare specialists access the medical data via a friendly and ergonomic web interface. The users of the Orthopedic Clinical Information System have remote access to the MDB either by their desktop personal computers or by Personal Digital Assistants (PDAs) wireless connected to database.

Data related to four diagnostic factors were stored for each patient, namely: age, sex, height and weight. The diagnostic factors for osteoporosis risk prediction as well as their values are presented in Table 1 and described in detail in [START_REF] Mantzaris | Medical Disease Prediction Using Artificial Neural Networks[END_REF]. The estimation of the osteoporosis risk factor was based on a T-score value, which is the patient's bone density compared to the normally expected in a healthy young adult of the specific sex. A T-score value less than or equal to -2.5 implies the development of osteoporosis, whereas a T-score greater than -2.5 is related to a normal person. These values of bone densitometry were divided into 2 classes, as presented in Table 2.

As it has already been mentioned, the present study is based on a data set comprising of 3426 records. Actually, the vast majority 3346 cases (97.7%) are related to women and only 80 cases (2.3%) are related to men with osteoporosis symptoms. The 1083 persons are pathological cases, as their T-score was less than or equal to -2.5.

Table 2. T-score values coding

T-score Value Classification ≤ -2.5 1 > -2.5
This data set was divided into a set of 2426 records for the training of both PNNs and LVQ ANN and another set of 1000 records for the evaluation and testing of their classification efficiency.

PNNs and LVQ Models in Medical Diagnosis Prediction

In this study, two osteoporosis risk prediction models based on a non-symbolic learning approach are presented. These proposed models use ANNs, particularly Probabilistic Neural Networks (PNNs) and Learning Vector Quantization (LVQ) ones.

PNNs are a variant of Radial Basis Function Networks and approximate Bayesian statistical techniques. The modus operandi of PNNs is familiar to the human decision making approach [START_REF] Orr | Use of a Probabilistic Neural Network to Estimate the Risk of Mortality after Cardiac Surgery[END_REF]. The patterns' classification by PNNs is based on Parzen's Probabilistic Density Function (PDF) estimator [START_REF] Orr | Use of a Probabilistic Neural Network to Estimate the Risk of Mortality after Cardiac Surgery[END_REF]. A PNN is a feed-forward neural network, consisting of two layers. The first layer, which consists of radial basis function units, computes the distances between each input vector and the training input vectors [START_REF] Iliadis | Intelligent Information Systems and applications in risk estimation[END_REF]. The obtained vector's values indicate the propinquity of the input vector to a training input. The second layer, which is a competitive layer, sums these contributions for each class of inputs to produce a vector of probabilities as output. These probabilities indicate the likelihood of the input vector to be classified in each of the available classes. The transfer function of the second layer detects the maximum probability and classifies the input vector to the corresponding class.

More details about the specific implementation of the used PNNs can be found in [START_REF] Mantzaris | Medical Disease Prediction Using Artificial Neural Networks[END_REF]. The PNN learns with exposure to training patterns with a single pass without the necessity of extended training. This feature implies that the PNN may manage large quantities of data much faster that other ANN architectures. The maximum accuracy requires the determination of a "smoothing factor", which represents the width of the calculated Gaussian curve for each probability density function.

The LVQ neural networks were first proposed by Kohonen. A LVQ network is a two-layer feed-forward network, consisting of a competitive layer and a linear layer. The first layer learns to classify the input vectors in the same way as the competitive layer of PNNs. The second layer transforms the competitive layer's classes into desired classifications defined by the designer of LVQ network. The classes of the competitive layer are called subclasses while the classes of the linear layer are called target classes [START_REF] Gray | Vector Quantization[END_REF]. Both of the competitive and linear layers have one neuron per class. The number of neurons for the hidden layer is always larger than the number of output neurons.

The LVQ method is used in training ANNs for pattern classification, where each output represents a particular class. Each class is referred by a vector of weights that sequentially, represents the centers of the classes. The training data set is used several times during the training phase in a random order. The training of LVQ ANNs is terminated when classes remain stable or a specific number of iterations has been carried out. A trained LVQ neural network is a vector comparator. When a new vector is presented to the input layer of a LVQ ANN it will be classified to a class with the closest center.

Experimental Results

The MATLAB Neural Network Toolbox was used for the construction and the assessment of the classification efficiency of the developed PNN and LVQ neural networks. The effectiveness as well as the user-friendly interface conduced to the selection of the specific software for the purpose of this study.

The implemented PNN and LVQ architectures, the number of neurons in the input, hidden and output layers, as well as the transfer functions used in the hidden and the output layers for each network type, are summarized in Table 3. The spread of the radial basis function, representing the width of the Gaussian curve, varied during the experimental design phase of the PNNs. The three level architecture of the optimal PNN is 4-2426-2, whereas the spread value offering the best performance was equal to 0.6.

The three level architecture of the optimal LVQ neural network was 4-4-2. A statistical analysis over osteoporosis data set indicated that the data is grouped into four subclasses. As it was mentioned, the number of hidden neurons of an LVQ neural network equals to the number of subclasses, so the implemented LVQ has four neurons for its hidden layer. The obtained results from the optimal PNNs and LVQ ANNs for the osteoporosis risk prediction are summarized in Table 4. The performances of the proposed ANN models are depicted in columns two to seven. In this study, the classification efficiency of PNNs and LVQ ANNs was based on two criteria. The first criterion was the percentage (numbers in parenthesis correspond to real cases) of correct classified cases over testing (1000 cases), training (2426 cases) and overall data set (3426 cases). These percentages are recorded in columns two to four of Table 4. An important criterion for the evaluation of the ANN's generalization ability is the proper classification of the pathological cases. The implemented ANNs have to recognize patients with increased osteoporosis risk factor, so the fields five to seven store the percentage of pathological cases that have been categorized correctly, for testing, training and overall data, respectively. It is shown clearly that PNN outperforms LVQ neural network, as the percentages of successful prognosis for overall and pathological cases for testing, training and for the entire data set are higher. Therefore, the PNN has been characterized as the optimal choice of ANN for being potentially used towards osteoporosis risk prediction.

The PNN was used for the significance estimation of the diagnostic risk factors and it was trained with 4 pruned data sets. Each of these sets used values related to 3 diagnostic factors instead of the total 4. In other words, one different diagnostic factor was omitted in each data set. The PNN was constructed and tested with the pruned data sets, and the obtained results are recorded in Table 5. The first column presents the diagnostic factor which was not considered during the PNN's development. The 2nd to 7th columns depict the performance of PNN for each of pruned data sets. The results of the 2nd to 4th columns are the percentages of successful prognosis over testing (1000 cases), training (2426 cases) and overall pruned data sets (3426 cases). The 5th to 7th columns record the percentage of successful prognosis of pathological cases for testing, training and overall pruned data sets. The results of the pruned PNN were compared to the ones related to the full-sized PNN. The performance of PNN dropped dramatically in the case of the omission of the "age" feature. The PNN's effectiveness remained stable when the "sex" diagnostic factor was omitted, as the vast majority is women with osteoporosis symptoms. The absence of "height" improved the PNN's performance.

The omission of "weight" did not improve the classification efficiency of the pruned PNN according to the percentages of successful prognosis for testing, training and overall data set, however the percentages of successful prognosis over pathological situations are better than ones of the full-sized data set PNN. The results of Table 5 prove that the height and weight diagnostic factors reduce the generalization ability of PNN.

ROC ANALYSIS

The available data set of osteoporosis records underwent statistical processing using Receiver Operating Characteristic (ROC) analysis for the determination of the contribution of each diagnostic factor to osteoporosis risk prediction [START_REF] Streiner | What's Under the ROC? An Introduction to Receiver Operating Characteristics Curves[END_REF].

The essential statistic from ROC is the Area Under Curve (AUC) for each diagnostic factor. The mathematical expressions for AUC, sensitivity and specificity are explained in [START_REF] Streiner | What's Under the ROC? An Introduction to Receiver Operating Characteristics Curves[END_REF]. The obtained results are summarized in Table 6. The 1st line presents the osteoporosis' diagnostic factors, while the AUC of ROC for each factor is recorded in the 2nd line of the Table 6.

As mentioned above, the AUC is the value of visual depiction of ROC. An AUC value greater that 0.5 indicates the importance of the contribution of a specific diagnostic factor. According to results of Table 6, the most important diagnostic factor is Age. The Sex's AUC is equal to 0.5, so this diagnostic factor seems not to have important contribution for osteoporosis risk estimation. This result was expected as the used data set consists of 3346 women, while the number of men is negligible. The results of pruned PNN and ROC analysis are convergence in terms of proposed diagnostic factors for osteoporosis risk prediction. Consequently, the Age factor is strongly recommended to be recorded for each patient.

Conclusions

Despite the fact that osteoporosis is an enormous public health problem with huge recourses required to deal with the immediate and long-term effects of fractures, no investigation has been performed on the effectiveness and weightiness of the various diagnostic factors in the clinical evaluation of patients. This paper evaluates the performance of two ANN topologies for osteoporosis risk prediction. The PNN outperformed the LVQ neural network in terms of successful prognosis of osteoporosis.

The PNN, which had the best performance, was used for further processing of the osteoporosis prediction data set. The PNN was designed, implemented and tested with pruned versions of the data set, for the evaluation of the most significant diagnostic factor towards osteoporosis risk. It was concluded that "age" is the most significant factor towards osteoporosis prediction.

Moreover, the available data were processed using the ROC analysis approach. The results of the optimal PNN were in accordance with the output of the ROC analysis.

In future work, it would be preferable to make the same experiments in an extended data set consisting of more male patients and more factors (such as smoking), which affect the presence of osteoporosis. The limited number of male data records used was an obstacle in the effort to reach generalized conclusions related to the "sex" factor. The additional diagnostic factors would contribute to an extensive study in terms of the osteoporosis disease. Also the scoring of the T-code values can be implemented by the use of fuzzy logic, offering a more comprehensive approach.

Table 1 .

 1 Osteoporosis diagnostic factors coding.

	NN inputs	1	2	3	4
	Variables	Age	Sex	Height	Weight
	Coding	Numeric value (years)	1 (Female) 2 (Male)	Numeric value (cm)	Numeric value (kg)

Table 3 .

 3 The optimal ANNs for the osteoporosis risk factor prediction

	ANNs	Input Layer -Neurons	Hidden Layer Transfer Function	Neurons	Output Layer Function	Neurons
	PNN	4	Radial Basis (spread = 0.6)	2426	Competitive (compet)	2
	LVQ	4	Competitive	4	Linear	2

Table 4 .

 4 Experimental results using PNN and LVQ architectures.

	ANN model	Percentage of Successful Prognosis	Percentage of Successful Prognosis Over Pathological Situations
		Testing Set	Training Set	Overall Set	Testing Set	Training Set	Overall Set
	PNN	83.10 (831)	84.95 (2061)	84.41 (2892)	95.90 (304)	96.87 (742)	96.58 (1046)
	LVQ	82.60 (826)	82.11 (1992)	82.25 (2818)	94.95 (301)	96.48 (739)	96.03 (1040)

Table 5 .

 5 Experimental results using Pruned PNN.

	Omitted Factor	Percentage of Successful Prognosis Testing Set Training Set Overall Set	Percentage of Successful Prognosis Over Pathological Situations Testing Set Training Set Overall Set
	Age	82.90	83.02	82.98	94.95	96.01	95.75
	Sex	83.10	84.87	84.35	95.58	96.87	96.49
	Height	83.70	82.98	83.19	99.68	99.22	99.35
	Weight	83.00	82.85	82.89	99.68	99.87	99.82

Table 6 .

 6 Area of diagnostic factors' curves.

	Diagnostic Factor	Age	Sex	Height	Weight
	AUC	0.646	0.503	0.560	0.641


Andrei V Chugunov
email: chugunov@egov-center.ru

Yury Kabanov
email: ykabanov@hse.ru

Ksenia Zenchenkova

Russian e-Petitions Portal: Exploring Regional Variance in Use

Keywords: E-Petitions, E-Participation, E-Government, Russian Public Initiative, Resource Model, Digital Divide, Institutions, Russian Regions, Automated

The paper presents the results of research on factors explaining the level of e-petitioning in Russian regions. The main goal is to reveal socioeconomic, technological and institutional problems the regions face, and hence to embed the Russian case into the broad research agenda on online engagement. We concentrate on the federal e-petitions portal -Russian Public Initiative -and use the automated monitoring system to analyse subnational dynamics of online petitions submissions and voting on the aggregate level. The data are used to quantitatively assess the drivers and obstacles for e-participation. Our findings suggest that more active e-petition portal usage in regions is associated with higher socio-economic and technological development, as well as with democratic institutions and better e-government policy. One of the main obstacles to active use of the portal is its institutional design that at the moment provides regions with different opportunities and reinforces participation divides. Future steps, implications for automated monitoring system and some policy recommendations are also discussed.

Introduction

Electronic petition systems are considered an important field of inquiry within multidisciplinary e-participation research [33; 26]. They are usually characterized as "[o]ne of the most prominent and widely used e-democracy tools," [39:453] being "at the forefront of official, fully operational e-democracy activities of governments and parliaments" [24:1]. As more countries are entering the era of e-participation, more opportunities for e-participation students have arisen to test existing theories with empirical data and provide tools for new projects' assessment. Russia is not an exception. In 2012 a campaign pledge of Vladimir Putin to make the Internet work for "di-rect referendum democracy" 1 turned into the Russian Public Initiative portal (www.roi.ru, RPI), a national e-petition portal launched in April 2013. 2 Despite the fact that few petitions really gain the required number of votes and achieve any practical results, the dynamic of e-petitioning seems more complicated, especially on the regional level. While some regions are relatively active in submitting and voting for petitions, many others remain reluctant to new take advantage of opportunities for participation. Exploring and understanding these disproportions seems quite topical and relevant, both for testing existing theories and better policy-making.

This paper seeks to explore patterns, dynamics and factors of RPI usage variance by Russian regions. Using aggregate level data on RPI petitions and vote counts from the automated monitoring system developed by the eGovernance Center at ITMO University, as well as drawing on existing theories on public engagement, we run quantitative analysis to answer the following research question: What factors can explain the regional differences in e-petitioning (submitting and voting for epetitions)? Although being a part of a broader online-engagement concept, RPI usage seems a valid and measurable proxy to study the Russian case and contribute to the comparative studies of e-petitions initiatives around the globe.

The paper is structured as follows. First we give an overview of the automated monitoring system developed by the eGovernance Center and used for analysing RPI dynamics. Secondly, using this tool, we describe the retrospective and current state of RPI usage. Thirdly we review existing relevant theories on online engagement, epetitioning and e-participation. Finally, we present the results of the analysis to find predictors of e-petitioning in Russia, and define future steps of research.

2

The Dynamics of E-Petitioning in Russia: Application of Automated Monitoring Approach

Automated Monitoring Tool for RPI Analysis

Since the opening of the RPI portal in 2013, the eGovernance Center of ITMO University has launched an automated monitoring system for it. 3 To aggregate data from the portal we use the official Application Programming Interface that provides information about all initiatives and their status: name, description, votes for and against, status, progress and dates of voting. The system allows monitoring dynamics of voting for petitions at a minimum interval of one hour, overall number of votes a day, total voting in the country and regions. It also gathers data of all petitions and has several filters: (1) level of an initiative (federal, regional, and municipal); (2) region;

(3) status; (4) categories (topics); ( 5) votes for and against, etc. In short the system allows for getting any data that is presented in the portal and is valuable for research, in a format ready for analysis. The key research topics it is tuned to address include: 1) positive feedback on the initiative; 2) negative feedback analysis; 3) issue salience in certain regions and on the federal level; 4) dynamics of citizens' interest in epetitioning facilities; 5) petition submitting and voting patterns.

Exploring data retrieved from e-participation portals has proven to make valuable contributions to understanding civic engagement, especially when it comes to the analysis of voting behavior and petitions' success and failure. Here we can mention studies of punctuated equilibrium formation in the case of the US portal We the People [START_REF] Dumas | Examining political mobilization of online communities through e-petitioning behavior in We the People[END_REF], voting dynamics, e-petition success factors and strategies, and media effects in the UK [12; 40], correlations of social media use and e-participation in Russia [START_REF] Bershadskaya | Evaluation of E-Participation in Social Networks: Russian E-Petitions Portal[END_REF]. All cases show the advantages of automated monitoring of usage in several respects. First, unlike surveys, it allows work with a larger sample, if not a general population. Secondly, it helps to see detailed dynamics of petitioning and voting behaviour in short time intervals. Thirdly, the monitoring is run online to instantly access the effectiveness of e-participation that could be valuable both for citizens and decisionmakers. Generally it facilitates building and testing hypotheses on citizens' behavior and issues' salience. However there are some limitations. The major one is that data cannot be analysed at the individual level of a petitioner or a voter. Hence to reveal factors of e-participation we need to use aggregate level data.

RPI and E-Petitioning in Russia: National and Subnational Dynamics

This section addresses the dynamics and state-of-the-art in RPI usage that can be revealed via the system described above. As figures show, neither is public interest in RPI stable, nor are citizens overactive in placing their ideas on the portal. In terms of e-petition submission (Fig. 1), the number of initiatives submitted declined rapidly in two months after RPI had been launched, apparently with the loss of media attention to this platform. In August 2015 a rise in activity can be seen, since several salient issues were put into the form of e-petitions, like those connected to the Ukrainian crisis (e.g. to ban destruction of foodstuffs under sanctions). However, at the moment the number of submissions is decreasing and is far from its initial rates. It should be noted that of all the e-petitions about 88% are federal ones, meaning that citizens tend to influence the national government to establish a federal legal framework rather than to persuade regional or municipal authorities, although these levels seem to be closer to people and easier to get to. The overall voting dynamics (Fig. 2) is to a large extent preconditioned by topics' salience and media attention. The majority of votes are given to popular initiatives, while the rest gain few votes to go any further.

Although the national dynamics is as described, the picture is much more complicated when we consider a regional dimension of RPI usage. Eighty five regions of Russia demonstrate different patterns of submission and voting, as well as a repertoire of topics. About 40 per cent of all petitions are submitted by three regions: Moscow, the Moscow Region and St. Petersburg, while others on average constitute from 0.5 to 2.5 percent. In the case of regional petitions, the abovementioned 3 regions' share is nearly 60 percent. Moscow and the Moscow region are also active on the municipal level, jointly forming 26 percent of e-petitions, while other regions' share varies from 0 to 5.5 percent (the Nizhegorod Region). It means, first, that against the background of the decline in public interest, we have as many as 85 different dynamics of epetitioning and voting. Secondly, despite the democratic and mobilisation promise of RPI, there are severe disproportions of regional representation, interest to e-petition and opportunities to participate. This problem needs to be addressed in order to determine the factors affecting RPI usage and improve decision-making.

3

Exploring Divides in E-Petitioning: RPI and Russian Regions

Factors of Online Engagement: A Review and the Russian Context

To approach the question of regional disproportions in e-petitioning we employ several major theoretical perspectives and concentrate on the overlapping ideas that political participation can be shaped by social and economic characteristics, costs and incentives to participate, as well as institutional context. These theories seem quite applicable to the analysis of a broad range of participation practices and tools, both online and offline, and are frequently used by scholars. Plenty of works emphasise that political participation is practiced by wealthier and more educated citizens, i.e. it is the socio-economic status that matters. But the causal mechanisms that unite education, occupation and income are different. A popular concept is the Resource Model, which includes time, money and civic skills as necessary resources to participate, and which appear to be unequally distributed and possessed by people of higher socio-economic status [START_REF] Brady | Beyond SES: A Resource Model of Political Participation[END_REF]. The rise of the Internet has provoked a debate on whether e-participation will have a mobilisation or reinforcement effect, and whether the digital divide will add to the political one [START_REF] Norris | Digital divide: Civic engagement, information poverty and the Internet worldwide[END_REF]. Empirical literature mainly supports the reinforcement effect, although the structure of divides has been in some respects altered. The fact that those participating and petitioning online are usually men with a higher level of education and income, but usually younger than traditional offline participants, has been found in cases of the United States [START_REF] Best | Analyzing the representativeness of Internet political participation[END_REF], Germany, Scotland and Norway [23;24;8;32]. The patterns of inequalities are not the same everywhere. For instance, online petitions in Australia, as argued by Sheppard, can help to overcome traditional barriers like income or gender [START_REF] Sheppard | Online petitions in Australia: Information, opportunity and gender[END_REF]. In the case of Taiwan, the research by Lee et al. shows that e-petitions may mobilise those Internet-users that will not otherwise participate offline [START_REF] Lee | The Interplay Between Digital and Political Divides: The Case of e-Petitioning in Taiwan[END_REF]. As shown by Vicente and Novo, e-participation may alter gaps surprisingly: while in Spain a gender gap remains, unemployed people are more engaged online due to the lower costs [START_REF] Vicente | An empirical analysis of e-participation. The role of social networks and e-government over citizens' online engagement[END_REF]. Despite traditional resources, new Internet-skills are becoming important [START_REF] Min | From the digital divide to the democratic divide: Internet skills, political interest, and the second-level digital divide in political internet use[END_REF].

Another explanation of the importance of socio-economic status derives from the Theory of Social Capital. It seems that it can also be a meaningful driver of online participation [START_REF] Gil De Zúñiga | Social media use for news and individuals' social capital, civic engagement and political participation[END_REF], as well as its key components -high level of general and institutional trust [START_REF] Kim | E-Participation, Transparency, and Trust in Local Government[END_REF], although some studies have found an inverse relationship [START_REF] Goldfinch | The Participation Divide? Political Participation, Trust in Government, and E-government in Australia and New Zealand[END_REF]. One more theory is proposed by Inglehart, who argues that modernisation leads to culture and value shifts. Political actions, like petitions, correlate strongly and positively with the rise of postmaterialist values [14: 210-230]. So, be it due to resources, social capital or values, socio-economic characteristics may seriously affect e-petitioning.

Another perspective points out the significance of incentives and motivations, starting from Olson's theory pointing out the necessity of selective incentives or coercion for collective actions [29:2] Although some scholars argue the Internet has altered the way collective actions work [25; 5], Olson's logic remains relevant to epetition portals like RPI, where the activities remain voluntary and anonymous. One way to solve the free-riders problem are collective incentives, generated by social media and deliberation [START_REF] Warren | Social media effects on fostering online civic engagement and building citizen trust and trust in institutions[END_REF]. Another factor is political efficacy, as in the perception of ability to influence politics, or of government responsiveness [START_REF] Finkel | Reciprocal Effects of Participation and Political Efficacy: A Panel Analysis[END_REF]. Some studies have shown a strong positive relationship between e-participation and political efficacy [21; 19], meaning that citizens' intent to participate is based not only on rational calculation, but some personal perceptions of this decision.

Incentives and efficacy always operate within a certain institutional environment and are shaped by public policy. Institutions shape behavior, provide information and incentives, minimize costs and provide collective actions [START_REF] Hall | Political science and the three new institutionalisms[END_REF]. There are plenty of institutions that affect online participation. We can start from a political regime that may restrict free flows of information and build e-participation for the sake of legitimacy only [17; 18]. The policy towards e-government and open government also matters [START_REF] Vicente | An empirical analysis of e-participation. The role of social networks and e-government over citizens' online engagement[END_REF]. Finally, we should consider the institutional design of e-participation portals as well as the procedures of e-petition processing [START_REF] Wright | Democracy, deliberation and design: the case of online discussion forums[END_REF]. Government policy can support the mobilisation effect or reinforce existing inequalities, provide incentives or impose costs. Several works successfully combine social and institutional perspectives and reveal that resources, incentives and institutions are interrelated in shaping the level of online engagement [31; 15].

What are the implications of the theories to the Russian case? It seems that epetitioning in the country can be explained by all of them. Public opinion polls indicate low interest in traditional petitions: just 4% of the population in 2013 participated in such an activity, and the level of political efficacy is low. There are no signs that the Internet has changed anything. 4 While institutional trust is high towards the President (80%), the addressees of petitions -the national Parliament, regional and municipal authorities -are trusted much less (40, 38 and 32 per cent accordingly). 5 It may explain why the lower the level of government is, the fewer petitions are submitted. Public participation in Russia is also highly disproportionate in social and economic terms [START_REF] Sedova | The Formats, Factors, and Social Base of Civic Activism in Today's Russia[END_REF]. The situation is more complicated on the regional level, while regions differ drastically in terms of economic, social and political development.

On the other hand, institutional development of e-government and e-participation in Russia should be considered. The first feature is a variety of subnational political regimes [START_REF] Petrov | Rating of Democracy by Moscow Carnegie Center: 10 Years in Service[END_REF] and problems with democracy on the national level, which creates costs to public participation. Russia is not an exception to use e-services as legitimacybuilding tool rather than to encourage online engagement [1; 2], but regions demonstrate different approaches to e-government and participation policy [START_REF] Kabanov | Regional E-governments in Russia: Institutional and Resource Constraints[END_REF].

Another feature is the institutional design of RPI. 6 To submit or vote for a petition one must register via the Unified System of Identification and Authentication (USIA), which is also used to get e-services. Registration requires time-consuming official procedures and hence creates additional costs. To be considered by authorities a federal petition should get 100 000 votes in favor, regional or municipal petitions require 5 per cent of the population of the respective regions or municipalities to vote (if the population of a region is over 2 million, 100 000 votes are needed). The problem is that although the number of citizens registered in the USIA has increased since 2013, the USIA population varies drastically within the regions. To illustrate how it works we have developed a simple index of the USIA effect for federal and regional petitions (Table 1). We divide the USIA population by a number a votes needed for a petition to be considered by authorities. The higher the index rate, the higher is the probability of petition success at this stage. We see that while citizens of Moscow can cast the necessary votes nearly 28 times it is impossible for Ingushetia to make their petition successful at any level. For the majority of regions about half of users should be mobilised, which is nearly impossible.

One more institutional feature that might hinder collective incentives is the absence of deliberation opportunity on the RPI portal. It is impossible to launch a discussion or information campaign within the portal, unless a petitioner has resources to attract media support from the outside. Another problem of the institutional design is that there is a special commission that decides whether a petition goes any further. It has rejected several popular initiatives and insults that such a system lacks legitimacy and trust, and in fact lowers the potential efficacy of participants and increases costs of engagement, despite the promise to change the existing institutions.7 In sum, it seems relevant to apply these theories to the Russian case. We hypothesise that higher levels of submission and voting for petitions are associated with: a higher socio-economic performance of the region, in terms of education (1), income (2), Internet use (3) and social well-being (4); more favorable institutional and policy environment, i.e. a more democratic political regime [START_REF] Bimber | Reconceptualizing collective action in the contemporary media environment[END_REF], effective e-government [START_REF] Brady | Beyond SES: A Resource Model of Political Participation[END_REF] and open government [START_REF] Dumas | Examining political mobilization of online communities through e-petitioning behavior in We the People[END_REF] policies; institutional design of RPI itself (i.e. lower USIA effect (8), i.e. opportunities for e-petitioning are structured by the rules of registration.

Research Design

To test hypotheses formulated in section 3.1 we use quantitative methods of correlation and regression analysis: while the former helps to see whether any relationship exists, the latter allows understanding causal mechanisms and relative weight of possible e-participation predictors. Our analysis is run on the aggregate level; we analyse the activity of the region in RPI usage rather than a particular individual's attitude. It helps to attract aggregate data on significant characteristics of the region. There are 83 cases in our sample out of 85 Russian regions.

We use two dependent variables: the number of all e-petitions submitted by a region on federal, regional and municipal levels via RPI (RPI_PET) and the number of votes for all petitions cast in a region (RPI_VOTE). The data for variables is retrieved by means of the automated monitoring system described above. In order to solve the problem of data skewness for analysis we calculate a mean for the period of 2013 -2015 and then use natural logarithm of RPI_VOTE and a square root of RPI_PET.

To measure independent variables we use data from the Russian Statistics Service, the Ministry of Communication of the Russian Federation, and indices provided by several Russian analytical centers. To overcome some problems with regional statistics we employ a mean of variables taken for the available period within 2007-2015. All variables are divided into two groups. The first one describes the key socioeconomic characteristics of the region: the level of higher education (EDU), natural logarithm of middle income (INCOME), unemployment rate (UNEMP) the share of urban and rural population in the region (URBAN and RURAL), and the Internet use (INTERNET). The second group includes variables that depict institutional and policy features of a certain region: regional political regime in 2012 (REGIME) [START_REF] Petrov | Rating of Democracy by Moscow Carnegie Center: 10 Years in Service[END_REF], egovernment policy performance (eGOV), 9 information openness of regional executive authorities' websites (OPEN) 10 and the index of the USIA factor presented in the previous section, for federal and regional e-petitions (USIA_REG and USIA_FED).

Analysis, Results and Discussion

The results of correlation analysis are presented in Table 2. First, we can see a strong and positive correlation between two dependent variables, which means that some regions are overall active in petitioning and voting, others might show no signs of both types of activities. Secondly, the analysis indicates that practically all chosen variables have strong and significant associations. The socio-economic portrait of a region active in submitting and voting for epetitions looks as follows. First, its citizens tend to be more educated and wealthy, and a region should have less unemployment, which speaks well for resource models and the reinforcement effect of online participation. Secondly, there are clear urban / rural and digital divides among regions that affect their opportunities to participate: more urbanised and Internet-connected regions are more active in RPI use. These factors seem relatively less important for voting (especially income), which might suggest that these two forms of activities require different resources to mobilise.

Institutional settings matters no less than socio-economic characteristics. First, active e-petitioning and voting is positively correlated with a more democratic subnational political regime (REGIME) that apparently allows more in terms of free opinion sharing, media freedom and public policy openness. Secondly, the need for egovernment development, which is also strongly associated with e-petitioning, might be interpreted in several ways. On the one hand, it can be a technical factor: as better e-government facilities increase their importance and convenience for citizens, more people register into the USIA, which in turn means that they can submit or vote for petitions. On the other hand, we can speak about institutional learning, when authorities and citizens tend to trust and become more accustomed to new technologies as a means of political communication. On the contrary, regional government openness appears insignificant and even negative. This confirms that regional authorities are not the key point of reference for citizens. Thirdly, the analysis shows that the institutional design of RPI is crucial, particularly in the case of petition submission Correlation analysis cannot grasp the interrelationship of factors and tells nothing about causality, hence the second step we have taken is a multiple linear regression analysis (ordinary least squares). Our task was to look at how independent variables interact with each other and the dependent one.

The results presented in Table 3 seem confusing: while many factors have shown strong correlation, few remain significant in regression models. Models 1 and 2 take RPI_PET as a dependent variable, and show that e-petitions submission can be explained by level of education and regional e-government performance. These factors lose their significance when controlling for the USIA effect. Models 3 and 4 that use RPI_Vote as a dependent variable show almost the same situation: no factors seem significant except the USIA effect. Of course a further model specification is needed to address the problem of predictors' correlations. However the analysis shows complicated dynamics of e-petitioning in Russian regions, bearing in mind that the USIA effect correlates strongly with all other factors (e.g. ,693** with the level of education, ,532** with e-government development and ,451** with rural population). Both the explanatory force of the USIA effect and its relationship to socio-economic and institutional factors should be interpreted.

First, we assume that inequalities in the USIA registration reinforce socioeconomic disparities and regional institutional context. On the one hand, since the USIA is used primarily to get public services online, we may suppose that people with higher education, income and well-being are more likely to have accounts in the system, because they tend to apply for e-services more often. 12 Rural areas and low Internet penetration, e.g. in the regions of Caucasus, are also obstacles to successful [START_REF] Goldfinch | The Participation Divide? Political Participation, Trust in Government, and E-government in Australia and New Zealand[END_REF] Correlation is significant at the 0.01 level, * -Correlation is significant at the 0.05 level (2-tailed). 12 For instance, the most popular e-services in Russia are payments of fines for road laws violations, tax payments and applications for travel documents, which seem more topical for people with high income and education in the Russian context.

diffusion of e-services, while citizens of urbanised and Internet-developed regions, like Moscow and St. Petersburg, have much more motivation and opportunities to use them. On the other hand, regional policies matter as well. Some regions are active in promoting the USIA (Primorsky Krai, Khabarovsky Krai), some show progress in open government (Rostov and Tula regions) and e-government (Tatarstan). The citizens of such regions are hence more informed and motivated to use USIA and eservices in general. The connection of the USIA to RPI may hence divide participation among people in one region, and exacerbate the gap between regions with different levels of socio-economic and policy development. Secondly, taken broadly, the institutional design of RPI presents a range of obstacles for active e-petitioning: time costs for registration via the USIA, absence of deliberation mechanisms and need for extra media attention, as well as high number of initiatives rejected. These factors negatively affect political efficacy and collective action. But again, the importance of such problems may vary across the regions due to differences in subnational political regimes, social capital, government transparency, media freedom, as well as the penetration of alternative online platforms to promote initiatives (e.g. social networks). The findings need to be further examined by more elaborate research models. Overall we conclude that though regional e-petitioning dynamics depends on political, digital and socio-economic divides, as well policy context, the institutional design of RPI strongly and negatively affects this causal relationship.

Conclusion, Recommendations and Future Steps

Institutionalisation of e-petitioning in Russia in a form of the official governmental portal is a new topic that requires constant attention, as changes affecting online participation patterns are constantly emerging. It is the key rationale to apply automated monitoring systems, which unlike surveys are more precise in fixing the dynamics of submitting and voting for petitions. The data retrieved from the system, as we have shown, can be applicable to a range of research tasks, and helps to understand the complexity of regional variance in use of RPI and test theories on empirical data.

In this paper we have explored some patterns of regions' inclusion in e-petitioning, and have confirmed the necessity for further research here. On the one hand, the results are well in line with the resource model and previous case studies (Germany, the USA, etc.) showing that e-petitioning replicates existing socio-economic and digital divides, as well as those works that emphasise the importance of favorable institutional environment and effective government policy for incentives, efficacy and collective actions. On the other hand, the institutional design of the petition portal seems to play a meaningful role as an obstacle to equity in regional representation.

To provide more robust results several techniques should be further applied. First, we are planning to use panel data and see the dynamics of change in factors' significance (as the USIA share is changing rapidly at the moment), as well as to use other dependent variables (like the salience of issues in a region) and more elaborate research models. Secondly, new hypotheses should be tested, for example, the role of media effects that can be done via the automated monitoring system as well. Thirdly, the analysis can be well accompanied by case studies to understand details.

The analysis shows the necessity for policy changes as well. First, extra effort should be given to provide equal representation of the regions in the USIA. For the transition period it might be better to change the procedure of petition consideration, and calculate the necessary percent of votes from the share of the USIA population in the region. Secondly, anonymity and lack of deliberation facilities should be addressed, to provide incentives for better collective actions. Thirdly, regarding the opportunities for automated monitoring, the provision of generalised data on social and demographic characteristics (age, gender and residency) could enhance the monitoring process and help to understand the existing divides to properly address them.

Fig. 1 .

 1 Fig. 1. The number of petitions submitted via RPI portal. (Source: Automated E-Petition Portals Monitoring System by eGovernance Center).

Fig. 2 .

 2 Fig. 2. The number of votes submitted via RPI portal. (Source: Automated E-Petition Portals Monitoring System by eGovernance Center).

Table 1 .

 1 Indices of the USIA effect on regional and federal e-petitions (Source: Authors calculations based on data by the Russian Ministry of Communication and Russian Statistics Service)8

	Region		Accounts in the	Votes needed	Index of the re-	Index of the federal
			USIA, 2015	for regional	gional USIA effect	USIA effect
				petition
	Moscow	2 793 113	100 000	27.93	27.93
	St. Petersburg	1 415 858.4	100 000	14.16	14.16
	Murmansk	201 381.4	38 300	5.26	2.01
	Region
	Novgorod	62 457.1	30 950	2.02	0.624
	Region
	Republic	of	19 998.4	23 200	0.862	0.2
	Ingushetia

Table 2 .

 2 Results of Pearson's correlation analysis (Source: Authors' calculations)11

	Region	RPI_PET	RPI_VOTE
	RPI_PET	1	.607**
	RPI_VOTE	.607**	1
	EDU	.692**	.426**
	INCOME	.427**	.273*
	UNEMP	-.383**	-.419**
	URBAN	.563**	.504**
	RURAL	-.563**	-.504**
	INTERNET	.391**	.347**
	REGIME	.408**	.322**
	eGOV	.597**	.402**
	OPEN	-.158	-.097
	USIA_REG	.845**	.497**
	USIA_FED	.887**	.548**

Table 3 .

 3 Results of regression analysis, dependent variables: RPI_PET and RPI_VOTE (Source: Authors' calculations)

	Models		Std. Beta -Coefficients
	Variables	Model 1	Model 2	Model 3	Model 4
	EDU	.435**	.083	.118	-.126
	INCOME	-.041	-	-	-
	UNEMP	-.023	-	-.120	-.148
	RURAL	-.183	-	-.251	-.220
	INTERNET	-.135	-	.020	-.004
	REGIME	.082	-	.042	.040
	eGOV	.385**	.161*	.098	.034
	USIA_FED	-	.745**	-	.473**
	Adjusted R -square	.578	.809	.188	.290
	Std. Error	1.77211	1.36486	1.68089	1.57207

Policy of Non-Interference [in Russian], WCIOM, 10.04.2013, http://wciom.ru/index.php?id=236&uid=113870

Institutional Trust [in Russian], Levada -Center, 07.10.2015, http://www.levada.ru/old/07-10-2015/institutsionalnoedoverie

6 Decree of President of the Russian Federation № 183 On Consideration of Public Initiatives Submitted by Citizens of the Russian Federation with the Usage of Internet -Resource "Russian Public Initiative" [in Russian], 4.03.2013, http://base.garant.ru/70326884/#ixzz44ErQGaGk

The Paranormal on RPI, or Something Must Have Gone Wrong [in Russian], 28.11.2014, https://navalny.com/p/3976/

Indices are calculated as follows: we divide the USIA population by a number a votes needed for petition to be considered by authorities. The higher the index rate, the higher is the probability of petition success at this stage.

Index of Russian Regions E-Readiness (http://eregion.ru/en/ information-inequality-regions),2007 -2014

The "Infometer" Research Project (http://www.infometer. org/), 2013 -2015