Annabelle Mercier
email: annabelle.mercier@emse.fr

Michel Beigbeder
email: michel.beigbeder@emse.fr

Sphere of influence Model in Information retrieval

We present a new method based on fuzzy proximity for scoring and ranking relevant documents according to the user's information need. Our study takes place in the information retrieval domain and uses the terms localization in documents, we assume that the more the occurrences of the query terms are found close to each other in a document the more this document must be in the top of the retrieved document list. After a brief description of some traditional models and the few approaches which use proximity between the occurrences of terms, we present our "sphere of influence" model which scores documents according to the fuzzy proximity between the query terms in them. First, we detail this model and then we demonstrate that our model includes the traditional ones.

I. INTRODUCTION

The information retrieval domain which is well known with the www search engines uses different models. These models give a way to select and rank documents answering user's information needs. There are three main kinds of models [START_REF] Baeza-Yates | Modern Information Retrieval[END_REF] : (i) set theoretic models (Boolean model, fuzzy set model and extended Boolean model) (ii) algebraic models (vector model and latent semantic indexing) and (iii) probabilistic models (inference network, bayesian network and belief network).

Our focus is on the two first kinds of models and on one of the first ideas about IR given by Luhn [START_REF] Luhn | The automatic creation of literature abstracts[END_REF] : "It is here proposed that the frequency of word occurrences in an article furnishes a useful measurement of word significance. It is further proposed that the relative position within a sentence of words having given values of significance furnishes a useful measurement for determining the significance of sentences. The significance factor of a sentence will therefore be based on a combination of these two measurement".

The first aspect, dealing with term frequency, was developed in the algebraic models but the second, about the relative position of words -thus the term occurrence proximity -wasn't deeply studied.

First of all, the section 2 reminds two classical information retrieval models and the few approaches using term proximity. Then, the section 3 presents our sphere of influence model. Afterwards, we explain how we can derive boolean and vector method in our model. Finally, the section 5 presents the conclusion.

II. STATE OF THE ART

Information retrieval systems based on classical models use an indexing method to build the documents representation. The index is usually grounded on term occurrences. In this study, T is the set of terms and D the set of documents.

In the classical Boolean model, each document is represented by the set of terms occurring in its text and the query is a boolean expression. The query is represented by a tree whose leaves are terms and nodes are AND and OR operators. In this model, the relevance decision criterion is binary : the document score is in the set {0, 1}. So the main drawback is that the responses cannot be ranked. Nevertheless, the main advantage is that the query language is quite expressive.

Various models are based on term frequencies which catch the Luhn's first idea. In the vector model the weight w (d , t ) of the term t in the document d usually depends in increase order on term frequency and in decrease order on document frequencythat is to say the number of documents where a given term occurs. The document score can be computed with various formulas based on the tf •idf scheme (tf stands for term frequency and idf stands for inverse document frequency). Documents and queries are represented by term vectors. The similarity measure between a document and a query can be taken as the cosine of the angle between the document and the query vectors. The query model is a bag of words so it is simple but less expressive than the Boolean one. The main advantage of this model over the Boolean one is the capacity to arrange documents according to their score, so they can be shown in decrease system relevance order to the user. This ranking capacity is fundamental in information retrieval because the evaluation methods use this to compare systems. So, the lack of ranking in Boolean model led to the introduction of extended Boolean model [START_REF] Salton | Introduction to Modern Information Retrieval[END_REF] and fuzzy set models [START_REF] Miyamoto | Fuzzy Sets in information retrieval and cluster analysis[END_REF].

In order to graduate the score given by the basic Boolean model, different models based on fuzzy set theory were built [START_REF] Miyamoto | Fuzzy Sets in information retrieval and cluster analysis[END_REF]. In these models, a function µ t is associated to each term t ∈ T . This function expresses the membership level of the documents to the fuzzy set corresponding to a term t . In this model, a query is also represented by a tree. The membership level to a node with the OR operator (resp. AND) is the maximum (resp. minimum) of its sons' membership level, that is to say this node is the fuzzy union (resp. intersection) of its sons' fuzzy subsets. Finally, we have a membership level at the query tree root. This permits to score a document with a value in the interval [0, 1] which allows to rank documents on the contrary to the basic Boolean model.

These three latest models (Boolean, vector and fuzzy models) do not consider the position of term occurrences. A classic extension of Boolean model adds an operator to the query language to express proximity constraints. This operator is called NEAR, ADJacent, or WINDOW in the systems which implement it [START_REF] Salton | Extended Boolean information retrieval[END_REF]. It works like the AND operator with a constraint on the position of term occurrences. It allows to specify a maximal distance between two term occurrences. For example, if we want to find A and B with a distance of 5 or less, we give the query: A NEAR 5 B. In our model, we do not use the NEAR operator because it can only be used with leaves and its generalization to sub-trees is not consistant [START_REF] Mitchell | A note about the proximity operators in information retrieval[END_REF]. Some works deal with the implementation issues of these operators and their consequences on the index. Keen studied [START_REF] Keen | The use of term position devices in ranked output experiments[END_REF], [START_REF]Some aspects of proximity searching in text retrieval systems[END_REF] the recall and precision performances of different implementations of the proximity operator and showed that the NEAR operator improves the precision for the retrieved documents set. However, the relevance is still binary and the documents cannot be ranked. Some recent approaches straightly use term proximity to score the documents [START_REF] Clarke | Relevance ranking for one to three term queries[END_REF], [START_REF] Hawking | Proximity operators -so near and yet so far[END_REF], [START_REF] Rasolofo | Term proximity scoring for keyword-based retrieval systems[END_REF]. These methods start with the selection of intervals which contain the query terms in the documents. Each method has its own rules to select the intervals. Clarke and al. method [START_REF] Clarke | Relevance ranking for one to three term queries[END_REF], [START_REF] Clarke | Shortest substring ranking[END_REF], [START_REF] Clarke | Interactive substring retrieval: Multitext experiments for trec5[END_REF] selects the shortest intervals which contain all the query terms so that the selected intervals are not nested. In Hawking and al. method [START_REF] Hawking | Proximity operators -so near and yet so far[END_REF], for each term occurrence, the shortest interval which contains all the terms and beginning on this occurrence is selected. The Rasolfo and al. method [START_REF] Rasolofo | Term proximity scoring for keyword-based retrieval systems[END_REF] selects the intervals including two query terms and the interval length has to be less than 5 words. Then, each interval obtains a score (the shorter the interval, the higher its score) and contributes to the global score of the document. Finally, the document score is the sum of the selected intervals scores. The results with these methods are reported to be better than those obtained with the classical ones [START_REF] Mercier | Etude comparative de trois approches utilisant la proximite entre les termes de la requete pour le calcul des scores des documents[END_REF]. The next section present our model based on proximity.

III. OUR MODEL

On one hand, the Boolean model takes into account the membership of a term in a document to a term and on the other hand, the vector model takes into account the term frequency. These two models proceed with a global approach of the influence of any term, on the the score of the documents according to the query. This means that the relevance score does not depend on the position of terms occurrences. However, meaning of the sentences in a document doesn't only depend on the vocabulary used but on the arrangement of the vocabulary terms too. Thus, our model is local in the sense that we modelize the locality of term occurrences influence. At a given position, we can consider two notions of locality:

• A term proximity :

At a precise text location, are we near a query term occurrence? This proximity will be graduated and so it will be a "fuzzy proximity". • A local relevance :

Is a precise text location relevant to a query term? The more occurrences are nearby this location, the higher it will be considered relevant.

In each case, an influence function is used to represent the influence of the words. Such a function is a relation from to [0, 1] with a finite support, increasing on -, decreasing on + . Various functions can be used. Firstly, it's possible to choose different function families (Hamming, Hanning or Gaussian functions, rectangular or triangular functions and so on). Then, in a family, it's possible to choose various values for the function parameters, for instance to obtain different influence function for the query terms. In particular, we call k the parameter which allows to control the support of the function and defines the influence area length. The triangular influence function can be expressed with :

f (x )=max( k -|x | k , 0).
For one term occurrence at position i , the translation g (x )= f (xi ) of an influence function f , allows to modelize the fuzzy proximity to this occurrence (resp. the local relevance carried by this occurrence).

In both models, the query evaluation for a given document is computed from the leaves. Firstly, the local relevance value functions (resp. fuzzy proximity) of query terms associated to the tree leaves are computed. These functions are defined at each position x in the documents. Then, going upward, these functions are combined at each tree level using the functional operators assigned to the OR and AND operators. Finally, we compute the document score by integrating the local relevance value function (resp. fuzzy proximity) obtained at the query tree root.

A. Fuzzy proximity model

It is natural to consider that the fuzzy proximity value p d t (x ) to a given term t at a position x of a document d is the proximity value of the nearest occurrence of the term t . For example, consider the document of figure 1 where the term t occurs at the positions 2, 5 and 10. The fuzzy proximity value at the position x =3is that of the nearest occurrence that is to say the occurrence at the position 2.

The influence functions defined before are decreasing with regard to the distance to 0, so the fuzzy proximity function to a term occurrence are decreasing with regard to the distance to the occurrence position. So obtaining the proximity value of the nearest occurrence consists in taking the maximum of the different fuzzy proximity functions of the different occurrences :

p d t (x )= max i∈Occ(t,d) f (x -i )
where O cc(t , d ) is the set of the term t occurrences positions in the document d and f is the chosen influence function. These functionsx → p d t (x ) are associated to the query tree leaves. We now want to define the fuzzy proximity value functions at the internal nodes of the query tree. Given a node, the function will be defined with the fuzzy proximity functions of its sons.

Consider two documents, the first one including the terms B an C at the positions 7 and 12 (cf. fig. 2) and the second one including two occurrences of the term B at the same positions (cf. fig. 3). The function p d B (resp. function for these 2 documents (cf. third curve in figures 2 and 3) and this can be obtained with

♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦♦♦♦♦♦ 0 1 3 6 9 12 15 ♦♦♦♦♦♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ r d1 (B OR C) 0 1 3
♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦♦♦♦♦♦ 0 1 3 6 9 12 15 ♦♦♦♦♦♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 0 1 3 6 9 12 15 ♦♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦
p d B OR C (x )=max(p d B (x ),p d C (x )).
We generalize this by setting p d q OR q ′ = max(p q , p q ′ ) for a node which sons are not only terms but are the queries q and q ′ . This corresponds to the operation made in the fuzzy set model (section 2.3) for the union operation. With this interpretation, q OR q ′ appears as the (fuzzy) union of the fuzzy sets q and q ′ . By analogy for an AND operator, the fuzzy proximity at a node q AND q ′ is obtained with p d q AND q ′ =min(p q , p q ′ ) which corresponds to the fuzzy intersection. Moreover, our model can easily use other functions applied in fuzzy logic for the AND and OR operators [START_REF] Bouchon-Meunier | La logique floue et ses applications[END_REF], [START_REF] Zadeh | Fuzzy sets as a basis for a theory of possibility[END_REF]. For example, the OR operator can be associated to the function max(x + y -1, 0) and the AND operator to the function min(x + y , 1) with x and y taken in two different fuzzy sets. The last step is to determine the relevance score s (q, d ) for the document d according to the query q . In the vector model, the relevance score values are either inner products or cosines. Both of them are sums that can be interpreted as accumulations of pieces of relevance. The integral calculus methods capture this accumulation idea by computing the surface below a curve. So, we express the score as

♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦♦♦♦♦♦ 0 1 3 6 9 12 15 ♦♦♦♦♦♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ r (B OR C) d 1
s (q, d )= +∞ -∞ p d q (x )d x .
An approximation consists in adding the fuzzy proximity values at each position x of the document, the result is a score in + . This score depends on the fuzzy proximity of each term. We have already experimented this alternative (fuzzy proximity) of our sphere of influence model, some results are available in [START_REF] Beigbeder | Evaluating boolean queries taking into account the fuzzy proximity of term occurrences[END_REF].

B. Local relevance model

In this approach, we consider that the term occurrences give a piece of local relevance around their positions. The relevance signal is represented by an influence function like those described before. We use these functions to compute the document relevance score. First of all, we consider the signals for each query term occurrence. Then given a term t and a document d ,i n order to gather the different pieces of relevance given by each occurrence of t , at each text position we add the local relevance values (signals) computed for all the term occurrences and we express the local relevance at the text position x with

r d t (x )= i∈Occ(t,d) f (x -i ).
For the query evaluation, we have to combine the signals according to the AND and OR operators. Firstly, we consider the case of disjunctive queries. As in the proximity model, we want that the contribution of either two occurrences of the same term B or one of the term B and one of the term C are equivalent. So, we set for the OR operator

♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦♦♦♦♦♦ 0 1 3 6 9 12 15 ♦♦♦♦♦♦♦♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ 0 1 3 6 9 12 15 ♦♦♦♦♦♦♦♦♦♦ ♦♦♦♦♦♦♦ r (B OR C) d 2
r d q OR q ′ = r d q + r d q ′ .
We must define a functional operator to apply on AND nodes. If we try to use the min function as in the fuzzy proximity model, the query A AND (B OR C) leads to an incoherence. In fact, we should have r d (A AND (B OR C)) (8.5) = min(0.12, 0.12 + 0.62) = 0.12 and r d1

((A AND B) OR (A AND C)) (8.5) =min(0.12, 0.62) + min(0.12, 0.12) = 0.24 so, the Morgan's laws are not verified and we cannot use this function at the operator AND nodes of the tree. These laws can simply be verified by setting for the AND operator

r d q AND q ′ = r d q • r d q ′ .
The figures 4 and 5 show the local relevance value functions for the query (B OR C) of the two example documents, in this second model we also have the same local relevance for the query if the As in the fuzzy proximity case, the score of the document d for a given query q is defined with

s (q, d )= +∞ -∞ r d q (x )d x .
The score, in + , is totally determined by the local relevance values so it allows to take into account the relative position between terms which corresponds to the second Luhn's idea (cf. section 1).

IV. SPECIAL CASES

Varying the parameter k allows to control the influence sphere width. With such variations the usual formulations of the classical models like the coordination level, the vector and the Boolean ones can be derived.

A. Coordination level and vector model

In the information retrieval domain, one of the first similarity measures between a document and a query was the coordination level. In this case, the query is a set of keywords. Computing the relevance score by the coordination level method consists in counting the query terms occurrences number in a document. We can reproduce this behaviour in our model by : 1) choosing a rectangular influence function of width 1 and height 1 (cf. fig. 8) ; so the sphere of influence of any term occurrence is limited to this occurrence as the spheres of influence do not overlap, 2) using a disjunctive query. So, by only taking into account the raw term frequency, our computing method is equivalent to the coordination level one.

The behaviour of the vector model can be reproduced if we assign at the positions where the query terms occur a local relevance value (resp. fuzzy proximity value) which depends on the document frequency 1 . so, we get documents scores which 1 We can also use various idf functions with normalised value for that. depend on document frequency and term frequency which well corresponds to the vector model.

B. Boolean Model

In our fuzzy proximity model, if the sphere of influence is extended to the whole document, what will be done by taking limits when the parameter k tends towards the infinity, our computing method behaves like the Boolean one. Here is the demonstration.

First of all, an influence function which is a rectangular function of width 2k and height

1 2k x → 1 2k • [-k,l+k] (x )
will be used 2 . This function is illustrated in figure 9.

f (x -i ) ≤ max i∈[0,l] f (x -i ) ≤ 1 2k • [-k,l+k] (x ).
Given a query q , this maximisation is true for every leaf, so trivially it is true for every nodes in the tree. Using this maximization at the tree root, we have

s k (q, d )= +∞ -∞ p d q (x )d x ≤ +∞ -∞ 1 2k • [-k,l+k] dx = l +2k 2k and lim k→+∞ s k (q, d ) ≤ lim k→+∞ l +2k 2k =1.
A query q in our model is composed of leaves with terms and internal nodes with AND and OR operators. When such a query is developped by distributing the AND operators over the OR operators, we obtain a disjunctive normal form q = q 1 OR q 2 OR . . . OR q n where all the conjunctive terms 3 (q i ) 1≤i≤n are composed of elements of T. Such a document scores to 1 in the Boolean model and we will now proove that lim k→+∞ s k (q, d ) is equal to 1.

2 E denotes the characteristic function of the set E. 3 Here, "term" is used in its algebraic meaning.

Consider now a document which matches the boolean query. Such a document matches at least one of the (q i ) 1≤i≤n , say q i0 . And we have

p d q =m a x 1≤i≤n p d qi ≥ p d qi 0 .
Remembering that q i0 is a conjunctive query, it can be written t 1 AND t 2 AND . . . AND t k for some (t j ) 1≤j≤k ⊂ T . As d matches (q i0 ), each term t j , for 1 ≤ j ≤ k , appears in the document d . The function r d q i0 is the "intersection" of every influence functions and thus is the "intersection" of the two farthest one. Let us denotes u (resp. v ) the first (resp. the last) position where an occurrence of one of the (t j ) 1≤j≤k does appear, formally

u =min 1≤j≤k O cc(t j , d) and v =max 1≤j≤k O cc(t j , d).
With these notations, we can derive

(x ) ≥ p d qi 0 (x )= 1 2k • [v-k,u+k] (x )
and then

s k (q, d )= +∞ -∞ p d q (x )dx ≥ +∞ -∞ 1 2k • [v-k,u+k] (x )dx .
The last sum can be computed: As we previously proved that this limit was lower than 1, it is then equal to 1.

+∞ -∞ 1 2k • [v-k,v+k] (x )dx = 1 2k •(u +k )-(v -k )= 2k +(u -v ) 2k so lim k→+∞ s k (q, d ) ≥ lim k→+∞ 2k -u + v 2k =1. 0 1 2k u-k u v-k u+k v v+k
Reciprocally, consider now a document d which does not match the boolean query. So d does not match any of the (q i ) 1≤i≤n . Given some i , 1 ≤ i ≤ n , q i is a conjunctive query : Thus, the integral is zero whatever the value of k and its limits is zero too. Therefore, on one hand if a document d matches a boolean query q we showed that lim k→+∞ s k (q, d )=1and on the other hand if the document d doesn't match the query q we have s k (q, d )=0for any value of k , so a function lim k→+∞ s k (q, d )=0 . So we proved that the classic Boolean scores can be retrieved by our model when we consider the limit as k tends towards the infinity.

V. C ONCLUSION

In this paper, firstly, we reminded the classical models and made the link with the use of term occurrences proximity in information retrieval. Then, from our assumption that documents having nearby query terms occurrences should be highly ranked, we detailed our "sphere of influence" model which uses boolean queries. We also have seen that classical information retrieval models are special cases either with k = 1 2 for the vector model or with k →∞for the Boolean model. Actually, this parameter controls the spread of the terms occurrences influence. A value about 5 specifies a phrase level proximity. A value from 15 to 30 is at the sentence level and a value near 100 at the paragraph level. Consequently, our model reaches our first aim that is to say scoring a document according to the query terms localisation but also can be set to reproduce the behaviour of classical information retrieval models.

Fig. 1 .

 1 Fig.1. At the position x =3, the fuzzy proximity value is the maximum value between the fuzzy proximity values of occurrences in positions x =2and x =5 thus this of occurrence at the position x =2

  p d C ) associates to each position in the document d the fuzzy proximity value to the term B (resp. C). Consider the query B OR C, for such an information need, finding B or C in the text is equivalent. Thus we want the same proximity

Fig. 3 .

 3 Fig. 3. Document 2 -fuzzy proximity. The first curve represents the influence functions of the two occurrences of the term B. The second function (influence function of the term C) is flat because the term C does not occur in the document d 2 . The last curve represents the fuzzy proximity to the query (B OR C).

Fig. 4 .

 4 Fig. 4. Document 1 -local relevance (signal). The first (resp. second) curve represents the local relevance of the term B (resp. term C), the last curve represents the local relevance for the query (B OR C).

Fig. 5 .Fig. 6 .

 56 Fig. 5. Document 2 -local relevance (signal). The first curve represents the influence functions of the two occurrences of the term B. The second function (influence function of the term C) is flat because the term C does not occur in the document d 2 . The last curve represents the local relevance to the query (B OR C).

  ((A AND (B OR C)) = r d (A AND B) OR (A AND C)) at each position of the document d , but this is not the case. For example, at the position x =8.5 in the first document where A, B and C occur, the local relevance values at the position x are r d A =0.125, r d B =0.625 and r d C =0.125, we obtain : r d1

Fig. 7 .

 7 Fig. 7. The query tree for (A OR B) AND (A OR C). The local relevance values at position 8.5 are at the leaves, the functions used at the nodes are before the boolean operators and the evaluations of these functions are displayed at each nodes.

1 Fig. 8 .

 18 Fig.8. Influence function which limits the influence area, the zero value match with the normalized idf value for the given term.

1 Fig. 9 .

 19 Fig. 9. Rectangular influence function. Given a term t and a document d of length l +1, we maximize the function p d t at any position x p d t (x )= max i∈Occ(d,t)

  p d qi 0 = p d t1 AND ... AND tk =m i n 1≤j≤k p d tj and this is equal to min(p d U , p d V ) for the term U that appears at position u in d and for the term V that appears at position v in d (cf. fig 10). As p d U = 1 2k • [u-k,u+k] and p d V = 1 2k • [v-k,v+k] we have min(p d u , p d v )= [v-k,u+k] (as shown by 10). So we have p d q

Fig. 10 .

 10 Fig. 10.The intersection of the rectangles represents the local document relevance. We have two term occurrences one at position u and the other one at position v.

  6 9 12 15 Fig.2. Document 1 -fuzzy proximity. The first (resp. second) curve represents the fuzzy proximity to the term B (resp. term C), the last curve represents the fuzzy proximity to the query (B OR C).

	d 2	A		B					B
		4	5	6	7	8	9	10	11	12	13	14	15	16
		1
		0
			3 6 9 12 15

  AND t 2 AND . . . AND t k and at least one of the (t j ), 1 ≤ j ≤ k , say t j0 does not appear in the document d .S o

	(∀x )	p	d tj 0 (x )=0,
	and then
	(∀x )	p	d qi (x )=0,
	and finally,
	p	d q =m a x 1≤i≤n	p	d qi =0.

t 1


Metaproteomics for the

come

XVII International Italian Proteomics meeting_Rome_20231129

Metaproteomics for the functional analysis of microbiomes: recent achievements & prospects

Jean ARMENGAUD Microorganisms play a major role in human, animal and vegetal health, as well as in key terrestrial geochemical processes. To understand how microbial communities function, how they interact with the host and the risks of dysbiosis, we need to identify the diversity of microorganisms present and quantify the numerous molecular players at work, especially proteins which are the workhorses of biological systems. Metaproteomics is a key technology for such functional studies, as it can provide important answers for these highly complex samples: 1) identification of the taxa present, 2) quantification of the biomass of these organisms, 3) identification of the proteins of these taxa and their function, 4) identification of host biomarkers explaining their global response, and 5) overall functional representation of the biological system. The first important key step in metaproteomics is the selection of the database best suited to the specificities of the sample. Proteotyping of organisms enables us to establish the identity of micro-organisms and their corresponding biomass. Several examples will be presented to demonstrate the power of proteotyping. The challenges of metaproteomics in terms of mass spectrometry, interpretation and exploitation of results will be discussed addressed. Moreover, results from recent technologies such as the Astral tandem mass spectrometer will be presented to demonstrate the new power of next-generation metaproteomics for deep functional analysis of microbiomes.


Jean Armengaud

Jean Armengaud Metaproteomics

Metaproteomics, the path to rapid microbiota diagnosis

Metaproteomics, the path to rapid microbiota diagnosis


Sabah Al-Fedaghi
email: salfedaghi@yahoo.com

Exploring Conceptual Modeling Metaphysics: Existence Containers, Leibniz's Monads and Avicenna's Essence

Keywords: Conceptual model, software notions, ontology, metaphysics, software requirement development. I

Requirement specifications in software engineering involve developing a conceptual model of a target domain. The model is based on ontological exploration of things in reality. Many things in such a process closely tie to problems in metaphysics, the field of inquiry of what reality fundamentally is. According to some researchers, metaphysicians are trying to develop an account of the world that properly conceptualizes the way it is, and software design is similar. Notions such as classes, object orientation, properties, instantiation, algorithms, etc. are metaphysical concepts developed many years ago. Exploring the metaphysics of such notions aims to establish quality assurance though some objective foundation not subject to misapprehensions and conventions. Much metaphysical work might best be understood as a model-building process. Here, a model is viewed as a hypothetical structure that we describe and investigate to understand more complex, real-world systems. The purpose of this paper is to enhance understanding of the metaphysical origins of conceptual modeling as exemplified by a specific proposed high-level model called thinging machines (TMs). The focus is on thimacs (things/machine) as a single category of TM modeling in the context of a two-phase world of staticity and dynamics. The general idea of this reality has been inspired by Deleuze's 'the virtual' and related to the classical notions of Leibniz's monads and Avicenna's essence. The analysis of TMs leads to several interesting results about a thimac's nature at the static and existence levels.

INTRODUCTION

Every science presupposes and requires some sort of metaphysical foundation [1] [START_REF] Lowe | Metaphysics as the science of essence[END_REF]. Metaphysics can be defined as the study of categories with the purpose of identifying them, defining them if possible, and determining the relationships among these categories [START_REF] Gracia | Metaphysics and its Task: The Search for the Categorial Foundation of Knowledge[END_REF]. According to [START_REF] Sider | Writing the Book of the World[END_REF], metaphysics is once again a thriving subdiscipline within philosophy [START_REF] Godfrey-Smith | Theories and models in metaphysics[END_REF].

According to [START_REF] Paul | Metaphysics as modeling: The handmaiden's tale[END_REF], metaphysics involves the construction and evaluation of model classes. A model is an imagined or hypothetical structure that we describe and investigate to understand some more complex, real-world target system or domain. A growing number of scientists in the modeling community are exploring ways to address issues related to ontology. Some philosophers recognize the value of models for providing -a revolution in metaphysics issues‖ [START_REF] Shults | Modeling metaphysics: The rise of simulation and the reversal of Platonism[END_REF]. Reference [START_REF] Godfrey-Smith | Theories and models in metaphysics[END_REF] stated that much metaphysical work, especially of the contemporary systematic kind, might best be understood as model-building, in a specific sense of this term that draws on recent philosophy of science.

Specially, [START_REF] Shults | Modeling metaphysics: The rise of simulation and the reversal of Platonism[END_REF] claims that developments in -computer modeling […] have the potential to contribute to what may be the most significant change in Western philosophy since the foundational work of Aristotle's teacher Plato in the 4th century BCE.‖ In computer science, finding solutions to practical problems employs models of the world and applied metaphysics [START_REF] Yoran | Objects in object-oriented ontology and objectoriented programming[END_REF]. In this paper, the focus is on conceptual modeling utilized to describe proposed requirements and designs for software systems. Conceptual models are typically represented in terms of a graphic structure.

Metaphysics is very close to conceptual modeling. Notions such as classes, object orientation, properties, instantiation, algorithm, etc. are metaphysical concepts developed thousands of years ago. Exploring the metaphysics of such notions aims to establish quality assurance though some objective foundation not subject to misapprehensions and conventions. The closeness of metaphysics and conceptual modeling has driven some researchers to propose the feasibility of the graphical representation of philosophical concepts in terms of UML (unified modeling language) diagrams and methods [START_REF] Komáromi | A proposal for the usage of OntoUML and UML diagrams for conceptual modeling in philosophy[END_REF]. According to [START_REF] Komáromi | A proposal for the usage of OntoUML and UML diagrams for conceptual modeling in philosophy[END_REF], this approach could help philosophy in mapping, explaining, clarifying, and model-checking because UML has the capability of representing abstract conceptual structures in a highly standardized and formalized manner.

Conceptual modeling in software engineering concerns metaphysics. An example is viewing the software as a unique sort of being. According to [START_REF] Northover | Towards a philosophy of software development: 40 years after the birth of software engineering[END_REF], researchers have not yet captured what software actually is or how software can be characterized and need to understand the ontological status of software as the product of software engineering. Reference [START_REF] Penrose | The Emperor's New Mind[END_REF] viewed the notion of algorithm, which is, metaphorically speaking, -the ‗soul' of a computer program,‖ in eternal forms [START_REF] Northover | Towards a philosophy of software development: 40 years after the birth of software engineering[END_REF]. Some software engineering researchers have already contributed to understanding similar issues, such as programming and software system design. According to [START_REF] Ontiveros | Programming as Metaphysics[END_REF], "Metaphysicians are aiming for theories that describe the fundamental structure, nature, or entities in the world. They"re trying to develop an account of the world that properly conceptualizes the way it is. Software design is the same."

The new contribution of this paper consists of a metaphysical exploration of conceptual modeling, which is one of the central activities in software engineering, as an intermediate artifact for system construction. Specifically, such an exploration is applied to a new high-level model called thinging machine (TM) modeling [START_REF] Al-Fedaghi | Conceptual data modeling: Entity-relationship models as thinging machines[END_REF]- [START_REF] Al-Fedaghi | Validation: Conceptual versus activity diagram approaches[END_REF]. Focusing on the TM is motivated by the subtle nature of TMs that include one-category ontology (things/machines) and five actions (create, process, release, transfer and receive). This facilitates easier mapping to metaphysical notions. The results contribute to further understanding TM modeling, in addition to introducing some metaphysical insights of conceptual modeling.

A. Aims

In the field of conceptual modeling, ontologies provide a foundational theory to describe the structure and behavior of the modeled domain (e.g., [1]). Such ontology-driven conceptual modeling is defined as the utilization of ontological theories to develop engineering artifacts to improve the theory and practice of modeling [START_REF] Verdonck | Ontology-driven Conceptual Modeling: Model Comprehension, Ontology Selection and Method Complexity[END_REF]. One purpose of such an approach is to improve the process and quality of engineering software systems because ontologies provide real-world semantics for language constructs or assess the adequacy and sufficiency of modeling constructs that represent constructs in domains [START_REF] Verdonck | Ontology-driven Conceptual Modeling: Model Comprehension, Ontology Selection and Method Complexity[END_REF]. According to [START_REF] Verdonck | Ontology-driven Conceptual Modeling: Model Comprehension, Ontology Selection and Method Complexity[END_REF], in this context, several research gaps and shortcomings can be identified that still pose challenges for further development in the field (e.g., model comprehension, complexity). More research would be beneficial for the field of ontology-driven conceptual modeling, as the principal purpose of a model is to be understood and comprehended by anyone who uses it [START_REF] Verdonck | Ontology-driven Conceptual Modeling: Model Comprehension, Ontology Selection and Method Complexity[END_REF].

This paper aims at gaining insight into the model of TMs. Specifically; the paper concentrates on the metaphysical characteristics of TMs by analyzing its notions, such as event, time, object, action, etc. Metaphysics here is viewed as an interpretation of TM modeling in terms of creation, processing, releasing, transferring and receiving for the sphere of actions common to all TM-proposed universe of elements: thimacs (thing/machines).

The paper is a continuation of sequel of research work about TMs. For example, TM modeling describes the dual status of reality that involves studying the questions in Fig. 1.

B. Content of paper

The Section 4 explores thimacs at two levels of potentiality/actuality, adopting an idea that goes back to the Stoic view of reality. Things subsist in the static level (plane of reality) and are brought above the threshold of subsistence/existence to actuality. In Section 5, the interiority of the thimac is analyzed in terms of two directions: the thimac acting on itself and the thimac as an agent that acts on other things (objects).

This analysis leads to the interesting results of defining what TM existence is, as illustrated in Fig. 2. (3) Focus is then turned to the Create action as a transformation from subsistence to existence vs. existence as duration of time.

Dynamic

(4) The analysis then isolates the event as the place where something is situated or occurs.

(5) The last step is abstracting the event (no specific thing or action) to arrive at a definition of a slot of existence.

Fig. 2 Summary of paper content

II. THE TM MODEL

The TM diagrammatic model has been applied in many applications. Each TM paper presents an application example; furthermore, each paper introduces additional development of the model as an underlying structure of the world. This paper focuses on the metaphysical TM aspects.

This TM modeling approach may relate to the view that at some fundamental level, the world is a graph of nodes and edges. The concrete world is a single, large structure best analyzed as a diagram [START_REF] Shackel | The world as a graph: Defending metaphysical graphical structuralism[END_REF]. According to [START_REF] Westerhoff | The Non-existence of Ontological Foundations[END_REF], dissatisfaction with -the resources of set theoretic semantics of predicate logic for describing ontological structure‖ motivates selecting graph theory, aiming to show that we can conceive of the underlying structure of the world as a graph.‖ A physical individual is a collection of joined subgraphs, each of which is a temporal part of the individual. Physical individuals come into and go out of existence, and hence, the necessity of the existence of the nodes does not entail the necessity of physical individuals [START_REF] Shackel | The world as a graph: Defending metaphysical graphical structuralism[END_REF].

In TM modeling, the response to the question, -what is there?‖ is a world of thimacsa network of thimacs that articulate the underlying structure of the world. Thimacs are the basic wholes (entities and processes) of composition that include thimacs that can be divided into subthimacs, which can in turn be divided, and so on. Every thimac is distinct from every other thimac by its superthimacs or subthimacs. Additionally, thimacs may attach themselves to other thimacs and form new thimacs.

Each thimac is woven from and in other thimacs, forming an organized whole. According to such a view, the whole holds together as one thimac. The whole is more than a mere entanglement of interconnections of similar thimacs. The thimac as a machine is the basic unit of the whole constructed as a repetition of crystal lattice structure.

Thimacs are the only foundational elements of regions (subdiagrams that represent atemporal things we talk about) and corresponding -existence pieces‖ (events) in reality. Reality is viewed as a composite thimac with a singular unified totality. Hereafter, a thimac may be referred to as a thing or machine (see Fig. 3).

A thimac is a machine when it acts on other thimacs, and it is a thing when it is the object of actions by other thimacs. A machine things (Heideggerian verb); that is, it creates, processes (changes), receives, transfers and releases. Thimacs are things that subsist of their own accord at the static level. They come into existence, persisting through time, and change when they manifest at the dynamic level. Being at a specific position is a standing in certain relations (inside/outside, flow connection) with other thimacs.

A. The Machine

According to [START_REF] Bryant | Machine-oriented ontology: Towards a panmechanism[END_REF], -To be is to be a machine. Rocks are machines, stars are machines, trees are machines, people are machines, corporations are machines, revolutionary groups are machines, tardigrades are machines.‖ In TM modeling, the thimac machine executes five actions: create, process, release, transfer and receive (see Fig. 4). Each of these static (outside time) actions is a capacity or power to act and becomes a generic event when merged with time. Thimacs are realized by creating, processing, releasing, transferring and/or receiving thimacs. Each thimac is affected by/affects the thimacs in contact with it through releasing, transferring and receiving.

A thimac's actions, in Fig. 4, are described as follows. 1) Arrive: A thing arrives to a machine. 2) Accept: A thing enters the machine. For simplification, the arriving things are assumed to be accepted (see Fig. 4); therefore, arrive and accept combine actions into the receive action. 3) Release: A thing is ready for transfer outside the machine. 4) Process: A thing is changed, handled and examined, but no new thing is generated. 5) Transfer: A thing is input into or output from a machine. 6) Create: A new thing manifests in a machine.

B. The thing

With a thing as a thimac, a thing is what can be created, processed, released, transferred and/or received. For example, the sentence things take time denotes what are -being created (brought into existence), processed, released, transferred and/or received‖ take time. Each of these things may be composed of (sub)things. In TMs, what is created is established or substantiated as a thing. A TM's existence designates manifestation in time and subsistence (discussed later), indicating timeless establishment, e.g., essence (discussed later). Additionally, the thimac exists and subsists as a machine that creates, processes, releases, transfers and/or receives.

A thimac could be a composite entity of networks of subthimacs that are a unified whole. This thimac will be a megathimac or simply a megamac (mega machine). For example, an immaterial thimac, such as traffic, is a megamac, as traffic is a complex of machines manifested (exists and subsists) by processing cars, roads, lights, rules, etc. These thimacs organize into a whole TM region such that they are responsible for the thimac of traffic. Note that a megamac is not an arbitrary composite or aggregate of a thimac, e.g., like human-plus-stone, but it has some kind of acting unity, e.g., transfer, receive, process and release as a self-unit. Weather, task, transportation and so forth, each is what creates, processes, releases, transfers and receives. At the dynamic level, this megamac as a collection of related events is a megaevent. An example of a unified whole as megaevent is the Aristotelian thesis that action and passion form a certain kind of whole [START_REF] Ford | Action and passion[END_REF].

In TMs, every existing thing is an event. Weand everything that isare events [START_REF] Artson | On the way: A presentation of process theology[END_REF] (referencing Alfred North Whitehead), we are, -inhaling air, ingesting food, absorbing heat or cold, sweating, defecating, shedding hair and skin. On atomic, molecular, biochemical, cellular, biosystemic, bodily, even conscious levels, we are not stable substances at all. We are constantly engaging in a give-and-take with the rest of creation, all simultaneously‖ [START_REF] Artson | On the way: A presentation of process theology[END_REF].

III. EXAMPLES

This section illustrates TM modeling with two examples: -The first example involves modeling the biography of a fictional man. -The second example models a chain-store company, offering various types of cheese.

The two examples focus on table representations with timebased data.

A. Modeling the life of John Doe

This example involves the following short biography of a fictional man (taken from [START_REF] Handwiki | Temporal database[END_REF]- [START_REF] Ramnath | Temporal data management: An overview. in: business intelligence and big data[END_REF]).

John Doe was born on April 3, 1975, as the son of Jack Doe and Jane Doe, who lived in Smallville. Jack Doe registered the birth of his firstborn on April 4, 1975, at the Smallville City Hall. John grew up and graduated in 1993. After graduation, he went to live in Bigtown. Although he moved out on August 26, 1994, he forgot to register the change of address officially. It was only at the turn of the seasons that he did a few days later on December 27, 1994. John accidentally died on April 1, 2001.

To store the life of John Doe in a database, a table, Fig. 5, is used to list the time of events in his life [START_REF] Handwiki | Temporal database[END_REF]- [START_REF] Ramnath | Temporal data management: An overview. in: business intelligence and big data[END_REF]. The method of analyzing the events is based on the natural language description. An alternative analysis on TM modeling is shown in Fig. 6. The diagram represents the biography of John as a whole megamac. Thimacs: person, address 1, address 2, father and database indicate the entities that exist at the TM events level. The action create in this picture denotes potential existence over the time period of the biography. Note that for simplification, sometimes create is not included under the assumption that the rectangle implicitly implies that. Fig. 6 is a picture of a static timeless worldnote the passive voice in the description. Dashed arrows in the figure denote triggering.

Thus, in Fig. 6, a person is born (number 1 in the figure) at address 1 (2). His father (3) goes to the database system (4) and registers him [START_REF] Godfrey-Smith | Theories and models in metaphysics[END_REF]. The person is processed (graduation process, 6) then is released and transferred to address 2 [START_REF] Shults | Modeling metaphysics: The rise of simulation and the reversal of Platonism[END_REF]. There, he registers his new address (8 and 9). Eventually, he dies 10.

The static model in Fig. 6 is atemporal and the sequence of actions (e.g., moving from address 1 to address 2) express a logical order. The corresponding events model (see Fig. 7) can be described (depending on how events are cut) as follows. E 1 : John is born at address 1. E 2 : Father reports John's birth. Note that each event by definition includes its time and other descriptions, such as duration and who reports the event. An event is defined as a subdiagram of the static model (region of the event) plus time. Fig. 7 is a megaevent that would form the foundation for any type of implementation in terms of tables discussed in such sources as [START_REF] Handwiki | Temporal database[END_REF]- [START_REF] Ramnath | Temporal data management: An overview. in: business intelligence and big data[END_REF]. The TM model (e.g., Fig. 6) is a unified whole (a single state of affairs) forced by complementary subthimacs.

Fig. 8 shows the chronology of events. If we want to represent the example in terms of events, then the database is a list of events, and each event contains its time stamp.

Contrasting the English and tables technique of [START_REF] Handwiki | Temporal database[END_REF]- [START_REF] Ramnath | Temporal data management: An overview. in: business intelligence and big data[END_REF] vs. TM modeling shows that the former method is based on an English description with a very large vocabulary, whereas the TM model uses just five basic verbs in addition to identifying entities (person, father, address, etc.). The TM model follows a systematic development in terms of a static description and dynamic specification and then identifies the chronology of events. This paper aims to clarify the metaphysical notions in TMs such as event, existence, etc. that give TM modeling additional advantages of comparison with the ambiguity of natural language.

B. Temporal databases

Consider the example given by [START_REF] Menne | The Potential of Temporal Databases for the Application in Data Analytics[END_REF] of a company called CheeseHut that is a chain store offering three types of cheese, namely young, mature and old cheese, with each cheese having its own price (see Fig. 9). Fig. 10 shows the product history table of CheeseHut as given in [START_REF] Menne | The Potential of Temporal Databases for the Application in Data Analytics[END_REF].

In TM, the modeling involves information about cheese in the form of a table. The table can be viewed as a thimac and its instantiation is a megaevent. Thus, the table has subthimacs and actions.

Accordingly, the static description of a table is shown in Fig. 11. First the table is declared (is created) -see number 1, and at this holistic level (the table itself). The table, at this holistic level, has a subthimac (2) that keeps tracking and updating the number of rows in the table. For simplicity, the mechanism for deleting a row is not shown. The table also has the subthimac row (3) that may have its own global information row, such as the number of attributes (not included in the figure). Then, there is the body of the row (4) which is constituted by the row key ( 5), ID [START_REF] Paul | Metaphysics as modeling: The handmaiden's tale[END_REF], name [START_REF] Shults | Modeling metaphysics: The rise of simulation and the reversal of Platonism[END_REF] and price (8) of the product. These values are constructed though an outside input (9) that causes, also, the number of rows in the table to update [START_REF] Northover | Towards a philosophy of software development: 40 years after the birth of software engineering[END_REF]. Fig. 12 gives an example of inserting a tuple in the table. An initial assumption is that the table has no tuples at the time of creation. Then, [START_REF] Menne | The Potential of Temporal Databases for the Application in Data Analytics[END_REF] utilizes the history table of CheeseHut when in 2014, CheeseHut changes the supplier for the old cheese, which results in a higher price of 12 euros per kilogram. Note that this history table is a table of TM events. Fig. 13 shows the TM events model, and Fig. 14 shows its corresponding chronology of events. To save space, these figures will not be described further. This seems to be a promising approach to temporal databases. Note that in TM modeling, the stoppage of an event at a certain region is a return to staticity in that region [START_REF] Al-Fedaghi | Lupascian non-negativity applied to conceptual modeling: Alternating static potentiality and dynamic actuality[END_REF]. Thus, TM modeling treats the absence (inexistence) of events as the subsistence of regions.

IV. EXPLORATION OF THIMACS

Henri Bergson [START_REF] Bergson | An Introduction to Metaphysics[END_REF] distinguished two ways of knowing a thing: "The first implies that we move round the object; the second that we enter into it." This section provides a foundation for analyzing the interiority of the thimac as a machine (see Fig. 15). The purpose is to further understand the action Create that embeds the metaphysical meaning of the notion of existence in the next section.

A. Two levels of TM: Potentiality regions vs. Actuality events

TM modeling describes reality in two levels of a potentiality/actuality scheme adopting an idea that goes back to the Stoic modes of reality. Fig. 16 defines the categorical structure of TM modeling. The two-level depiction is made to emphasize and illustrate the characteristics of each of the two levels; however, the two projected levels are superimposed over each other in TM modeling. Therefore, existence and subsistence are like a double-image impression (e.g., Rubin"s vase), which is possible with a geostatic figureground perception. When we see an event, we simultaneously perceive its region. Many thinkers have inspired the general idea of this reality. For example, according to [START_REF] Deleuze | Difference and Repetition[END_REF],

The virtual [potential in TM] is not opposed to the real but to the actual. The virtual is fully real in so far as it is virtual [potential].... Indeed, the virtual must be defined as strictly a part of the real [actual] object -as though the object had one part of itself [TM region] in the virtual into which it is plunged as though into an objective dimension.... The reality of the virtual consists of the differential elements and relations along with the singular points which correspond to them. The reality of the virtual is structure.

B. Regions and Events

A region is a TM-static description as illustrated in Fig. 17 in terms of the famous Aristotelian example of statue ≡ wood + form. The region has real subsistence, but such a type of reality is -absently present‖ [START_REF] Uršič | Shadows of Being: Four Philosophical Essays[END_REF]. The mind can conceive quasi-real subsisting things purely in itself without considering their existence, which is different from nonexistence (remember Rubin's vase).

An event in Fig. 17 is defined in terms of region and time. The event may denote the object (e.g., tree) or a process (e.g., traffic). Note that mentality is excluded in this TM discussion at this point of development of the model.

C. Potentiality and Actuality

TM potentiality and actuality in Fig. 17 are different notions than Aristotelian"s notions. Things subsist at the static level (plane of reality) and are brought above the threshold of subsistence/existence to actuality. In TMs, potentiality refers to all things at the static level that are capable of existing, i.e., all possible relative configurations. Events stand out against regions, and regions are a precondition to events.

For example, in the Aristotelian scheme, the piece of wood and the actual, say, Hermes statue are two ways (potential and actual) of being Hermes [START_REF] Qingyun | Aristotle's concept of potentiality in metaphysics book Θ[END_REF]. Then, potential Hermes and actual Hermes are two ways of being Hermes. In a TM, the piece of wood, form of Hermes and Hermes statue are three potential things that can be transformed into existence as illustrated in Fig 17 .   In the figure, wood, form and statue and processing them are a potentiality in the subsistence level that actualizes at the existence level.

The static level where time is suspended includes all chains of potentiality that unfold when time flows through regions, e.g., the event man (being one and the same) may materialize with a subthimac "Pale" or in another time with a subthimac "Dark," just like an LED sign with parts turning the light on/off. Here, the fundamental aspect of change comprises various subdiagrams of the region. In the static level, regions are just as real as in present. According to [START_REF] Butterfield | The End of Time?[END_REF], Abraham Lincoln is just as real as Joe Biden, "just as Venus is just as real as Earth: Lincoln is merely temporally "far away from us," just as Venus is spatially far away."

The potential thing would emerge into existence according to its time. The possibility that follows such an event is predetermined at the static level. Note that the arrows used in the static thimac are atemporal, e.g., in the classical example, the hand that moves the key in the lock of a door: the movement of the hand and that of the key are simultaneous, and yet one is prior to the other [START_REF] Lizzini | Sina's Metaphysics[END_REF].

D. Regions constituents

Region constituents define what the thing [START_REF] Lizzini | Sina's Metaphysics[END_REF] (will be discussed in the next subsection) is or the being of a thing in the world. This definition is distinguished from the affirmation of the thing's existence (the fact that it is [START_REF] Lizzini | Sina's Metaphysics[END_REF]). An existing thing is composed of a region and an existence container (will be defined later). Regions are a kind of preexistence that freezes all actions and is the resemblance of events. A region is general in the sense that more than one event may have the same region (different locations in time). To preserve identity, it is not possible to have events of the same region and same location in time simultaneously. Regions and events are modes in which things come. When two events share the same region, then they are the same kind of event.

The definition of a region reflects a description of all potential permitted forms. A region has wholeness or an internal unity that is more than the totality of its constituents. If you have a region of a square and a region of a circle at the static level, then it is not possible to create a thimac of ‗square circle' using elementary quantum particles/waves.

E. Related classical notions: Nomads, Essence

Subsisting things in reality originate from first occurrences in reality [START_REF] Al-Fedaghi | Ontology for conceptual modeling: Reality of what thinging machines talk about[END_REF]. For example, cars were not a subsisting thing until January 29, 1886, when Carl Benz applied for a patent for his vehicle powered by a gas engine. Before that, there were gas engines, cooling fans, etc. that fitted together to create the first car. After that, cars became subsisting things in the catalog of reality, where a new region is preserved in its own instances of existence. Thus, regions are not found independently of events, just as processes cannot exist without their events, e.g., traffic embedded into existing cars, roads, lights, etc.

Such a notion that a first thimac continues in the catalog of reality may be traced to nature's preservation of constituent species. A natural thimac's (e.g., tree) region subsists in miniature in the original thimac to have its own existence. The natural machine survives in its region; it can never be completely destroyed (see Leibniz's ideas about natural machines [START_REF] Raymont | Leibniz's Distinction Between Natural and Artificial Machines[END_REF]). Each natural machine comes equipped with a substantial form (i.e., an entelechy that makes actual what is otherwise merely potential). According to Leibniz, the monad (as an existing thing) is made up of the organic machine (TM: the extension) in which innumerable subordinate monads come together that the dominating monad makes into one machine (TM: region) [START_REF] Raymont | Leibniz's Distinction Between Natural and Artificial Machines[END_REF].

Following Avicenna, to be a given entity in the world (the fact that [something] is established/knowable/predicated) without affirming its existence must be distinguished from the existence of something. In establishing the -thingness‖ (essence) [TM region] of the thing, no existential judgment is implied, and it is independent of its existence. Such a distinction has an Aristotelian origin in which a thing exists separate from what a thing is. In TMs, this separation of thingness and existence is projected in the TM region at the static level and existence at the dynamic level.

Following the Aristotelian philosophy, one thing and a thing are the same thing. Now if a particular thing goes out of existence, it disappears from existence, but not from subsistence. In previous studies of thimacs, for the purpose of limiting study, the focus is only on thimacs mapped to existence.

V. THE THING ITSELF VS. OTHER THINGS

According to [START_REF] Godfrey-Smith | Theories and models in metaphysics[END_REF], -Metaphysical system building is model-building.‖ This systematic metaphysics is work intended to be about the world itself and how the world is really constituted. Model is a hypothetical structure that we describe and investigate to understand some more complex, real-world target system or domain [START_REF] Godfrey-Smith | Theories and models in metaphysics[END_REF]. Specifically, in this paper, a model is understood as a high-level conceptual model in software engineering using diagrammatic methods.

In TM modeling, the thimac is the most important concept upon which the whole conceptual model of the notion of thimac is based. This thimac can be analyzed through two directions.

-The thimac itself is the agent that acts upon itself. For example, a human can move him/herself (release/transfer) from one place to another or process him/herself as in selflearning.

-The thimac is the agent that acts upon other things (objects). For example, when I experience things like cars, chairs, etc. that are not me. Accordingly, the thimac involves different flows among actions: flows for itself, in its subthimacs and exterior thimacs that flow in/to the outside, as shown in Fig. 18 with blue, purple and red arrows, respectively. The red arrows indicate flows of other thimacs coming in from the outside, (maybe) processing and then leaving to the outside. There is no create in this type of flow because creating another thimac is a triggering mechanism to generate another thing. Thus, the creation is realized in the box of another thimac. The blue arrows involve the thimac itself and apply to the whole thing.

A. Thing-in-itself

The TM thimac-in-itself, in which the thing as a whole is the object of actions, can be illustrated using the first example in Section 3 when John Doe moves, then he moves in his totality, i.e., body, information about his father"s reporting his birth, as shown in Fig. 20. The diagram does not reflect this movement explicitly; e.g., Father"s data does not seem to move with John. This implicit information can be extracted by processing (extraction information) from John.

Such a distinction between the flow routes inside a thimac uncovers two meanings of the Create action as discussed in the next subsection.

B. Create: transformation vs. persistence

Consider the TM stages from subsistence to existence levels that involve generating an event from a region. The thing is subject to alteration from the state of static/dynamic transformation to the state of steady existence. Certainly, the transformation process involves (1) the destruction of the region into pieces of generic actions; (2) giving each piece its substance (energy, materiality and so forth) then (3) constructing the region from these newly formed pieces into a region of an event. After this transformation to the existence level, the region would never be equivalent to the static region just as a house blueprint is different from the actual house.

Accordingly, there are two meanings of the Create action in TM.

-Create as becoming and -Create as an existence container (acronymized as that holds a thing (See Fig. 21). The term existence container is borrowed from [START_REF] Murphy | Existence-based access the future of cybersecurity[END_REF] who stated, "The existence environment is an empty container much like a bottle. When a bottle is filled with milk, soda, juice, etc., it is referred to by the content of the bottle. You go to the refrigerator for milk, soda or a juice never thinking about the container, be it a bottle or can. Similarly, existence containers take on the properties of what is loaded into them, much like the bottle." Note that the thing is a region (subdiagram) at the subsistence level; hence, it can be an object (e.g., tree) or a process (e.g. traffic).

Becoming Create (obtains or is given existencean act of bringing into existence) that triggers (causes) the derivation of a new thimac, e.g., an order thimac triggers the creation of an invoice thimac. This Create is the source of an internal spark that leads to emergence from subsistence to existence and involves constraints, such as bodies, situations, etc. See this becoming Create in Fig. 22 (red letters).

Existence Create preserves existence (persisting through time -see Fig. 22, green letters) after becoming. It represents the thing existence progressively in time changing (while existing) through actions: process, release, transfer and receive. For example, the famous ship of Theseus has this existence while loosening subthimac parts (un-manifestation at the static level) and gaining parts (manifestation at the dynamic level) through the history of its repairs. We conceive the ship at the static level as a pure placeholder to which various parts attached.

C. Existence Container

In this section, the focus is on Create as persisting existence in an attempt to isolate existence in its pure form: exicon. Consider Fig. 23, which shows the events, John exists, and John creates an order and sends it somewhere. Let us concentrate on the event John exists (Fig. 24). Create in TM is different from the other four TM actions in given a region. It stands for the existence of a thimac. After becoming, the create role in the region of an event alters to there is (see Fig. 25). At the dynamic level (existence), create stands for there is. Here, we can define existence as,

Existence of a thing ≡ There is a thing in time

Consequently, the TM diagram can be simplified as John exists as shown in Fig. 26.

Suppose that we define pure existence (existence without specific thimac or time), previously called an exicon, as the blend of time and other phenomena (e.g., entropy [decay] and energy) that regions soaked in (see Fig. 27). This exicon is born (becoming) to go through decay and fade away when it becomes part of the past. It encompasses time and change aggregated according to events.

The exicon has no specific event. It may be similar to pure awareness without thought or attention. Awareness is different from the objects of awareness. Also, the exicon is existence without event. The exicon embraces things just as awareness of ideas/concepts is the content of thought. Things stand up in existence and fade away from existence, while existence itself seems to continue unaffected.

Future research can explore the relationship of this pure existence to Leibniz's monad as constituents of the world. The word monad is said to be used by Pythagoras around 500 BCE to refer to the first being that came into existence: the absolute source of creation.

An exicon can be described as a ‗slot' of existence (of different sizes). John Dewey [START_REF] Dewey | The Collected Works of John Dewey, 1882-1953[END_REF], rejecting the classical metaphysics of substance, stated that -Every existence is an event.‖ In TM, every event is an existence that occupies an exicon.

D. Glimpse of related metaphysical issues

An exicon can be described as a slot of existence, say, C to be filled with an event, e, thus it can be specified as C(e).

According to [START_REF] Van Inwagen | Metaphysics: The Big Questions[END_REF], -Is there any such-and-such?‖ (Emphasis added) means merely, -Restricting our attention for the moment to just things that are so-and-sos, is there a such-andsuch among them?‖ hence, in a party, When we ask, for example, -Is there any beer?,‖ we usually mean merely -Restricting our attention to just beverages in the fridge, is there any beer?‖ If the last beer has been taken from the fridge at a party, and someone asks, -Is there any beer?,‖ it is a poor joke to say -Yes‖ and then explain that there is plenty in the grocery store (which is closed, by the way). The metaphysician interested in ontology wants to know what the world is like in its entirety, ignoring nothing.

In TM, -Is there any beer?‖ means C(beer)? While the correct question is does C(refrigerator) include C(beer)? Note that all actors: the questioner, the one who replies with -yes,‖ the refrigerator and the beer are exicons. Thus, an exicon asks about an exicon in the exicon to be answered by yet another exicon.

This may be called a democracy of exicons, a generalization of the so-called democracy of objects approach that adopts the thesis that -all objects ought to be treated equally. The democracy of objects is the ontological thesis that all objects equally exist while they do not exist equally. The claim that all objects equally exist is the claim that no object can be treated as constructed by another object‖ [START_REF] Bryant | Introduction: Towards a Finally Subjectless Object[END_REF].

VI. CONCLUSION

This paper has introduced an exploration of metaphysical origins of conceptual modeling as exemplified by a specific proposed high-level model called thinging machines (TM). The results showed several interesting results about the nature of thimacs at the static and existence levels. Especially, the analysis has led to define existence in TM modeling. The topic is too extensive and requires further exploration including, -Related notions such as Leibniz's Monads and Avicenna's Essence. -Related existence notions such as the democracy of exicons.

It is interesting that research that started with conceptual modeling in software engineering has headed to very deep issues in metaphysics. The interdisciplinary ramification of such an approach requires further research.

  Metaphysics, at bottom, is about the fundamental structure of reality. Not about what's necessarily true. Not about what properties are essential. Not about conceptual analysis. Not about what there is. Inquiry into necessity, essence, concepts, or ontology might help to illuminate reality's structure. But the ultimate goal is insight into this structure itself-insight into what the world is like, at the most fundamental level. Despite a long tradition of challenges to the viability of the metaphysical enterprise, *Retired June 2021, seconded fall semester 2021/2022

  next section includes an enhanced description of the TM model as a world of thimacsa network of thimacs that articulate the underlying structure of the world. Subsections are devoted to what is a TM thing and what is a TM machine? Section 3 illustrates TM modeling with two examples: -The first example involves modeling the biography of a fictional man (taken from [17]-[19]). -The second example models a chain-store company offering various types of cheese. Previous papers about TMs give many examples; however, for diversity purpose, the two examples above are different because their focus is on table representations with timebased data.

( 2 )

 2 Fig. 1 Some metaphysics question in the context of TM

ReceiveFig. 4 Fig. 3

 43 Fig. 4 Thinging machine without process

Fig. 7 Fig. 5 Fig. 6 Static 10 E 3 :

 756103 Fig. 7 Events Model (megaevent) of the life of John Doe

1

 1

Fig. 13

 13 Fig.13The events description of the example table

Fig. 18

 18 Fig. 18 Thinging machine with different types of flow

Fig. 19

 19 Fig. 19 shows how these three types of flows of TM merge together to eliminate redundant actions forming the TM machine, given previously in Section 2 as Fig. 4.

Fig. 19 Fig. 21 Fig. 23

 192123 Fig. 19 Redundant actions (left) are eliminated (right).

Fig. 24

 24 Fig. 24 Event: John as an object Create John Time

Chronology of events in the life of John. Fig. 10 Product history table of CheeseHut Fig. 9 Product history table of CheeseHut ID Enter data Company's Table

		E 1 John is born in certain address	E 2 Father reports the birth	E 3 graduated John	E 4 John moves to Bigtown	new address John reports E 5 E 6 John dies
	Create	Row key Fig. 8 Row itself (body, value) No. of rows (Init. Zero) Create	Create Process: increm. By 1
	Row	Process			Create	Process
			Name	Create
	Create
			Price		Create

Tuple construction Fig. 11 The static description of a table

Tuple construction Fig. 12 Example: Inserting a tuple in the table Thimac

	Company's Table	1	Create: 1	Process: zero+1
									Key =1,
	Create		Row itself (body, value)	Process	Create: 1				ID=1, Name="
		Row				Create: 1			Young",
							Process		Price=6
						Create: Young
		Create:
		(1,1,Young, 6)				Create: 6
		E 1 Company's Table	(Init. Zero)	No. of rows	Create	Process: increm. By 1 E 3
	Create	Row Create	Row itself (body, value) E 8	Process Tuple construction	ID Name Price Row key Create Create Create Create E 4 E 5 E 6	Process	E 2	Enter data
					E 7

Static and dynamic world (

Starting with thimacs and the TM two-levels view of the world The thimac interiority is analyzed in terms of actions of the thing itself vs. agent actions over input and out things taking into considerations actions of subthimacs. Fig. 15 Content of section 4. E 3 E 2 E 3 E 4 E 5 E 6 E 7 E 8 Fig. 14 Events of creating a row and adding it to a table, repeatedly

17 TM Potentiality and actuality for the Aristotelian example Dynamic Existence (actuality) Subsistence (Potentiality) Events= regions + time Regions Fig. 16 Two-level TM modeling Static

			Form			Wood
	Create	Release	Transfer	Create	Release	Transfer
					Transfer
					Receive
	Actuality		Process
	(events)	Statue	Create
		Form				Wood
	Create	Release	Transfer	Create	Release	Transfer
					Transfer
	Potentiality		Receive
	(region)			Process
			Statue		Create

Fig.


Jean Armengaud Proteotyping

High-throughput identification of microorganisms is key for clinical diagnostics and microbiology in general. Mass spectrometry for proteotyping microorganisms has been shown efficient because rapid and low cost. Recent studies have demonstrated the discriminative power of proteotyping based on tandem mass spectrometry. As this technology can quickly identify the most probable taxonomical position of any microorganism, even if not yet previously characterized in terms of taxonomy, and discriminate closely related strains, its application on environmental isolates, new emergent threats, or large collections has been promoted. Here, I will introduce the phylopeptidomics methodology with striking examples, its potential to be multiplexed and thus applicable on thousands of samples, and review the pre-analytical factors required for its application. The potential and perspectives of this methodology will be also commented, as it apply even on mixtures of microorganisms and complex microbiota. The methodology is thus applicable on collections of more complex samples.

  technologies for Detection and Diagnostics», ProGénoMix IBISA platform CEA, Bagnols-sur-Cèze, France Short abstract:


Jean Armengaud

Jean Armengaud Disentangling

Disentangling microbiota functions with metaproteomics

Microbial ecosystems play a major role in biogeochemical cycles, plant development and animal health. How microorganisms interact with each other, with their hosts, and with their environment are key questions. Understanding the functioning of microbial communities requires identifying the diversity of microorganisms present and quantifying the numerous molecular players in action. Proteins are the workhorses of biological systems. Metaproteomics is a key technology for such functional studies as it can provide for these particularly complex samples four types of answers: 1) identification of the taxa present, 2) quantification of the biomass of these organisms, 3) identification of the proteins of these taxa and their function, and 4) overall functional representation of the biological system. Challenges in terms of mass spectrometry, interpretation and mining of results will be addressed.


Jean Armengaud

Mélodie Kielbasa

Guylaine Miotello

Olivier Pible

Paleoproteomics & Metaproteomics exploration of unique historical samples

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

EUPA 2023 Conference Newcastle, July 18 th 2023 Paleoproteomics & Metaproteomics exploration of unique historical samples Jean Armengaud, Mélodie Kielbasa, Guylaine Miotello, Olivier Pible Abstract Introduction: How microorganisms interact with each other, with their hosts, and with their environment are key questions addressed by metaproteomics [START_REF] Armengaud | Metaproteomics to understand how microbiota function: the crystal ball predicts a promising future[END_REF]). The study of proteins from these particularly complex samples provides four types of answers: 1) identification of the taxa present, 2) quantification of the biomass of these organisms, 3) identification of the proteins of these taxa and their function, and 4) overall functional representation of the biological system. Paleoproteomics is the science of ancient samples. The best of both worlds is needed for characterizing ancient and complex samples that are only available in minute quantities.

Methods: For some historical artifacts, metagenomics cannot be performed due to the limited amount of material and the level of degraded DNA. To circumvent this time-consuming step, the list of organisms actually present in the sample can be established on the basis of the most reliable taxon-specific peptides. To do so, our proposal relies on an unbiased search of an extensive generic database, followed by a peptide search restricted to the most representative organisms.

Results: This forensic style approach will be illustrated by very "unique" samples such as dental remains of monks from the 16th century for which traces of coronavirus were identified [START_REF] Hama | An ancient coronavirus from individuals in France, circa 16th century[END_REF], cardiac relics of a blessed woman for which no trace of embalming were evidenced [START_REF] Bourdin | Deep paleoproteotyping and microtomography revealed no heart defect nor traces of embalming in the ( cardiac relics of Blessed Pauline Jaricot[END_REF], as well as with samples from very hostile environments such as nuclear storage pools [START_REF] Pible | Taxonomical composition and functional analysis of biofilms sampled from a nuclear storage pool[END_REF]. The challenges in terms of mass spectrometry, interpretation and exploitation of the results will be discussed.


Eurozone enlargement in the

Balkans

NEBOJSA VUKADINOVIC*PUBLIÉ LE19/02/2024 ÉCONOMIE Since the end of communism in the 1990s, the new currencies have had a triple function in the Balkans, particularly in the Yugoslav area. When they were first adopted, the idea was that they should primarily serve an economic function. But their symbolic and political functions must not be overlooked.

After the disintegration of Yugoslavia, adopting new currencies enabled the new governments to pursue an independent monetary policy. In Croatia, for example, the macroeconomic stabilization program known as the "Valentic Plan" (1) was launched in 1993 with a new currency, the kuna. Croatia returned to modest growth of 0.8% the following year, and a balanced budget was restored. Unlike the other states of the former Yugoslavia, Slovenia opted for an economic policy in line with the recommendations of IMAD (2) , the Center for Prospective Macroeconomic Analysis, which had recommended a policy of macroeconomic stabilization and a gradualist economic transition model as early as 1991. A new currency, the tolar, was introduced on October 8, 1991.

Introducing new currencies in these newly-created states was seen as conferring additional legitimacy on the elected authorities. The first free elections of 1990 were not held on a federal scale but on different dates in each republic, thus reinforcing the legitimacy of the republican and nationalist elites and the emergence of many ethnic parties. However, the adoption of new currencies also had a symbolic dimension since it was intended to support the national identity of the majority ethnic group in a context of separation and distinction from the other peoples of the former Yugoslavia. It was also intended to underline historical continuity. The kuna was used in the Middle Ages and during the Second World War as part of the independent Croatian state. The kuna's symbolic function is matched by its political role, as it is used in the rhetoric of political parties. Furthermore, it is necessary to distinguish between the use of the euro as a national currency and formal membership of the eurozone when the country becomes a member of the European Monetary Union. In the Balkans, we need to distinguish between countries that have adopted the euro without being part of the eurozone and without having followed the necessary steps and conditions to adopt the common currency as their national currency (Montenegro and Kosovo) and countries that are formally part of the eurozone and have therefore had to meet the necessary conditions (Slovenia, Croatia).

Montenegro and Kosovo: Euroisation without eurozone membership criteria

The political and historical conditions that led to using the euro as the national currency are specific to these two states. The hyperinflation characteristic of the 1990s in Serbia and Montenegro led the Montenegrin government, on November 2, 1999, to declare the dinar and Deutsche Mark (DM) legal tender in the country. Then, at the beginning of 2001, the Deutschmark became the country's official currency, even though Serbia and Montenegro formed a common state. In 2002, the disappearance of the Deutschmark in connection with Germany's transition to the euro naturally led Montenegro to adopt the new European currency as well.

In Kosovo, until 1999, many transactions were carried out in Deutsche marks, US dollars, or Swiss francs. This was due to a large Kosovo Albanian diaspora in Germany, the USA, and Switzerland. Following the NATO bombardment of Serbia and Montenegro (which ended in June 1999), UNMIK (the United Nations Interim Administration Mission in Kosovo) decided on September 3, 1999, that the Deutsche Mark would be the main currency. However, the Dinar remained in circulation, mainly in northern Kosovo. As in Montenegro, when the German currency gave way to the euro on January 1, 2002, Kosovo adopted the euro. Recently, at the beginning of 2024, the Albanian authorities in Pristina attempted to ban the use of the dinar in the Serbian parts of northern Kosovo and impose the euro, demonstrating once again the political dimension of monetary policy. So, de facto, Montenegro and Kosovo have "adopted" the euro without meeting the conditions for membership in the eurozone.

Slovenia and Croatia: enlargement of the eurozone

Slovenia was the first Eastern European country to adopt the euro on January 1, 2007. The tolar had a short life of 15 years. In 2006, Slovenia successfully met the conditions set out in the Maastricht criteria for membership of the Monetary Union (3) . Since then, the country has enjoyed steady growth and slowly continued its reforms. For example, privatization of the banking sector was not completed until June 2019, 29 years after the start of the transition. Croatia adopted the euro on January 1, 2023. The benefits of this transition are manifold: firstly, Croatia will be able to take advantage of the economic power of the EU and, in particular, benefit from a high borrowing capacity from the European Central Bank. Secondly, the European currency should provide the country with more excellent protection against inflation and, consequently, greater stability, particularly in times of economic crisis. Finally, adopting the euro should benefit the tourism sector, which is vital to the country's economy. However, fears of a resurgence in inflation have emerged among the population. This was confirmed in 2023, with inflation hovering around 7% in the final quarter, down from the peak at the beginning of the year but higher than in other eurozone countries.

Bosnia-Herzegovina: from Deutsche mark to convertible mark

Due to the hyperinflation affecting the Yugoslav dinar, the Deutsche mark was widely used in Bosnia-Herzegovina. After the Dayton Accords were signed in December 1995 and the international administration of post-war Bosnia-Herzegovina was set up, the country decided to change the name of its currency and introduce a Convertible Mark (KM or konvertibilna marka). The first banknotes were printed in 1998. Following Germany's transition to the euro, Bosnia-Herzegovina retained the Convertible Mark as its currency.

Can we speak of a currency board in this specific case? A currency board aims to find a solution to compensate for the loss of credibility of the currency; technically, this board is a monetary authority managing a fixed exchange rate with an international currency (in the case of the Balkan countries, the euro). The currency board (4) in Bosnia-Herzegovina is the result of this situation imposed by the country's international administration.

Serbia and Northern Macedonia: two cases apart?

After the fall of Slobodan Milosevic on October 5, 2000, a group of 17 economists opposed to the former regime addressed the question of Serbia's monetary policy, meeting within the framework of the G17. As elsewhere, priority was then given to macroeconomic stabilization, and reforms, notably privatizations, were carried out rapidly, even though the reform of the financial systems had not yet been completed. Serbia has enjoyed monetary stability and sustained growth for more than a decade. As a result of the war in Ukraine, monetary policy was tightened to ensure continued stability in the face of inflationary risks. The monetary policy pursued with the Serbian dinar for more than ten years enabled the country to weather the crisis of 2008 and the period of the pandemic.

After proclaiming its independence on November 20, 1991, North Macedonia introduced a national currency. The denar was introduced on April 26, 1992. The Macedonian government quickly adopted a monetary policy to combat inflation and ensure stability. As a result, the national currency was pegged to the Deutsche Mark.

In May 1993, the new denar was introduced. In 1998, the denar was indexed to the euro.

On the scale of the ex-(or post-)Yugoslav area, Croatia's accession to the euro zone in January 2023 (as well as to the Schengen area on the same day) represents the culmination of an integration process that began three decades ago and now marks new border lines.

Notes:

(1) Nikica Valentic (Prime Minister of Croatia from 1993 to 1995) implemented a macroeconomic stabilization program in 1993.

(2) Institute for macroeconomic analysis and development.

(3) Nebojsa Vukadinovic, "Slovenia", in Central and Eastern Europe Scoreboard, Les études du CERI, 2007.

( 4 )

 4 Sabrina Silajdzic, "The currency board trap: the case of Bosnia and Herzegovina," International Journal of Applied Econometrics and Quantitative Studies, 2005, pp. 47-79. * Nebojsa Vukadinovic teaches at Sciences Po Paris (Dijon campus) and is a research associate at IRM-CMRP. Link to the French version : https://regard-est.com/lelargissement-de-la-zone-eurodans-les-balkans Translated from French by Assen SLIM (Blog) To quote this article: Nebojsa VUKADINOVIC (2024), "Eurozone enlargement in the Balkans", Regard sur l'Est, 19 February. DOI : 10.5281/zenodo.10685483