Michele Della Ventura
email: dellaventura.michele@tin.it

Voice Separation in Polyphonic Music: Information Theory Approach

Keywords: entropy, information, music segmentation, overlapping musical notes, voice separation

Voice Separation is a delicate stage in a music information retrieval process intended to be used in the automated music analysis processes through textual segmentation or for the indexation of a music score. This article presents a method that is capable of separating polyphonic music, considered in its symbolic aspect, into its individual parts (or voices). This method considers every single note as an individual entity and assigns it to the part (or voice) where the information content that it assumes in relation to the alreadyexisting notes of the same score is maximum. The algorithm may separate the voices identifying them even in the points that intersect. The algorithm was tested against a handful of musical works that were carefully selected from the repertoire of Bach and of Mendelssohn.

Introduction

Computerized music analysis is an constantly-changing discipline, both thanks to the consequences originating from technology research and to the ongoing influences deriving from the study of cognitive sciences. Focusing on the comprehension of the brain processes involved in the musical activities [START_REF] Deliège | La musique et le sciences cognitives[END_REF][2], the latter may assume a decisive role in the analysis of the computerized music analysis. This kind of approach is important to musicians and to IT developers alike. To musicians it provides an innovative means to obtain the composing elements of a composition (pre-thematic elements, themes/melodies, rhythmic cells,...) [START_REF] Pancini | Problematiche e modelli formali per la segmentazione automatica/interattiva di partiture musicali simboliche[END_REF][4][5] [START_REF] Ventura | The Influence of the Rhythm with the Pitch on Melodic Segmentation[END_REF]. To IT developers, these techniques are used to perfect the text segmentation systems in order to improve the capacities of a search engine in the identification of the information on the web [START_REF] Hui | Selective Labeling and Incomplete Label Mitigation for Low-Cost Evaluation[END_REF]. The amount of information on the web is growing fast as well as the number of new users lacking experience in the art of web searching. The automated search engines based on the correspondence of keywords usually deliver too many low-quality matches. In general, the more precise the collection of data to be analyzed is, the better the results of the elabora-tions will be. The starting point is therefore the reading of the notes that is carried out from a MIDI file or from the more recent XML file.

In case of a polyphonic composition (figure 1), which entails a simultaneous ensemble of several voices on several pitches and in parallel or opposite directions, data (sound) reading and their proper assignment to a certain voice rather than to another voice becomes vital: both in case of the analysis of the musical text and in case of the information retrieval by the search engine. The analysis of a score is usually carried out by the main algorithms through a process of segmentation that considers the sounds of the various voices, one after another (figure 2). In polyphonic music and, in particular, in the FUGUE form, there are many examples where a voice intersects another voice (figure 3). In these cases an incorrect reading of the data would lead the segmentation processes (which precede the analyses described above) to rather inaccurate and, in certain cases, even erroneous results. In the example from figure 4 the ''subject'' of the FUGUE is no longer recognizable. In recent years various methods have been proposed for the separation of the voices of a polyphonic composition. Some works include algorithms which are capable of separating the voices based on specific preset rules [START_REF] Chew | Separating Voices in Polyphonic Music: A Contig Mapping Approach[END_REF][10] [START_REF] Madsen | Separating voices in MIDI[END_REF]: the computer does not learn these rules and develop its own knowledge, but rather simply uses the knowledge provided by the human analysis.

In other cases the algorithm is able to autonomously learn the rules [START_REF] Kirlin | Voise: Learning to seg-regate voices in explicit and implicit polyphony[END_REF][13] [START_REF] Valk | A Machine Learning Approach to Voice Separation in Lute Tablature[END_REF]: parameters that are trained on music already labeled with voice information. Some algorithms [START_REF] Chew | Separating Voices in Polyphonic Music: A Contig Mapping Approach[END_REF] take on the problem of overlapping musical notes, even if the results are not always satisfying. These are systems that take into consideration the sound vicinity concept. A marked improvement is the study by Gray and Bunescu [START_REF] Gray | A neural greedy model for voice separation in symbolic music[END_REF], a neural model for voice separation in symbolic music that assigns notes to active voices using a greedy ranking approach, or the study by Guiomard-Kagan [START_REF] Guiomard-Kagan | Traitement de la polyphonie pour l'analyse informatique de partitions musicales[END_REF], which taking inspiration from the method of Chew and Wu [START_REF] Chew | Separating Voices in Polyphonic Music: A Contig Mapping Approach[END_REF] that defines what contigs to connect and how to connect them, improved these connections by using musical parameters such as the average pitch difference between neighbor contigs. This article presents a method that, drawing inspiration from the preceding studies, is able to reconstruct the various voices of a polyphonic composition, by reading the sounds from a MIDI file: every single note is considered as an individual entity and inserted into the voice where the information content that it assumes in relation to the already-existing sounds in the same score is maximum. It is a system based on two clearly distinct principles: a musical one, related to the structure of the thematic material (interval structure -distance between various sounds) and a mathematical-statistical one, derived from the Information Theory elaborated by Weaver and Shannon [START_REF] Weaver | The mathematical theory of information[END_REF], tied to the possibility of transition from one interval to the other. This paper is organized as follows. Section 2 describes the information theory. Section 3 describes the analysis of the musical message. Section 4 shows some experimental tests that illustrate the effectiveness of the proposed method. Finally, conclusions are drawn in Section 5.

Information Theory

The analysis based on the Information Theory, considers the audio message as a linear process endowed with a syntax formulated not on the basis of preset rules, but on the probability of occurrence of each element of the audio message in relation to the element preceding it [17][18]. From the definition of a "message" as a chain of discontinuous speech "units of meaning" [START_REF] Angeleri | Information, meaning and universalit[END_REF], there follows that the speech "units of meaning" coincide with the minimum events of an audio message. Any event of a chain built in this fashion requires a prevision in relation to the event that will follow it [START_REF] Nattiez | Fondements d'une sémiologie de la musique[END_REF]. In a communication happening by means of a given alphabet of symbols, the information is associated to every single transmit-ted symbol [START_REF] Angeleri | Information, meaning and universalit[END_REF]. Information, therefore, may be defined as the reduction of the uncertainty that might have been, a priori, present on the transmitted symbol. The ampler the range of messages that the source may transmit (and the larger the uncertainty of the receiver in relation to the possible message), the larger the quantity of transmitted information is -and, along with it, its own measure: the entropy [START_REF] Nattiez | Fondements d'une sémiologie de la musique[END_REF]. In the Information Theory, the entropy measures the quantity of uncertainty or of information existing in a random signal. If every message has the probability p i of being transmitted, the entropy is obtained as the sum of all the set of functions p i log 2 p i , each of them being related to a message, i.e.:

The voice separation model

To separate the voices of a score starting from a musical input, the sounds must be, first of all, divided into movements, according to the beat of the composition (figure 5a), thus obtaining chords (i.e. the simultaneous overlapping of several sounds). Bear in mind that every voice may be even made up by several sounds within the same movement (figure 5b). The assignment of the notes to the various voices is therefore performed in chronological order, from the left to the right, beginning with the first movement: every note of the first movement is considered in itself as sound of a voice. Subsequently, the algorithm determines all the possible musical segments obtainable by combining the sounds of a voice with the sounds of the other voices of the movement following the analyzed one (figure 6). Finally, the information value is calculated for every identified segment: the segment having the larger value will represent the succession of the sounds for the specific voice (figure7). To compare various segments among them, in order to determine which is more important, each entropy is calculated: the less the entropy value, the greater the information carried by the sound [START_REF] Lerdhal | A Grammatical Parallel between Music and Language[END_REF]. In order to calculate the entropy it is necessary to take into consideration a specific alphabet: the alphabet is language -specific [START_REF] Nattiez | Fondements d'une sémiologie de la musique[END_REF] and, as it may be immediately deduced from the formula (based on the probability of certain symbols rather than other symbols to be transmitted) it demonstrates to be associated to language.

For the melodic analysis the various melodic intervals were classified as symbols of the alphabet [START_REF] Lerdhal | A Grammatical Parallel between Music and Language[END_REF]. For every single musical piece a table, which represents its own alphabet, is filled in: in the melodic analysis every interval has been considered for its ascending or descending trend (Table 1). A peculiarity of the proposed method is related to the fact that only the sounds of the initial subject of the FUGUE are taken into consideration to define the alphabet table. The definition of the alphabet is not enough in order to calculate the entropy of a musical segment: it is necessary to consider the manner in which the sound succeeds one another inside the musical piece.

In order to do this, the Markov process (or Markov's stochastic process) is used: we chose to deduce the transition probability that determines the passage from a state of the system to the next uniquely from the immediately preceding state [14] [18]. On the base of the above considerations, the transition matrix is created. It consists of the transition probabilities between the states of the system (conditional probability). In our case, the matrix represents the probabilities for a sound to resolve to another sound (Table 2).

Obtained results

The method presented in this article was tested by analyzing some musical compositions written in the form of a FUGUE, carefully selected from the repertoire of Johann Sebastian Bach (48 fugues of the well-tempered clavier) and of Felix Mendelssohn (6 fugues op. 35). Both cases regard polyphonic compositions that include from 2 to 5 voices and some of them even have overlapping musical notes.

The algorithm, realized on purpose, does not provide any limitation with respect to the dimensions of the table representing the alphabet and the matrix of transitions that will be automatically dimensioned in every single analysis on the basis of the characteristics of the analyzed musical piece. This allows conferring generality to the algorithm and specificity to every single analysis (Strength). Furthermore, the algorithm does not entail any limitation as to the number of possible voices to be extracted (Strength). The analysis of the time needed for every single elaboration was not taken into consideration inasmuch as the objective of the study was solely to separate the voices of a polyphonic composition to further improve potential subsequent segmentations for analyses of a different nature: musical or web indexation.

The larger the number of decimals used to express the information content value of every segment, the more precise the results of the elaborations. The larger the number of decimals, the smaller the error risk.

Some examples of the obtained results are given below (figure 8

Discussion and Conclusions

This article described an approach to the separation of the voices of a polyphonic musical composition, considered on their symbolical level, based on the Information concept.

The algorithm was applied to musical compositions in the form of FUGUE by authors such as Bach, Frescobaldi and Mendelssohn.

The results show on the one hand how the musical fabric of a composition is characterized by a strong structural uniqueness; on the other hand how this method represents a solution for the problem of voice separation, even if the voices intersect. This method represents an alternative approach in the applications of computational methods to the voices separation problem: the high degree of complexity of musical phenomena imposes certain forms of achievement that must be adequate and that, for completeness' sake, must cope with the problems under a sufficiently large number of angles.

Figure 1 .

 1 Figure 1. Polyphonic composition

Figure 2 .

 2 Figure 2. Representation of the score for the segmentation process

Figure 3 .

 3 Figure 3. Overlapping musical notes.

Figure 4 .

 4 Figure 4. Representation of the score for the segmentation process

Figure 5 .

 5 Figure 5. Subdivision of the scores into movements.

Figure 6 .

 6 Figure 6. Possible segments between two consecutive movements.

Figure 7 .

 7 Figure 7. Constitution of the voices.

  and 9) as well as examples related to the specific moments in which the voices were intersecting. The first stave shows the subject of the FUGUE, presented in the first 2/3 beats; the second stave shows a segment of the FUGUE where the parts intersect; the third stave shows the final result with the various separated voices.

Figure 8 .

 8 Figure 8. J.S. Bach: fugue No.6 of "The Well-Tempered Clavier" (BWV 851).

Figure 9 .

 9 Figure 9. F. Mendelssohn: fugue No. 2 op. 35.

Table 1 .

 1 Example of alphabet.

	Sound	Number
	Fa	1
	Mi	1
	Re	1
	Do	4
	Si
	La	3
	Sol
	Fa	2

Table 2 .

 2 Transitions matrix drawn about the melodic segment of Table1.

		Fa		La		Do		Re		Mi		Fa
		a	d	a	d	a	d	a	d	a	d	a	d
	Fa	a d			1		1
	La	a d	2			1
	Do	a d		2					1
	Re	a d									1
	Mi	a d										1
	Fa	a d				1


Will Serrano
email: g.serrano11@imperial.ac.uk

The Random Neural Network with a Genetic Algorithm & Deep Learning Clusters in Fintech: Smart Investment

Keywords: Genetic Learning, Deep Learning Clusters, Reinforcement Learning, Random Neural Network, Smart Investment; Fintech

This paper presents the Random Neural Network in a Deep Learning Cluster structure with a new learning algorithm based on the genetics according to the genome model, where information is transmitted in the combination of genes rather than the genes themselves. The proposed genetic model transmits information to future generations in the network weights rather than the neurons. The innovative genetic algorithm is implanted in a complex deep learning structure that emulates the human brain: Reinforcement Learning takes fast local current decisions, Deep Learning Clusters provide identity and memory, Deep Learning Management Clusters take final strategic decisions and finally Genetic Learning transmits the information learned to future generations. This proposed structure has been applied and validated in Fintech; a Smart Investment application: an Intelligent Banker that performs Buy and Sell decisions on several Assets with an associated market and risk. Our results are promising; we have connected the human brain and genetics with Machine Learning based on the Random Neural Network model where biology; similar as Artificial Intelligence is learning gradually and continuously while adapting to the environment.

Introduction

Biology is gradually and continuously learning while adapting to the environment using genetic changes to generate new complex structures in organisms [START_REF] Kirschner | The Plausibility of Life Resolving Darwin's Dilemma[END_REF], the current structure of the organisms defines the type and level of future genetic variation that will provide a better adaption to the environment or increased reward to a goal function. Random genetic changes have more probability to be successful in organisms that change in a systematic and modular manner where the new structures acquire the same set of sub goals in different combinations; therefore they not only remember their reward evolution but also generalize goal functions to successfully adapt future environments [START_REF] Parter | Facilitated Variation: How Evolution Learns from Past Environments To Generalize to New Environments[END_REF]. The adaptations learned from the living organisms affect and guide evolution even though the characteristics acquired are not transmitted to the genome [START_REF] Hinton | Adaptive individuals in evolving populations[END_REF], however, its gene functions are altered and transmitted to the new generation; this enables learning organisms to evolve much faster.

The genome is the genetic material of an organism; it consists of 23 pairs of chromosomes (1-22, X and Y) for a human cell formed of genes (approximately 21,000 in total) that code for a molecule that has a function or instruction to make proteins [START_REF] Pellegrini | Assigning protein functions by comparative genome analysis: Protein phylogenetic profiles[END_REF], furthermore genes are formed of base pairs (approximately 3 billion in total). The DNA is a double helix formed by the combination of only four nucleotides (cytosine [C], guanine [G], adenine [A] or thymine [T]) where each base pair consists of the combination of two nucleoids G-C and A-T. The genetic code is formed of codons, a sequence consisted of three nucleotides or three-letter words. Proteins that have similar combination of base pairs tend to have a related functionality determination of protein functions from genetic sequences [START_REF] Suzuki | A framework for the DNA protein recognition code of the probe helix in transcription factors: the chemical and stereo chemical rules[END_REF].

Successful Machine Learning and Artificial Intelligence models have been purely based on biology emulating the structures provided by nature during the learning, adaptation and evolution when interacting with the external environment. Neural networks and deep learning are based on the brain structure which is formed of dense local clusters of same neurons performing different functions which are connected between each other with numerous very short paths and few long distance connections [START_REF] Smith | Small-World Brain Networks[END_REF]. The brain retrieves a large amount of data obtained from the senses; analyses the material and finally selects the relevant information [START_REF] Sporns | Organization, development and function of complex brain networks[END_REF] where the cluster of neurons specialization occurs due to their adaption when learning tasks.

This paper proposes a new genetic learning algorithm on Section 3 based on the genome and evolution; where the information transmitted to new generations is learned when interacting and adapting to the environment using reinforcement and deep learning respectively. Information in the proposed genetic algorithm is transmitted in the network weights through the different combinations of four different nodes (C,G,A,T) rather than the value of nodes themselves where the output layer of nodes replicates the input layer as the genome. This innovative genetic algorithm is inserted in a complex deep learning structure that emulates the human brain on Section 4: Reinforcement Learning takes fast local current decisions, Deep Learning clusters provide identity and memory, Deep Learning Management Clusters takes final strategic decisions and finally Genetic Learning transmits the information learned to future generations. This innovative model has been applied and validated in Fintech, a Smart Investment application on Section 5; an Intelligent Banker that performs Buy and Sell decisions on several assets with an associated market and risk. The results shown on Section 6 are promising; the Intelligent Banker takes the right decisions, learns the variable asset price, makes profits on specific markets at minimum risk and finally it transmits the information learned to future generations.

2

Related work

Artificial Neural Networks have been applied to make financial predictions. Leshno, M. et al [START_REF] Leshno | Neural network prediction analysis: The bankruptcy case[END_REF] evaluate the bankruptcy prediction capability of several neural network models based on the firm's financial reports. Chen, W. et al [START_REF] Chen | Using neural networks and data mining techniques for the financial distress prediction model[END_REF] uses Artificial Neural Networks for a financial distress prediction model. Kara, Y. et al [START_REF] Kara | Predicting direction of stock price index movement using artificial neural networks and support vector machines: The sample of the Istanbul Stock Exchange[END_REF] apply an Artificial Neural Network to predict the direction of Stock Market index movement.

Guresen, E. [START_REF] Guresen | Using artificial neural network models in stock market index prediction[END_REF] evaluates the effectiveness of neural network models in stock market predictions. Zhang, G. et al [START_REF] Zhang | Artificial neural networks in bankruptcy prediction: General framework and cross-validation analysis[END_REF] analyse Artificial Neural Networks in bankruptcy prediction. Kohara, K. et al [START_REF] Kohara | Stock Price Prediction Using Prior Knowledge and Neural Networks[END_REF] investigate different ways to use prior knowledge and neural networks to improve multivariate prediction ability. Sheta, A. et al [START_REF] Sheta | A Comparison between Regression, Artificial Neural Networks and Support Vector Machines for Predicting Stock Market Index[END_REF] compares Regression, Artificial Neural Networks and Support Vector Machines for predicting the S&P 500 Stock Market Price Index. Tung, T. et al [START_REF] Khuat | An Application of Artificial Neural Networks and Fuzzy Logic on the Stock Price Prediction Problem[END_REF] includes Artificial Neural Networks and Fuzzy Logic for market predictions. Pakdaman, M. et al [START_REF] Naeini | Stock market value prediction using neural networks[END_REF] use a feedforward multilayer perceptron and an Elman recurrent Network to predict a company's stock value. Iuhasz, G. et al [START_REF] Iuhasz | Neural Network Predictions of Stock Price Fluctuations[END_REF] create a hybrid system based on a multi Agent Architecture to analyse Stock Market behaviour to improve the profitability in a short or medium time period investment. Nicholas, A. et al [START_REF] Nicholas | Stock performance modeling using neural networks: A comparative study with regression models[END_REF] examine the use of neural networks in stock performance modelling.

Several survey papers haven been published. Bahrammirzaee, A. [START_REF] Bahrammirzaee | A comparative survey of artificial intelligence applications in finance: artificial neural networks, expert system and hybrid intelligent systems[END_REF] presents a comparative survey of Artificial Intelligence Applications in Finance: Artificial Neural Networks, Expert System and hybrid intelligent systems. Coakley, J. et al [START_REF] Coakley | Artificial Neural Networks in Accounting and Finance: Modeling Issues[END_REF] reviews the use of Artificial Neural Networks in Accounting and Finance including modeling issues and guidelines. Fadlalla, A et al [START_REF] Fadlalla | An Analysis of the Applications of Neural Networks in Finance[END_REF] analyses the applications of Neural Networks in Finance. Huang, W. et al [START_REF] Huang | Neural Networks in Finance and Economics Forecasting[END_REF] reviews the use of neural networks in finance and economics forecasting. Li, Y. et al [START_REF] Li | On neural networks and learning systems for business computing[END_REF] summarize different applications or artificial intelligence technologies in several domains of business administration including finance, retail, manufacturing and management consultancy.

Machine learning has been applied to solve nonlinear models in continuous time in economics and finance by Duarte, V. [START_REF] Duarte | Macro, Finance, and Macro Finance: Solving Nonlinear Models in Continuous Time with Machine Learning[END_REF] and forecasting the volatility of asset prices by Stefani, J. et al [START_REF] Stefani | Machine Learning for Multi-step Ahead Forecasting of Volatility Proxies[END_REF]. Deep Learning has also recently incorporated in long short term memory Neural Networks for financial market predictions by Fischer, T. et al [START_REF] Fischer | Deep learning with long short-term memory networks for financial market predictions[END_REF] and Hasan, A. et al [START_REF] Hasan | Predicting financial market in big data: Deep learning[END_REF].

Genetic Algorithms have been proposed as method to increase learning. Arifovic, J. [START_REF] Arifovic | Genetic algorithms and inflationary economies[END_REF] analyses genetic algorithms in inflationary economies. Kim, K. et al [START_REF] Kim | Genetic algorithms approach to feature discretization in artificial neural networks for the prediction of stock price index[END_REF] uses a genetic Algorithm to feature discretization in artificial neural networks for the prediction of stock market index. Ticona, W. et al [START_REF] Ticona | Hybrid model based on genetic algorithms and neural networks to forecast tax collection: Application using endogenous and exogenous variables International Conference on Electronics[END_REF] applies a hybrid model based on Genetic algorithm and Neural Networks to forecast Tax Collection. Hossain, D. et al [START_REF] Hossain | Genetic Algorithm Based Deep Learning Parameters Tuning for Robot Object Recognition and Grasping[END_REF] present a Genetic Algorithm based Deep Learning Method. Sremath, S. [START_REF] Tirumala | Implementation of Evolutionary Algorithms for Deep Architectures[END_REF] and David, O. et al [START_REF] David | Genetic algorithms for evolving deep neural networks[END_REF] review of the latest deep learning structures and evolutionary algorithms that can be used to train them.

3

The Random Neural Network Genetic Deep Learning Model

The Random Neural Network

The RNN [START_REF] Gelenbe | Random Neural Networks with Negative and Positive Signals and Product Form Solution[END_REF][START_REF] Gelenbe | Learning in the Recurrent Random Neural Network[END_REF][START_REF] Gelenbe | G-Networks with Triggered Customer Movement[END_REF] represents more closely how signals are transmitted in many biological neural networks where they travel as spikes or impulses, rather than as analogue signal levels. The RNN is a spiking recurrent stochastic model for neural networks. Its main analytical properties are the "product form" and the existence of the unique network steady state solution. The Random Neural network has been Genetics [START_REF] Gelenbe | A class of genetic algorithms with analytical solution[END_REF][START_REF] Gelenbe | Steady-state solution of probabilistic gene regulatory networks[END_REF][START_REF] Gelenbe | Genetic algorithms for route discovery[END_REF][START_REF] Gelenbe | Dealing with software viruses: a biological paradigm[END_REF][START_REF] Gelenbe | Network of interacting synthetic molecules in equilibrium[END_REF][START_REF] Kim | Anomaly detection in gene expression via stochastic models of gene regulatory networks[END_REF][START_REF] Kim | Stochastic gene expression modeling with hill function for switch-like gene responses[END_REF][START_REF] Kim | Reconstruction of Large-scale Gene Regulatory Networks using Bayesian Model Averaging[END_REF][START_REF] Gelenbe | Natural Computation[END_REF][START_REF] Kim | Identifying disease candidate genes via large-scale gene network analysis[END_REF].

The Random Neural Network with Multiple clusters

Deep Learning with Random Neural Networks is described by Gelenbe, E. and Yin, Y. [START_REF] Gelenbe | Deep learning with random neural networks[END_REF][START_REF] Yin | Deep Learning in Multi-Layer Architectures of Dense Nuclei[END_REF][START_REF] Yin | Single-cell based random neural network for deep learning[END_REF]. This model is based on the generalized queuing networks with triggered customer movement (G-networks) where customers are either "positive" or "negative" and customers can be moved from queues or leave the network. G-Networks are introduced by Gelenbe, E. [START_REF] Gelenbe | G-Networks: A Unifying Model for Neural Nets and Queueing Networks[END_REF][START_REF] Fourneau | G-Networks with Multiple Class Negative and Positive Customers[END_REF]; an extension to this model is developed by Gelenbe, E. et al [START_REF] Gelenbe | Random Neural Networks with Synchronized Interactions[END_REF] where synchronised interactions of two queues could add a customer in a third queue.

q 1 q k q 2 q n Cluster Neuron 1 Neuron 2 Neuron k Neuron n λ + q u w -(u) λ -

Fig. 2. Clusters of Neurons

Deep Learning management cluster

The Deep Learning management cluster was proposed by Serrano, W et al [START_REF] Serrano | An Intelligent Internet Search Assistant Based on the Random Neural Network[END_REF][START_REF] Serrano | A Big Data Intelligent Search Assistant Based on the Random Neural Network[END_REF][START_REF] Serrano | Intelligent Search with Deep Learning Clusters[END_REF][START_REF] Serrano | The Deep Learning Random Neural Network with a Management Cluster[END_REF]. It takes management decisions based on the inputs from different Deep Learning clusters.

Genetic Learning Algorithm model

The proposed Genetic learning algorithm is based on the auto encoder presented by Gelenbe, E. and Yin, Y. [START_REF] Gelenbe | Deep learning with random neural networks[END_REF][START_REF] Yin | Deep Learning in Multi-Layer Architectures of Dense Nuclei[END_REF][START_REF] Yin | Single-cell based random neural network for deep learning[END_REF] based on two instances of the Network shown on Figure 3, the auto encoder models the genome as it codes the replica of the organism that contains it. Network 1 is formed of U input neurons and C clusters and Network 2 has C input neurons and U clusters. The organism is represented as a set of data X which is a U vector X Є [0,1] U . The proposed Genetic learning algorithm fixes C to 4 neurons that represent the four different nucleoids G, C, A and T and it also fixes W 1 to generate 4 different types of neurons rather than random values.

Network 1 encodes the organism, it is defined as:

 q 1 =(q 1 1, q 1 2, … , q 1 u ), a U-dimensional vector q 1 Є [0,1] U that represents the input state q u for neuron u;  W 1 is the U x C matrix of weights w 1 -(u,c) from the U input neurons to the neurons in each of the C clusters;

 Q 1 =(Q 1 1, Q 1 2, … , Q 1 c ), a C-dimensional vector Q 1 Є [0,1]
C that represents state q c for the cluster c where Q 1 =ζ(W 1 X).

Network 2 decodes the genome, as the pseudo inverse of Network 1, it is defined as:

 q 2 =(q 2
1, q 2 2, … , q 2 c ), a C-dimensional vector q 2 Є [0,1] C that represents the input state q c for neuron c with the same value as

Q 1 =(Q 1 1, Q 1 2, … , Q 1 c );  W 2 is the C x U matrix of weights w 2
-(c,u) from the C input neurons to the neurons in each of the U cells;  Q 2 =(q 2 1, q 2 2, … , q 2 u ), a U-dimensional vector Q 2 Є [0,1] U that represents the state q u for the cell u where Q 2 =ζ(W 2 Q 1 ) or Q 2 =ζ(W 2 ζ(XW 1 )). (u,c)

q 1 Q 1 1 -Cluster 1 q 1 q 1 q 1 q c Q 1 c -Cluster c q c q c q c q 1 q 2 q k q u q 1 q 2 q k q u w 2 - (u,c) Q 1 1 -Cluster 1 = Nucleoid C 0.00 < C ≤ 0.25 Q 1 2 -Cluster 2 = Nucleoid G 0.25 < G ≤ 0.50 Q 1 3 -Cluster 3 = Nucleoid A 0.50 < A ≤ 0.75 Q 1 4 -Cluster 4 = Nucleoid T 0.75 < T < 0.99

Fig. 3. Genetic Learning Algorithm

The learning algorithm is the adjustment of W 1 to code the organism X into the four different neurons or nucleoids and then calculate W 2 so that resulting decoded organism Q 2 is the same as the encoded organism X:

min‖X-ζ(W 2 ζ(XW 1 ))‖ s.t. W 1 ≥0
(1) Following the Extreme Learning Machine on [START_REF] Kasun | Representational learning with extreme learning machine for big data[END_REF]; W 2 is calculated as:

W 2 =pinv(ζ(XW 1 ))X
(2) Where pinv is the Moore-Penrose pseudoinverse:

pinv(x)=(x T x)x T

Asset Banker Reinforcement Learning

The Reinforcement Learning algorithm is used to take fast binary investment decisions "Buy or Sell", it is based on Cognitive Packet Network presented by Gelenbe, E. [START_REF] Guresen | Using artificial neural network models in stock market index prediction[END_REF][START_REF] Zhang | Artificial neural networks in bankruptcy prediction: General framework and cross-validation analysis[END_REF][START_REF] Kohara | Stock Price Prediction Using Prior Knowledge and Neural Networks[END_REF][START_REF] Sheta | A Comparison between Regression, Artificial Neural Networks and Support Vector Machines for Predicting Stock Market Index[END_REF][START_REF] Khuat | An Application of Artificial Neural Networks and Fuzzy Logic on the Stock Price Prediction Problem[END_REF]. The Intelligent Banker is formed of two interconnected neurons "q 0 or Buy" and "q 1 or Sell" where the investment decision is taken according to the neuron that has the maximum potential. The state q 0 and q 1 is the probability that it is excited [START_REF] Guresen | Using artificial neural network models in stock market index prediction[END_REF][START_REF] Zhang | Artificial neural networks in bankruptcy prediction: General framework and cross-validation analysis[END_REF][START_REF] Kohara | Stock Price Prediction Using Prior Knowledge and Neural Networks[END_REF][START_REF] Sheta | A Comparison between Regression, Artificial Neural Networks and Support Vector Machines for Predicting Stock Market Index[END_REF][START_REF] Khuat | An Application of Artificial Neural Networks and Fuzzy Logic on the Stock Price Prediction Problem[END_REF], these quantities satisfy the following system of non linear equations:

q 0 = λ + (0) r(0)+λ(0) q 1 = λ + (1) r(1)+λ(1)
(3) where:

λ + (0) = q 1 w 10 + +Λ 0 λ + (1) = q 0 w 01 + +Λ 1 λ -(0) = q 1 w 10 -+λ 0 λ -(1) = q 0 w 01 -+λ 1 r(0) = w 01 + +w 01 r(1) = w 10 + +w 10 -(4) On the above equations, w + ij is the rate at which neuron i transmits excitation spikes to neuron j and w - ij is the rate at which neuron i transmits inhibitory spikes to neuron j in both situations when neuron i is excited. Λ i and λ i are the rates of external excitatory and inhibitory signals respectively. Buy Neuron 0 The Reward R is based on the economic profit that the Asset Bankers achieve with the decisions they make, successive measured values of the R are denoted by R l , l=1,2… these are used to compute the Predicted Reward:

q 0 = q 1 Sell w + 01 q 1 q 0 w - 10 w + 10 w - 01 Λ 0 λ 0 Λ 1 λ 1 Sell Neuron 1 λ + (0) r(0)+λ -(0) q 1 = λ + (1)
PR l =αPR l-1 + (1-α)R l (5) where α represents the investment reward memory.

If the observed measured Reward is greater than the associated Predicted Reward; Reinforcement Learning rewards the decision taken by increasing the network weight that point to it, otherwise; it penalises it.

Experimental results

"GoldAI Sachs" is evaluated with eight different assets to assess the adaptability and performance of our proposed Smart Investment solution for eleven days. The assets are split into the Bond Market with low risk and slow reward and the Derivative Market with high risk and fast reward. Experiments are carried with very reduced memory α =0.1 where the Reinforcement Learning is first initialized with a Buy Decision.

Bond Market

Asset Banker Reinforcement Learning Validation

Table 1 represents the Profit that each Asset Banker makes when buying or selling 100 Assets for 11 days with the Maximum Profit, the number of winning decisions against the losing ones and the number of buy decisions against the sell. The Profit made in assets that start downwards such as Asset 2, Asset 4, Asset 6 and Asset 8 is worse than the upwards ones because the Asset Bankers are initialized with a buy decision. The Reinforcement Learning Algorithm adapts very quickly to variable asset prices.

Market Banker Deep Learning Management Cluster Validation

The profits the Market Bankers can make are shown in Table 2 and Table 3. The Market Bankers take market decisions rather than individual asset decisions form the Asset Bankers. Market Bankers invests 400 assets which is the combination of the four Asset Bankers purchasing power.

Genetic Algorithm Validation

The Genetic Algorithm validation for the four different Nucleoids (C,G,A,T) during the 11 different days is shown in Table 5 with the Genetic Algorithm Error.

Conclusions

This paper has presented a new learning Genetic Algorithm based on the Genome where the information is transmitted in the network weights rather than the neurons. The algorithm has been incremented in an Smart Investment model that simulates the human brain with reinforcement learning for fast decisions, deep learning to memorize properties to create asset identity, deep learning management clusters to make global decisions and genetic to transmit learning into future generations .

In the Smart Investor Model, "GoldAI Sachs" Asset Banker Reinforcement Learning Algorithm takes the right investment decisions; with great adaptability to asset price changes whereas Asset Banker Deep Learning provides asset properties and identity. Market Bankers success to increase the profit by selecting the best performing Asset Bankers and the CEO Banker, "AI Morgan" increases the profits considering the associated market risks, prioritizing low risk investment decision at equal profit. Genetic learning algorithm has a minimum error and it exactly codes and encodes the CEO Banker, "AI Morgan".

Future work will validate our model in a Fintech cryptocurrency environment with real market values. In addition the relevance of memory in investment with its optimum value will be analyzed.

Appendix

Fig. 1 .

 1 Fig. 1. The Random Neural Network

Fig. 4 .

 4 Fig. 4. "GoldAI Sachs" Smart Investment Model

10 Fig. 5 .

 105 Fig. 5. Asset Banker Reinforcement Learning

Fig. 6 .

 6 Fig. 6. "GoldAI Sachs" Smart Investment Model assets

  The Smart Investment model, called "GoldAI Sachs", combines there different learnings: Reinforcement Learning, Deep Learning and Genetic Learning. "GoldAI Sachs" is formed of clusters of Intelligent Bankers that take local fast local binary decisions "Buy or Sell" on a specific assets based on Reinforcement Learning through the interactions and adaptations with the environment where the Reward is the profit made. Each Asset Banker has an associated Deep Learning cluster that memorizes asset identity such as price and reward properties. Asset bankers are dynamically clustered to different properties such as investment reward, risk or market type and managed by a Market Banker Deep Learning Management Cluster that selects the best performing Asset Bankers. Finally, a CEO Banker Deep Learning Management Cluster manages the different Bankers and takes the final investment decisions based on the Market Reward and associated Risk prioritizing markets that generate more reward at a lower Risk as every banker would do. This approach enables decisions based on shared information where Intelligent Bankers work collaborative to achieve a bigger reward.

	4	Smart Investment model
					"GoldAI Sachs" Smart Investment
	Asset	Asset	Asset	Asset	Asset	Asset	Asset	Asset	Market Place
	Asset Banker	RL DL Cluster	Asset Banker	RL DL Cluster	Asset Banker	RL DL Cluster	Asset Banker	RL DL Cluster	Asset Banker	RL DL Cluster	Asset Banker	RL DL Cluster	Asset Banker	RL DL Cluster	Asset Banker	DL RL Cluster	Binary Decisions Asset Property
		Market Banker DL Management Cluster			Market Banker DL Management Cluster		Market Reward
						CEO Banker DL Management Cluster							Market Risk
						Genetic Learning C-G-A-T						Next Generation

Table 1 .

 1 Asset Banker Reinforcement Learning Validation

	Asset	Profit	Maximum Profit	Win	Loss	Buy	Sell
	1	1000	1000	10	0	10	0
	2	800	1000	9	1	1	9
	3	600	600	6	0	10	0
	4	300	500	4	1	6	4
	5	2000	2000	8	0	4	6

Table 2 .

 2 Bond Market Banker Profits

	Day	Total Asset Banker	Bond Market	I	Maximum Asset	Maximum Market	I
	2	0	400	400.00%	200	400	100.00%
	3	200	400	100.00%	200	400	100.00%
	4	200	400	100.00%	200	400	100.00%
	5	200	400	100.00%	200	400	100.00%
	6	300	400	33.33%	300	400	33.33%
	7	200	400	100.00%	400	400	0.00%
	8	400	400	0.00%	400	400	0.00%
	9	400	400	0.00%	400	400	0.00%
	10	400	400	0.00%	400	400	0.00%
	11	400	400	0.00%	400	400	0.00%
	Total	2700	4000	48.15%	3100	4000	29.03%

Table 3 .

 3 Derivative Market Banker Profits

	Day	Total Asset Banker	Derivative Market	I	Maximum Asset	Maximum Market	I
	2	0	800.0	400.00%	800	800.0	400.00%
	3	1000	1200	20.00%	1000	1200	20.00%

Table 4

 4 represents the CEO Banker, "AI Morgan" profits at different Risks ratios with a total of investment of 800 assets. A risk value β=0.2 represents 640 assets in the Bond Market and 160 is the Derivative Market whereas a risk value β=0.8 is 160 assets in the Bond Market and 640 in the Derivative Market respectively.

Table 4 .

 4 CEO Banker Profits

	Day	B	Risk β= 0.2 D Total	B	Risk β= 0.5 D	Total	B	Risk β= 0.8 D	Total	Max Profit
	2	640	320	960	400	800	1200	160	1280	1440	1440
	3	640	480	1120	400	1200	1600	160	1920	2080	2080
	4	640	480	1120	400	1200	1600	160	1920	2080	2080
	5	640	320	960	400	800	2800	160	1280	1440	1440
	6	640	0	640	400	0	400	160	0	160	640
	7	640	-320	320	400	-800	-400	160	-1280	-1120	320
	8	640	320	960	400	800	1200	160	1280	1440	1440
	9	640	480	1120	400	1200	1600	160	1920	2080	2080
	10	640	480	1120	400	1200	1600	160	1920	2080	2080
	11	640	640	1280	400	800	1200	160	1280	1440	1440
	Total	6400	2880	9280	4000	7200	11200	1600	11520	13120	15040

Table 5 .

 5 Genetic Algorithm Validation

	Day	Error	Nucleoid-C	Nucleoid-G	Nucleoid-A	Nucleoid-T
	2	3.05*10E-31	0.2048	0.3893	0.6295	0.9268
	3	5.85*10E-31	0.2026	0.3861	0.6263	0.9259
	4	6.78*10E-32	0.2025	0.3859	0.6262	0.9259
	5	1.17*10E-31	0.2029	0.3865	0.6267	0.9260
	6	4.44*10E-31	0.2033	0.3870	0.6272	0.9262
	7	1.29*10E-31	0.2049	0.3894	0.6296	0.9269
	8	3.61*10E-31	0.2031	0.3868	0.6271	0.9261
	9	2.96*10E-31	0.2021	0.3852	0.6255	0.9257
	10	6.90*10E-31	0.2020	0.3851	0.6254	0.9256
	11	1.36*10E-31	0.2023	0.3856	0.6259	0.9258


Rubén Solozabal

Aitor Sanchoyerto

Miren Cava

Bego Blanco

Hicham Khalife

Mathieu Bouet

Damien Lavaux

Emmanouil Kafetzakis

Providing Mission-Critical services over 5G Radio Access Network

Keywords: Mobile Edge Computing, 5G, Cloud-Enabled Radio Access Network, CUPS, IOPS

5G is called to introduce a major transformation in communication network architectures with its transition to cloud native networks. This transformation will enable new unique service capabilities that will drive the development of innovative applications. But, for 5G being successful in this task, the identification of the vertical sectors' requirements is of outmost importance in order to map them into the design of the network architecture. This paper proposes a novel Cloud-Enabled Radio Access Network (CE-RAN) architecture to support Public Safety services at the edge of the network. This proposal leverages Network Functions Virtualisation, Software Defined Networking and Mobile Edge Computing principles to provide Mission-Critical services through an isolated network slice. We suggest a CE-RAN architecture with two levels of cloudification to bring the service closer to the end user.

Introduction

Even though 5G is obviously the natural evolution of current mobile broadband networks, it is called to make a disruptive change in communication network architectures, becoming the broader transition to cloud native networks. 5G is expected to bring new unique network and service capabilities, becoming a key enabler for emerging, revenue-generating 5G applications.

With this aim, the design of 5G is based on three main pillars: the flexibility of Network Functions Virtualisation (NFV), the programmability of Software Defined Networking (SDN) and the proximity to users of Mobile Edge Computing (MEC). The application of these trending technologies enables the creation of isolated service slices over the same physical network, allowing to adapt the network in order to meet the requirements of specific services.

All these forthcoming capabilities encourage the development of new applications and vertical industries. Consequently, it is also decisive for the success of 5G to identify the key vertical sectors' requirements and map them into the design of the network architecture. On this point, from Release 11 onwards 3GPP is considering the requirements of Mission-Critical (MC) communications as a central topic to address the key requirements of the next generation broadband Public Safety (PS) networks. There is a clear trend towards different forms of network sharing models as opposed to building out dedicated legacy PS networks.

In order to support the demanding set of requirements of the new verticals, 5G standardisation bodies aim to define a new Radio Access Network (RAN) architectural framework that leverages NFV and SDN to provide a complete virtualised ecosystem suitable for the execution of Virtual Network Functions (VNF). To this aim, we consider that the most appropriate place to build 5G infrastructure foundations is the edge of the network, in order to relieve the core network from the traffic that can be efficiently processed and served closer to the end user and, thus, to reduce the response time. We use Small Cell-as-a-Service (SCaaS) paradigm to build a highly flexible and scalable platform, able to support new business models and revenue streams by creating a neutral host market that reduces the operational costs by providing new opportunities for ownership, deployment, operation and amortisation.

The technical approach for exploiting the benefits of the centralisation of RAN functions is based on a two-tier architecture: a first distributed tier for providing low latency services and a second centralised tier with high processing power for access network control applications. Decoupling the control and user planes of the Radio Access Network (RAN) frees from the enormous fronthaul latency restrictions. The use of end-toend network slicing mechanisms will allow sharing the infrastructure among multiple operators/vertical industries and customising its capabilities on a per-tenant basis.

This paper is organised as follows: Section 2 defines the use case for Public Safety applications, a vertical sector that is attracting appreciable interest in the latest years. Next, in Section 3 we describe the 5G Cloud-Enabled RAN with edge computing capabilities to support the defined used case. Then Section 4 proposes a solution that exploits MEC capabilities to provide MC services. Finally, Section 5 concludes this paper.

Description of the Public Safety use case

The current trends in the Public Safety ecosystem lead towards a future Mission-Critical (MC) communications framework based on standardised commercial technologies. In the recent years, several worldwide administrations have collaborated in the 3GPP to create the first operational solution in Release 13, named Mission Critical Push to Talk (MCPTT). This solution defines the service and network level specifications to provide mission-critical services over 4G LTE technologies. Currently, Release 14 evolved the solution towards a more mature state, including also other mission-critical services such as video and data. The adoption of the solution for future 5G networks will be specified during Release 15 normative work (scheduled for 2018).

In order to provide MC services the network provider must guarantee the required levels of QoS, security / privacy and resiliency. This use case considers one or several Public Safety organisations using the resources provided by a third-party dense small cell deployment, which could be owned by the mobile network operator or by a venue owner such as the case of a stadium. In this case, the owner will exploit the proposed two-tier cloud edge platform to provide the required network slicing capabilities with dedicated characteristics to different types of tenants.

The public safety use case presented in this paper is organised in three main stages: Stage 1. In a first step, the small cell deployment owner is providing the required network slices to the different tenants (Fig. 1). Each network slice is composed by a volume of radio data rate over a coverage area (which is mapped by the edge cloud RAN Controller to a volume of small cell radio resources) and a volume of edge service capabilities (which is mapped to a volume of processing power in the lower level distributed cloud).

For the case of Public Safety organisations, normal operations may require a certain number of group communications supported in the area of the SC cluster. This requirement can be mapped to a number of radio KPIs in the SCs and the deployment of edge group communication service instances at the edge (i.e., MCPTT Application Servers deployed at the edge) to enhance the responsiveness of the service.

In addition to the QoS guarantees for each tenant, the deployment owner has to assure the required levels of isolation in the provisioning of the different network slices.

Radio slice

Edge Stage 2. In case there is an incident in the area, the Orchestrator has to be able to react to the new service requirements (illustrated on Fig. 2). A Public Safety organisation may require additional service capacity in the geographical area, in order to cope with increased number of first responders or additional types of service such as missioncritical video transmissions. Based on pre-arranged or on-demand service scaling policies, the Orchestrator would implement the new resource allocation scheme taking into account both radio (for the access connections) and cloud resources (for deploying more resource-consuming edge services).

The deployment of edge service instances serves a twofold objective: first, it enables close-to-zero delay in the mission-critical services; second, it allows maintaining the operability even when the backhaul connection is damaged.

Stage 3. Addresses the potential need for coverage extension (Fig. 3). The typical situation is that a Public Safety organisation decides to use a deployable system, e.g. to mitigate the damage of a macro base station. In the proposed use case, the deployable system also offers an (evolved) LTE connectivity to the first responders in the field, consolidating the interoperability requirements.

In order to better orchestrate the radio transmissions, the deployable system will be considered as a new small cell that can be dynamically added to the cluster. In this way, the enhanced SON and RRM features of the platform can be applied to the coverage extension unit. The connectivity of the deployable unit with the SC cluster would be made through a wireless backhauling technology.

Radio slice

Edge cloud slice Once the Public Safety use case has been outlined, the next section describes the architecture proposed to provide PS services at the edge of the cloud-based RAN.

Elas city management -Reconfigura on of underlying resources

Virtualisa on & Slicing

5G Cloud-enabled RAN with MEC capabilities

It is estimated that the user traffic volume over the mobile network will increase on the order of several magnitudes in the coming decade [START_REF] Chen | The requirements, challenges, and technologies for 5G of terrestrial mobile telecommunication[END_REF]. In addition, with the advent of Internet of Things (IoT) devices, outsourcing tasks to powerful clouds is becoming a trend due to the lack power of these devices. Nevertheless, traditional cloud services may end in a high-latency not compatible with real-time services. To overcome these problems, service providers can take advantage of MEC [START_REF] Tran | Collaborative Mobile Edge Computing in 5G Networks: New Paradigms, Scenarios, and Challenges[END_REF].

MEC allows bringing computation and network management to the edge of the mobile network, within the Radio Access Network (RAN), allowing service providers to deploy applications closer to the end-user. MEC reduces service latency as well as the bandwidth consumption since the core network is not or at least less involved in traffic between UEs and application servers. The relocation of the services on the edge of the mobile network will be of outmost importance in order to achieve technological expectations of 5G with an end-to-end latency of one milliseconds, over one million connections per square kilometre, and traffic rates ten times higher than in 4G.

Currently, MEC deployments are limited due to the lack of flexibility on the mobile network. In order to overcome these barriers, 5G will leverage NFV and SDN technologies to bring a cloud execution platform at the edge of the network [START_REF] Blanco | Technology pillars in the architecture of future 5G mobile networks: NFV, MEC and SDN[END_REF]. For all these reasons, 5G will have to face architectural changes in the RAN. ENodeBs based on specific hardware will be aggregated in centralised cloud centres within the RAN, concentrating resources to simplify its deployment and management. RAN functions will be virtually executed and ideally connected to the remote radio heads through optical fibre fronthauls, as high fronthaul delays may degrade the performance of certain novel edge services that require close-to-zero latencies as prescribed by 5G objectives, As a consequence, this execution platform will be able to provide the computational power at the edge not only to virtualise network functionality but also third-party services.

The evolution of the current RAN to that envisioned in 5G represents a great effort for network operators. Therefore, intermediary solutions as [START_REF] Fajardo | Introducing Mobile Edge Computing Capabilities through Distributed 5G Cloud Enabled Small Cells[END_REF] adopt the aforementioned principles to propose a novel distributed CE-RAN architecture evolving the traditional commercial Small Cells eNodeB (SCeNB) to Cloud Enabled Small Cells eNodeB (SCeNBce). These solutions rely on currently installed Physical Network Functions (PNF) and complement them along with a virtualised platform that supports the execution of innovative edge services as Virtual Network Functions (VNFs).

Proposals as [START_REF] Ku | 5G Radio Access Network Design with the Fog Paradigm: Confluence of Communications and Computing[END_REF] envision the coexistence of both centralised and edge cloud. This two-tier cloud-enabled RAN forms which is known as a hybrid cloud in which both centralised and edge clouds will cooperate to take advantage of the resulting peculiarities of the architecture, ending in the benefits described below.

The First-tier is the Edge Cloud. It remains distributed over a SCeNBce cluster for providing close-to-zero service latency directly from the networks' edge. The edge cloud is used to support the executions of VNFs as deep packet inspection, GTP encapsulation or distributed SON. The Edge Cloud will reduce the cost of high bandwidth fronthaul over long distances to centralised data centres while being able to provide close-to-zero latency services.

The edge cloud consists in a Multi-RAT 5G small cell cluster with its standard backhaul interface. It allows multiple core network operators to provide its services sharing the same physical infrastructure. In this environment, the small cell is the termination of the GTP-User Plane which communicates with each of the core networks.

The Second-tier is a high-scale cloud. The Central Cloud will provide high processing power for computing intensive network applications. It will benefit from its global vision of the underlaying infrastructure so as to be able to compute efficient scheduling algorithms. The central cloud hosts the RAN controller, which makes control plane decisions for all radio elements in the geographical area of the cluster, security, traffic engineering, mobility management, etc.

Both these clouds will be conceived as an integrated hybrid cloud infrastructure from the upper layers. In this context, a single orchestrator will coordinate a variety of both, being able to deploy VNFs along them in a unified manner.

3.1

Network slicing within the Radio Access Network 5G will enable logical network slicing, with which, a single physical network is partitioned into multiple virtual networks being able to personalize it for each type of services. With this technology, slices can be optimized to guarantee multiple characteristics for specific services including latency or bandwidth requirements.

In order to provide an end-to-end service, network slicing is required not only in the operator's core network but also within the RAN. Service slices must be achieved over the same physical infrastructure. Therefore, computational and radio resources need to be shared and isolated between different services and tenants. In this context, Mission-Critical (MC) services must be provided over a prioritised slice, guaranteeing the access to the needed end infrastructure. As a result, resources are delivered in an elastic manner based on on-demand service and the scaling policies applied.

The envisioned neutral RAN is an infrastructure shared between multiple virtual network mobile operators and content service providers. Guaranteeing resource isolation in a cloud environment is the key element in order to obtain an architecture capable of hosting multiple virtual network operators and vertical industries providing their services using the same infrastructure.

Radio Resource Management within the Radio Access Network

Currently, radio resource allocation remains inadequate, especially in urban areas, where, due to the increased in traffic and limited spectrum, operators may have to decrease the size of the cells. The dense deployment of small cells leads to interferences among neighbouring base stations. In order to solve this, a separation between control from data plane of the Radio Resource Management (RRM) is proposed. This way, the radio controller could be allocated in the Central Cloud, benefiting from the overall view of the underlying architecture and making decisions to the whole distributed data plane on how to operate, and reducing interference in a centralised manner and increasing the spectrum utilisation efficiency.

Therefore, the RAN evolves not only to provide multi-operator radio access, but also to achieve an increase in the capacity and the performance.

Management and orchestration of edge services

The approach for network control centralisation does not only remain for radio interfaces, but also for service managing and orchestration. The management and orchestration (MANO) will operate at multiple SCeNBces clusters at multiple point-of-presence, transforming them in a uniform virtualised environment, enabling the creation of optimization algorithms that would act over the whole deployment. The main part is the Network Function Virtualization Orchestrator (NFVO). It composes service chains and manages the deployment of VNFs over the edge cloud. The NFVO delegates the management of VNF lifecycle to the VNFM, which oversees the instantiation, update and overall scaling and termination of VNFs.

Inside the MANO an important part is the Element Management System (EMS). It provides end-user functions for management of both PNFs and VNFs. It is responsible for set the management functionalities that other entities as the Network Management System of each operator will see.

The MANO also encompasses telemetry and analysis to capture relevant indicators of the network operation, since it is responsible for the SLA agreements.

4

Deploying Mission-Critical service on MEC infrastructure Nowadays, 5G core architecture standardization is in an early stage [START_REF] Gpp | Technical Specification Group Services and System Aspects; System Architecture for the 5G System[END_REF]. It is envisioned that 5G New Radio will be first implemented using 4G EPC, give rise to what is known as 5G Non-Standalone. Therefore, the core nodes we are going to refer to belong to the legacy EPC core architecture.

The isolation that will be achieved in 5G enables the network to meet the specific requirements of services as Mission-Critical (MC) communications. As a reference, Mission-Critical Push-to-Talk (MCPTT) is an IP-based MC service that can benefit from the MEC infrastructure. This kind of service requires of a Session Initiation Protocol (SIP) core such as IP Multimedia Subsystem (IMS) to operate. An IMS aims to reach interoperability for session control in all-IP Next Generation Networks and currently are implemented as a centralized subsystem attached to the Evolved Packet Core (EPC) of each operator.

We propose to distribute MC services near the end-user, making use of MEC capabilities obtained throughout the virtualisation of the RAN. Distributing the User Plane (UP) in the proximities of the end-user benefits first responders from mouth-to-ear latency reduction. Thanks to NFV, it also enables service providers to scale the user plane on demand in specific locations straightforwardly. Distributing the service demands bringing the UP of the IMS and EPC to the edge of the mobile network. The deployment of an" IMS as a Service" (IMSaaS) and an" EPC as a Service (EPCaaS)" at the edge enables the necessary infrastructure to provide over-the-top services that otherwise would be located behind the operator's core network. As it will be discussed in the following section, it is common that none of the IMS nodes manage user data. And therefore, it will not be necessary to ensure with this layer near the user, service application located at the edge will be directly connected to the local EPC.

On the other hand, we propose to leave the Control Plane (CP) centralized due the complications that entails the synchronization of a distributed control.

4.1

Distributing core operator infrastructure at the edge of the network Extending the current EPC infrastructure next to the edge allows reducing latency, enables scaling the service horizontally in specific locations and reduces traffic over the central core network. Nevertheless, the standardized EPC by 3GPP was never designed for a centralised network architecture, where the EPC nodes are part of the Core Network: Mobility Management Entity (MME), the Home Subscriber Server (HSS), the Serving Gateway (SGW) and the Packet Data Network Gateway (PGW). Recently, 3GPP has addressed an initiative called CUPS (Control and User Plane Separation) [START_REF] Gpp | Architecture enhancements for control and user plane separations of EPC nodes" 3rd Generation Partnership Project (3GPP)[END_REF] with the aim to study possibilities for a separation of S/PGW functionality into user plane functions and control plane functions, so that the user plane functions can be placed flexibly at the edge while the control plane functions could still remain centralized.

Local edge nodes are able to manage user data plane functions of SGW (SGW-U) and PGW (PGW-U) (illustrated on Fig. 4). Nevertheless, the replication of the EPC at the edge entails some limitations. Providing a stable data path to terminals changing their point of attachment to the network is the essential issue that will drive the new architecture design. In the legacy network architectures, a terminal's user traffic is always routed through a centralised node in the core network. This centralised node acts as an anchor point for the data path and ensures that IP packets reach the terminal irrespective of its point of attachment. Mobile networks need to adopt the distributed nature of routing IP providing mobile data path management on top of a distributed architecture because, in case of unmanaged IP mobility, the transmission could be disrupted. Nevertheless, there is a way to achieve application session continuity managed in upper functional layers. For example, a session that has been established using the SIP can survive IP address changes using the mobility management support built into those protocols.

In the same way that the EPC has been partially re-located at the edge, IMS shall be replicated as well. Nevertheless, 3GPP has not specified yet how the separation between the CP/UP of the IMS would be handled.

As mentioned before, an IMS is a signalling core, it's main operation is controlling. There are some nodes in the IMS architecture that manage UP (e.g. the Media Resource Function), yet these nodes are dispensable in a basic configuration. For this reason, the IMS do not appear as layer of the UP we are deploying at the edge. And service communication with IMS centralized nodes only will take place during control operations (e.g. during communication establishment).

Therefore, an EPCaaS at the edge entails the necessary infrastructure to provide over-the-top services with independent user plane without relying in the core network, being the appropriate host MC services as MCPTT.

Isolated E-UTRAN Operation for Public Safety

A specific scenario in which public safety communications can take advantage of MEC is in case of network failure. As defined in 3GPP technical specification 22.346 [START_REF] Gpp | Isolated E-UTRAN operation for safety" 3rd Generation Partnership Project (3GPP)[END_REF], isolated E-UTRAN aims to restore the service of an eNodeB or a set of interconnected eNodeBs without backhaul connectivity. The goal of Isolated E-UTRAN Operation for Public Safety (IOPS) is to maintain the maximum level of communication for first responders when the connectivity with the EPC is either unavailable or non-ideal.

In an emergency scenario, the execution platform located in the edge of the network could be used not only to bring the core UP near end-users but also to provide the CP, resulting in a fully capable local Core able to provide MC services within the isolated zone. In that direction, policies of backhaul disconnection must be agreed, as well as a methodology to change between a fully connected eNodeB to an isolated situation.

Conclusions

Considering the envisioned disruptive capabilities of forthcoming 5G communications and the highly demanding requirements of the services that will be supported, a radical RAN paradigm change is foreseen. It is also expected that this transformation will leverage NFV, SDN and MEC technologies as key enablers of this philosophy turnaround.

We rely on the two-tier Cloud-Enabled RAN as the platform to execute the virtualised services in end-user proximity. This architecture benefits the network operator from CAPex/OPex reduction, but also provides the necessary infrastructure to share the point-of-presence between multiple operators and third-party service providers.

We present the benefits of transferring the user data plane close to the end user, both in terms of QoS and from an operation prospective. To achieve this goal a separation between user and control planes throughout the vertical infrastructure is needed. In this paper, a use case of a Mission-Critical service on MEC is described. Enabling the deployment of user plane over at the edge of the mobile network benefits the service latency, but also facilitates the deployment and scaling on demand from the operators' perspective. In future work, we will analyse the impact of applying these MEC architecture principles over key performance indicators (KPI) for a Mission-Critical service.

We conclude highlighting the opportunities of the edge architecture in an emergency scenario. Under exceptional circumstances, in which the interconnections with the operators' core or even between base stations is damaged, a complete service deployment on the described architecture is able to maintain the service locally, at the expense of service restoration.

Fig. 1 .

 1 Fig. 1. Public Safety use case Stage 1 -Default service agreement.

Fig. 2 .

 2 Fig. 2. Public Safety use case Stage 2 -Incident demanding extended capacity.

Fig. 3 .

 3 Fig. 3. Public Safety use case Stage 3 -Breakdown demanding extended coverage.

Fig. 4 .

 4 Fig. 4. Distributed MCPTT User Plane at the edge.

QoS & privacy management

Acknowledgement

The research leading to these results has been supported by the EU funded H2020 5G-PPP project ESSENCE (Grant Agreement Nº 761592) and the Spanish Government's MINECO project 5GRANVIR (TEC2016-80090-C2-2-R).


Konstantinos Demertzis
email: kdemertz@fmenr.duth.gr1

Vardis-Dimitris Anezakis
email: danezaki@fmenr.duth.gr2

Lazaros Iliadis
email: liliadis@civil.duth.gr3

Stefanos Spartalis

Temporal Modeling of invasive species' migration in Greece from neighboring countries using Fuzzy Cognitive Maps

Keywords: Fuzzy Cognitive Maps, Invasive Species, Species Distribution Model, Soft Computing Techniques, Bioclimatic Data, Climate Change Scenarios, Greece

A serious side effect of climate change is the spread of invasive species (INSP), which constitute a serious and rapidly worsening threat to ecology, to the preservation of natural biodiversity, to the protection of flora and fauna and it can even threaten human population health. These species do not seem to have particular morphological differences, despite the intense variations in their biological characteristics. This often makes their identification very difficult. The need to protect the environment and to safeguard public health requires the development of sophisticated methods for early and valid identification which can lead to timely rational management measures. The aim of this research is the development of an advanced Computational Intelligence (COIN) system, capable to effectively analyze the conditions that influence and favors spreading of invasive species, due to the problem of climate change. Fuzzy Cognitive Maps (FCM) have been used to determine the specific temporal period (in years) in which the rapidly changing average temperature and precipitation in Greece, will become identical to the respective values of the neighboring countries for the period 1996-2015. This climatic evolution will cause spread of INSP met in these Mediterranean countries, to Greece. Separate analysis has been done for several cases of invasive species. The whole analysis is based on climate change models up to 2100.

Introduction 1.1 Invasive species

The potential impacts of climate change are evident at various levels of biological organization and particularly in the disturbances of biodiversity, in the biodegradability of organisms and the emergence of invasive species [START_REF] Robert | A neutral terminology to define 'invasive' species[END_REF]. The Invasive species are entering new foreign habitats and they can stifle natural flora or fauna and harm the environment. They can even have negative social and economic impact on human health, agriculture, fisheries and food production. The usual reason for the movement of these species is search of colder climates, either because their natural environment does not meet the range of temperatures they can survive, or because they follow different species of plants or organisms that migrate to colder ecosystems. Although not all alien species are harmful, it is imperative to draw up a management plan according to their degree of risk. Control or eradication of these species and restoration of the ecosystems affected by them is necessary. Timely identification of INSP can slow down the uncontrolled expansion of the problem and it can increase the likelihood of eliminating the phenomenon before it is widely established and ultimately avoid the need for costly and long-term control efforts.

Related Literature -Innovations of the Proposed Methodology

There are some studies in the literature using statistical approaches and only a few employing Soft Computing Techniques to model the spread of invasive species in other countries. However, none of them aims in INSP expansion projection into the future, by estimating specific time intervals using fuzzy cognitive maps.

Coro et al., [START_REF] Coro | Forecasting the ongoing invasion of Lagocephalus sceleratus in the Mediterranean Sea[END_REF] constructed and produced an overall habitat suitability map and an effective geographical spread map for L. sceleratus at Mediterranean scale by using cloud computing-based algorithms to merge seven machine learning approaches. The results suggest that without an intervention, L. sceleratus will continue its rapid spread and will likely have a high impact on fisheries. Paini et al., [START_REF] Paini | Using a selforganizing map to predict invasive species: Sensitivity to data errors and a comparison with expert opinion[END_REF] using global presence/absence data of insect crop pests employed a self-organizing map (SOM) to categorize regions based on similarities in species assemblages. This technique enabled them to generate a list of species and rank them based on an index of the risk of establishment. Gevrey and Worner, [START_REF] Gevrey | Prediction of global distribution of insect pest species in relation to climate by using an ecological informatics method[END_REF] predicted the worldwide distribution of two pest species based on climatic factors. They used an artificial neural network, the multilayer perceptron, trained using the backpropagation algorithm, to model the distribution of each species. Capinha et al., [START_REF] Capinha | Predicting the impact of climate change on the invasive decapods of the Iberian inland waters: An assessment of reliability[END_REF] calculated consensus predictions for current conditions and 3 future time periods (2030, 2050 and 2080) under low and high scenarios of greenhouse gas emissions, from an ensemble of forecasts generated by 5 distinct algorithms (generalized linear models, artificial neural networks, support vector machines, random forests and alternating decision trees). Sadeghi et al., [START_REF] Sadeghi | Use of support vector machines (SVMs) to predict distribution of an invasive water fern Azolla filiculoides (Lam.) in Anzali wetland, southern Caspian Sea, Iran[END_REF] used support vector machines (SVMs) methods in order to predict distribution pattern of Azolla filiculoides. Various structural habitat and physico-chemical variables were used as inputs and 3 classes (low, medium and high) of cover percentage of Azolla were served as output for the models. Gras et al., [START_REF] Gras | An individual-based evolving predatorprey ecosystem simulation using a fuzzy cognitive map as the behavior model[END_REF] presented an individual-based predator-prey model in which each agent behavior is modeled by a fuzzy cognitive map and allows its evolution through the epochs of the simulation. Ramsey and Norbury, [START_REF] Ramsey | Predicting the unexpected: Using a qualitative model of a New Zealand dryland ecosystem to anticipate pest management outcomes[END_REF] used a method to assist decision making using FCM. Their approach took into account interactions between pests and conservation assets in complex food webs. Also, there are some research efforts on the expansion and distribution of INSP due to climate change [START_REF] Hoveka | Effects of climate change on the future distributions of the top five freshwater invasive plants in South Africa[END_REF][START_REF] Jung | Insect distribution in response to climate change based on a model: Review of function and use of CLIMEX[END_REF][START_REF] Jung | Invasion risk of the yellow crazy ant (Anoplolepis gracilipes) under the Representative Concentration Pathways 8.5 climate change scenario in South Korea[END_REF][START_REF] Qin | Predicting the potential distribution of Lantana camara L. under RCP scenarios using ISI-MIP models[END_REF][START_REF] Wang | Expansion potential of invasive tree plants in ecoregions under climate change scenarios: an assessment of 54 species at a global scale[END_REF] but none of them for the neighboring area of Greece.

This paper proposes an innovative system that performs analysis of the climate features that favor the expansion of five invasive species to Greece from neighboring countries. Also, it proposes a model of medium and long-term forecasting of temporal periods related to the potential future identification of these INSP in Greece, due to severe changes in the country's climate til 2100. Initially, the countries in which the five INSP have been listed and their climatic conditions for the period 1996-2015 have being explored. Correlation Analysis of 12 parameters for the above time-period has been performed by using values recorded in Greece. Finding the values of the positive and negative correlations and their fuzzy Linguistics, contributes to their comprehensive representation in the modeling process of the FCM. The fuzzy values of the positive and negative correlations are introduced as weights into the FCM, thereby specifying the degree of interaction of a parameter's change to the other interconnected parameters. The future climatic AVTE and AVPRE of Greece, have been formulated on the basis of the projections of a variety of climatic models and scenarios of the latest project CMIP5 (Coupled Model Inter-comparison Project Phase5) for the period up to 2100.

Description of data

Correlation analysis of twelve bioclimatic parameters with values from Greece was performed for the period 1996-2015 [START_REF] Qin | Predicting the potential distribution of Lantana camara L. under RCP scenarios using ISI-MIP models[END_REF], in order to make a symbolic representation of the complex associations of the climatic conditions with the FCM approach. Totally, five (5) INSP were studied in this research. The four of them are included in the 100 most dangerous species of the planet and they are: Trogoderma granarium (Insect) the Acacia mearnsii (Shrub) the Trachemys scripta elegans (Reptile) and the Acridotheres tristis (Bird) [START_REF] Lowe | 100 of the World's Worst Invasive Alien Species: A selection from the Global Invasive Species Database[END_REF]. The fifth is known as Eupatorium cannabinum (Herb) and it is the most frequently recorded in 10 neighboring countries (NECO). The average temperature (AVTE) and precipitation (AVPRE) values of the 11 NECO (where the above INSP were identified) were taken into consideration.

The estimation of the future AVTEM and AVPRE values in Greece for the period 2020-2099 was based on the consideration of sixteen timely and reliable climate models of the project CMIP5.

Theoretical Frameworks and Methodology

Correlation Analysis

The relativity analysis with the Pearson(r) parametric correlation coefficient method was used to test the existence of a linear relationship between the parameters. The Pearson linear correlation coefficient of two variables Χ and Υ is defined based on a sample of n pairs of observations (x i , y i ) i=1, 2, ..., n, and it is denoted as r (X, Y) or simply as r.

The variables and are the averages of (xi, yi). The r is the covariance (Cov X, Y) of the two variables divided by the product of their standard deviations (sx, sy). It is given by the following equation 1:

(1)

The correlation coefficient is a pure number in the closed interval More specifically, when , then Χ, Υ are positively linearly correlated. When , then Χ, Υ are negatively linearly correlated. When r = 0, there is no correlation at all [START_REF] Asuero | The Correlation Coefficient: An Overview[END_REF].

Fuzzy Cognitive Maps

In the fuzzy cognitive map models, the nodes are interconnected with edges and each edge connecting two nodes, describes the variation of the state activation value of the one node, in the configuration of the state activation value of the interconnected node. The direction of the edge implies which node affects which, where the sign of the causality relationship is positive, if there is a direct relationship of influence, negative if there is an inverse relation of influence and zero if the two nodes are uncorrelated. Relations of causality usually defined by specialists are described using fuzzy linguistic variables, and they are fuzzified by using membership functions in the interval [-1,1] [START_REF] Salmeron | Dynamic Optimization of Fuzzy Cognitive Maps for Time Series Forecasting[END_REF][START_REF] Vidal | Fuzzy cognitive map-based selection of TRIZ trends for eco-innovation of ceramic industry products[END_REF].

Unlike the majority of complex dynamic systems characterized by non-linearity and great uncertainty, FCM utilize advanced learning techniques to select appropriate weights for causal interrelationships between the variables examined.

This feature helps them to capture the problem in question with absolute realism. FCM cover the need of comparing and characterizing reference sets, solving and modeling complex problems for which there is no exact mathematical model. This is achieved by employing the theoretical background of fuzzy logic. FCM are an efficient tool in modeling multiparametric problems which call for long term decisions [START_REF] Anezakis | Fuzzy cognitive maps for long-term prognosis of the evolution of atmospheric pollution based on climate change scenarios: the case of Athens[END_REF][START_REF] Anezakis | [END_REF].

Climate change scenarios employed

Our research team has already modeled complex systems concerning climate change and its direct impact which is the increased concentration of atmospheric pollutants [START_REF] Anezakis | Fuzzy cognitive maps for long-term prognosis of the evolution of atmospheric pollution based on climate change scenarios: the case of Athens[END_REF][START_REF] Anezakis | [END_REF]. The Intergovernmental International Panel on Climate Change (IPCC) has published five reports to date. The objective of the program (CMIP5) set in the Fifth Assessment Report on Climate Change (IPCC-AR5, Assessment Report 5) was the planning of climate simulations, which aim at assessing future climate changes in both the short and the long term.

The goal is achieved using Earth System Models (ESM) and global Atmospheric-Ocean General Circulation Models (AOGCMs). In the last report (AR5) significant improvement was found in temperature and precipitation modeling mechanisms, in the study of anthropogenic effects on the environment and in the study of biochemical cycles. According to this report, four future scenarios of Green House Gases (GHGs) concentrations in the atmosphere have been developed, which are known as the Representative Concentration Pathways (RCPs).

According to the RCP2.6 scenario, a small increase in greenhouse gas emissions by the middle of the decade, would result in radiation increase to 3 W/m 2 by 2050, followed by a decrease to 2.6 W/m 2 by the year 2100. Based on the RCP4.5 and RCP6.0 scenarios, moderate increases in greenhouse gas emissions, would result in a standard increase of the radiation values. Based on the RCP4.5, the radiation values will be stabilized at about 4.5 W/m 2 before 2100, while based on the RCP6.0 they will be stabilized at 6.0 W/m 2 after 2100. Finally, according to the most extreme scenario (RCP8.5) which includes a rapid and continuous increase in greenhouse gas concentrations, the radiation will increase above 8.5 W/m 2 and it will continue to have an increasing trend for a certain period after 2100. The following climate models bcc_csm1_1, bcc_ csm1_1_m, ccsm4, cesm1_cam5, csiro_mk3_6_0, fio_esm, gfdl_cm3, gfdl_esm2m, giss_e2_h, giss_e2_r, ipsl_cm5a_mr, miroc_esm, miroc_esm_chem, miroc5, mri_cgcm3, noresm1_m included in the project CMIP5, were employed in this research as the most timely and reliable ones for the estimation of temperature and precipitation future fluctuations for the period 2020-2099 [START_REF] Scafetta | ACRIM total solar irradiance satellite composite validation versus TSI proxy models[END_REF].

Description of the proposed methodology

The basic methodology aims in modeling the occurrence of invasive species in Greece and moreover in predicting the time-period required for the Greek average temperature and precipitation values to become equal to the ones of the neighboring countries. It includes 4 distinct algorithmic stages (Modeling, Grid, Scenarios and Forecasting).

In the first step (modeling) all associated parameters are added and named. They are interconnected with synapses in order to develop the causative negative or positive correlations.

The Fuzzification of the obtained correlations is related to the description of any interconnections between features, with Linguistic terms. This has been implemented by selecting the following six terms: Low Positive (denoted in the FCM as +), Moderate Positive (++), High Positive (+++)), Negative (denoted as -), Moderate Negative (--), High Negative (---)). These linguistics, represent the Fuzzy weights (see Table 1).

Table 1. Linguistics describing the effect and their corresponding fuzzy weight value

The following table 2 includes the Fuzzy Classification of the correlations among the features of interest.

Step 3 (Grid): This step simulates the interactions between the FCM nodes. This is done by employing an iterative process, which calculates the updated value of each node. This value depends on the ones of the starting edges that point to it, and on the weight assigned to the acne that joins them. Transfer functions are used to transform the result of the sum of the Products of node activation values. A new node value is calculated and the corresponding weight of the connecting edge is estimated and assigned. This is practically the case that transfers the actual value of each variable in the closed interval [-1,1]. The negative type of influence is shown in orange and the positive in blue. The degree of influence depends on the thickness of each line. The greater the effect, the thicker the line is, as shown in Fig. 2 (Table 3). The parameters used in the correlation analysis and in the development of the fuzzy cognitive map, are related to Greek data vectors for the period 1996-2015. The degree of influence between involved variables is depicted in Temperature and precipitation changes due to climate change for the period 2020 to 2099 have been fuzzified and proper linguistics have been developed. The whole process was based on sixteen climatic models as well as on extensive testing of a variety of climate scenarios for Greece (RCP2.6, RCP4.5, RCP6.0, RCP8.5). At this stage the mean average temperature value and the mean average precipitation for Greece (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) were estimated to be 15.66 O C and 45.81mm respectively.

+++ --- +++ -- --- -- +++ --- - +++ +++ airtemp +++ 1 --- +++ -- --- -- +++ --- + +++ +++ fd --- --- 1 --- ++ +++ ++ --- ++ + --- --- pet +++ +++ --- 1 -- --- -- +++ --- + +++ +++ P -- -- ++ -- 1 ++ ++ -- ++ - -- -- rh --- --- +++ --- ++ 1 ++ --- +++ -- --- --- sm -- -- ++ -- ++ ++ 1 -- ++ ++ -- -- sf +++ +++ --- +++ -- --- -- 1 --- + +++ +++ wd --- --- ++ --- ++ +++ ++ --- 1 - --- --- ws - + + + - -- ++ + - 1 - + wvp +++ +++ --- +++ -- --- -- +++ --- - 1 +++ wvsp +++ +++ --- +++ -- --- -- +++ --- + +++ 1
---+++ -------+++ ---+ +++ +++ P -- -- ++ -- 1 ++ ++ -- ++ - -- --
Step 4 (Scenarios):

Step 4 performs classification of the parameters based on the future changes of the average temperature and precipitation of Greece, as they were estimated by the sixteen climate models. Four overlapping TRIMF and eight Semi-TRIMF were employed to fuzzify the crisp values of the parameters involved.

Regarding the period 2020-2099 two TRIMF and four Semi-TRIMF were applied on the crisp values of the average monthly temperature (AVTE) values that ranged in the closed interval [-0.98 O , +8.93 O ]. The 1st Semi-TRIMF, the first TRIMF and the 2nd Semi-TRIMF were applied on the reduction of the AVTE in the interval [-0.98 O , 0 O ]. These FMF correspond to the following fuzzy Linguistics: Low Negative (-), Moderate Negative (--), and High Negative (---) with the last containing values close to the highest estimated reduction.

The next Semi-TRIMF, the TRIMF and the last Semi_TRIMF were used for the increase of the AVTE. These FMF correspond to the Low Positive (+), Moderate Positive (++), High Positive (+++), with the late being close to the maximum temperature increase. In the same way, two TRIMF and four Semi-TRIMF were developed for the precipitation. Step 5: It includes extensive testing on various scenarios based on potential changes in average temperature and precipitation and their effect on other parameters.

Step 6 (Forecasting): The fuzzy Linguistics generated by considering the mentioned climate change scenarios are de-fuzzified in order to produce crisp future values related to all interconnected parameters. In this way a future projection regarding the appearance of invasive species in Greece (due to climate change) can be achieved.

For the defuzzification the centroid function was used which estimates the center of gravity of the fuzzy set distribution.

(3)

Step 7: The index of the magnitude of change for the other correlated parameters is calculated based on the amount of relative change of each parameter as it is given in equation 4.

Results and Discussion

The following table 5 presents the changes of the average temperature and average precipitation in Greece (for the four future periods A, B, C, D) based on the historical values of the period 1996-2015. Based on climate changes models, there are five countries where the Combination of Average Temperature and Precipitation (CATEP) (for the period 1996-2015) will become identical with the future respective values for Greece (2020-2099) namely: Cyprus, Italy, Lebanon, Portugal and Israel (Tables 5, 6 and7). The future CATEP intervals for Greece were fuzzified in order to estimate the temporal intervals for the appearance of specific Invasive Species. A variety of scenarios have been examined. Based on them and on the application of two climate models, the species Acacia mearnsii is expected to appear in the country during the period 2020-2039. This could be caused by the combination of a small increase +0.1 O C in the Average Temperature (AVTE) denoted as (+) with a High increase (+++) of the Average Precipitation (AVPRE) by +41.22mm. The combined effect of a small decrease (-) of the AVTE (-0.23 O C) with a small increase (+) of the AVPRE (+12.98 mm) would have similar result. The future values for these parameters in Greece from 2020 to 2039 will be identical to the corresponding values of Italy and Portugal for the period 1996-2015 (Table 7). The species Acacia mearnsii which appeared in Israel from 1996 to 2015 is expected to appear in Greece during the period 2080-2099, due to the combined Moderate increase (++) of the AVTE (+3.91 O C) and the Moderate decrease of AVPRE (---) (-28.09mm) (Table7). For the Acacia mearnsii the combined AVTE and AVPRE values (1996-2015) of the three countries (Italy, Portugal, Israel) will be identical with the corresponding values for Greece for the period 2080-2099. The Acacia mearnsii has been recorded (for the period 1996-2015) in four Mediterranean countries (Italy, Portugal, Spain, Israel). The species Eupatorium cannabinum (Ec) and Trogoderma granarium (Tg) are expected to appear in Greece from 2020-2039 because during these 20 years the Average Temperature and Precipitation (ATE_PR) in the country will become identical to the respective ones related to the time interval 1996-2015 in Lebanon, Italy and Portugal. The Eupatorium cannabinum (Ec) will increase the likelihood of appearance in Greece for the period 2080-2099, since at that time its ATE_PR will be similar to the ones of the 1996-2015 period, in 5 out of 10 countries (Tables 6 and7). The Trogoderma granarium (Tg) will have an increased likelihood to migrate in Greece in the temporal zone 2040-2059. The Trachemys scripta elegans (Tse) will be migrating to Greece from 2080-2099 due to the very close similarity between Greece's ATEPR (during these 20 years) and the ones of Italy and Israel for the period (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). The combination of the small temperature increase (+) with the high increase of precipitation mm (+++) results in the highest fluctuations for all interconnected parameters. On the other hand, the combination of Moderate average temperature increase (++) and the highest precipitation decrease in mm (---) causes mainly changes in the soil moisture. Overall, the highest positive relative change is observed in the soil moisture (+0.08) which is mainly determined by the mm of precipitation (+++).

Conclusions and Future Work

This paper proposes an innovative Soft Computing approach that estimates the temporal period in which five invasive species will be migrating to Greece. It is predicting the temporal period of their appearance based on the expected changes in average temperature and precipitation values in the country by 2100 due to climate change. Correlation Analysis has been performed with data from Greek repositories, related to twelve parameters for the period 1996-2015. The correlations have been fuzzified and the obtained Fuzzy Linguistics enabled the development of FCM. The model calculated the time-period during which the five most dangerous INS will expand in Greece. The projection of the AVPRE and AVTE of the country to the future, was based on sixteen well known and accepted climate models from today till 2100. In the near future we wish like to employ optimization methods like Genetic Algorithms and to combine them with heuristic approaches. Such hybrid modelling could enhance the dynamics of the system offering more effective and reliable results.

Fig 1 . 2 :

 12 Fig 1. Flowchart of the proposed model

Fig 2 .Fig 2 .

 22 Fig 2. The developed FCM connecting air temperature and precipitation with other variables

Table 9 .

 9 Related changes of the involved climate parameters as a result of the changes in the AVTE and AVPRE for the period 2080

Table 2 .

 2 Fuzzification of the correlation with corresponding Linguistics

		aah	airtemp	fd	pet	P	rh	sm	sf	wd	ws	wvp wvsp
	aah	1

Table 3 .

 3 Degree of influence of the average Temperature (airtemp) and average Precipitation to the other climatic variables

	aah airtemp fd pet P rh sm	sf	wd ws wvp wvsp
	airtemp +++	1

Table 4 .

 4 TRIMF and Semi-TRIMF boundary values for the Average Monthly Temperature and Precipitation in Greece.

	Fuzzy Sets	TRIMF and Semi-	TRIMF and Semi-
	corresponding to Average	TRIMF boundaries	TRIMF boundaries
	Monthly Temperature and	(AVTE in C degrees)	(Precipitation mm)
	Monthly precipitation
	changes
	---(Semi-TRIMF)	[-0.98 -0.588]	[-29.98 -17.99]
	--(TRIMF)	[-0.882 -0.49 -0.098]	[-26.98 -14.99 -2.998]
	-(Semi-TRIMF)	[-0.392 0]	[-11.99 0]
	+ (Semi-TRIMF)	[0 3.572]	[0 20.91]
	++ (TRIMF)	[0.893 4.465 8.037]	[5.232 26.15 47.06]
	+++ (Semi-TRIMF)	[5.358 8.93]	[31.38 52.29]

Table 5 .

 5 The intervals of the average monthly Temperature and Precipitation changes in Greece, for four future temporal periods till 2099

	Future	Boundaries of future average	Boundaries of future average
	Periods	monthly temperature change	monthly precipitation change
		(in Celcium degrees)	(mm)
	1996-2015	15.66 O C	45.81mm
	A 2020-2039	[-0.98 0] [0 +4.2]	[-21.95 0], [0 +49.18]
	B 2040-2059	[-0.75 0] [0 +5.55]	[-24.19 0] ,[0 +52.29]
	C 2060-2079	[-0.7 0] [0 +6.84]	[-27.37 0], [0 +49.26]
	D 2080-2099	[-0.8 0],[0 +8.93]	[-29.98 0] ,[0 +48.78]

Table 6 .

 6 Average monthly Temperature and Precipitation changes in Greece for the period 2020-2099. It determines the expansion of 5 INSP (recorded in 11 countries)

	Countries	Crisp	Crisp	Countries	Crisp	Crisp
		Values of	Values of		Values of	Values of
		temperature	precipitation		temperature	Precipitation
		change	change		change	change
		(Greece	(Greece		(Greece	(Greece
		2020-2099)	2020-2099)		2020-2099)	2020-2099)
	Cyprus	+4.29 O C	+15,52mm	Spain	-3.63 O C	-8.29mm

Table 7 .

 7 Presentation of: a) Changes in CATEP b) Estimated temporal period for the invasive species appearance in Greece

	Species-	Appearance in	Crisp Values of	Crisp Values of
	Countries	Greece	temperature change and	Precipitation change and
	1996-2015		fuzzy linguistics	fuzzy linguistics
	Am-Italy
	Am-Portugal

Table 8 .

 8 Countries where invasive species have been recorded 1996-2015

	Species			Countries
	Acacia mearnsii	I Is	P	Sp
	Acridotheres tristis		Is		Sp	T
	Eupatorium	I	Is	P	Sp	T	A	B	C	L	S
	cannabinum	I	Is		Sp
	Trachemys scripta	I		P	Sp	T		B	C	L	S	E
	elegans
	Trogoderma granarium
	* Italy=I, Israel=Is, Portugal=P, Spain=Sp, Turkey=T, Albania=A, Bulgaria=B,
	Cyprus=C, Lebanon=L, Syria=S, Egypt=E