Katell Berthelot

Clifford Ando

published or not. The documents may come

INTRODUCTION

Katell Berthelot (CNrS) and Jonathan PriCe (Tel Aviv University)

Roman citizenship was a unique phenomenon that broke precedent and defied expectation: it was both dynamic and a stabilizing force; it was a legal and political definition and an expansible, fungible idea; it had both particular and universalizing aspects. The Roman concept and application of citizenship played an essential role in the success of the vast and long-lived multi-ethnic Roman Empire. Yet its historical development, as both a practical legal-political status and a dynamic concept, is far from simple and straightforward; practically every detail and technical term, as well as the changing essence of Roman civitas, has engendered controversy. The modern historical debate about Roman citizenship began with Adrian N. Sherwin-White's fundamental study, first published in 1939, 1 which inter alia drew a direct connection between the spread of Roman citizenship and the strengthening loyalty of different provincial populations to Rome and their gradual incorporation into the Empire. Recently, Clifford Ando, in his study, Imperial Ideology and Provincial Loyalty in the Roman Empire, 2 has included citizenship as only one component in a universalizing tendency in all aspects of Rome's rule, including administration, ceremony, and art and architecture, combining into a process which he terms a shift "from imperium to patria".

While the importance of Roman citizenship for the building of empire is thus being rightly re-evaluated, the impact of Roman citizenship in all its political, legal and above all ideological aspects upon the inhabitants of the Empire, both citizens and non-citizens, has left many open questions. Most studies, beginning with Sherwin-White, while investigating the attitudes and action of provincials, take an unstated top-down, Roman perspective; this is partly the result of the sources used. Still insufficiently understood is the impact of the Roman model upon other types of citizenships, such as the local citizenships of the Greek poleis, and even more so upon the way other groups within the Empire that did not constitute civic communities came to define themselves either by imitating Roman discourses and practices, or by elaborating counter-models that were meant as an alternative to the Roman self-definition. This book aims to address these large issues, focusing in particular on Jews and Christians, their discourse about citizenship, peoplehood and membership in a community, their civic and communal practices, as well as the ways they integrated new members, sometimes designated as new "citizens," into their communities. What kind of an impact did the Roman discourse and practice of citizenship have upon the way Jews and Christians defined their own people or communities in the Roman imperial context, both before and after 212 CE? How did Roman discourse and practice differ from those of the Greeks, with which Jews had already been confronted in the framework of the Hellenistic kingdoms, and which, through their training in Greek paideia, also greatly influenced Christian authors?

Roman citizenship was an evolving phenomenon, but in all its stages differed in many ways from Greek citizenships. 3 First, at the end of the Republic and during the imperial period, the populus Romanus was not defined in reference to ethnicity (understood as implying not only a common language and a shared culture, but also a common descent, no matter how fictitious). 4 Rather, its definition Patrician families had a keen sense of their genealogy, and the Julio-Claudian dynasty made extensive use of their alleged connection with Aeneas and his mother Venus (through Caesar, Augustus's adoptive father), but the idea that all the Romans descended from the Trojans was indefensible in view of the numerous grants of citizenship (see below), and was not even argued for by Roman historians, who, on the contrary, emphasized the mixing of peoples at the origins of Rome and all along its history. Clifford Ando thus writes: "For the many and varied legends of the foundation of Rome agree on at least two details: Rome's original population had been heterogeneous, to say the least, and it had established and maintained itself in its early years through warfare" (Imperial Ideology, 52). Erich S. Gruen writes in a similar vein: "The idea of autochthony or indigenous origins never made 100668_Berthelot_ISACR21_01_Intro.indd 2 23/10/18 08:31

was political and legal: to be a member of the populus Romanus was equivalent to being a Roman citizen. Of course, for a long period of time, the most common way to be a Roman citizen was to be born to parents who were themselves Roman citizens, which comes close to the transmission of ethnicity. Hereditary transmission of citizenship, however, was not the only way of becoming Roman. Roman citizenship could be granted to individuals or to communities, for instance when a city received the status of a Roman municipium, using Roman law; after the Social War of 91-88 BCE, all the cities of Italy came to benefit from this political and legal framework. A city could also be refounded as a Roman colony. As far as individuals were concerned, a slave could become a Roman citizen through manumission, if the master of the slave was himself a citizen and if the manumission procedure was performed in accordance with Roman law. This ability of one person to confer citizenship upon another person was utterly unheard of in the world of the Greek poleis, in which grants of citizenships always had to be a collective decision. Individuals could also become Roman if they had served in the Roman army as auxiliaries for a certain number of years, or if they lived in a Latin municipium and had held local political offices. Exceptionally, Roman citizenship was also granted to individuals who had served Roman interests and proved very faithful to Rome; from the Principate onward, this decision was taken by the emperor alone.

The second fundamental aspect of Roman citizenship therefore was its "openness" or, to use Philippe Gauthier's expression, its "permeability". Much has been written, first by ancient Greek and Roman authors and then by modern historians, about the supposed "Roman generosity" in granting citizenship, often compared to the "avarice" of the Greek poleis. The ideological dimension of this discourse has been duly analyzed by the French historian and epigraphist Philippe Gauthier, who has drawn attention to the radical difference in nature between the Greek poleis and the Roman civitas. 5 To put it in a nutshell, much headway in Rome. […] Romans represented themselves without embarrassment as a composite people who belonged intimately to the broader Mediterranean world" (Rethinking the Other in Antiquity [Princeton; Oxford: Princeton University Press, 2011], 249).

Greek poleis can be described as structures of participation, whereas Rome is rather characterized as a structure of integration. The Roman civitas was of a different nature from the Greek politeiai, first and foremost because Roman citizens were far more numerous and spread out than those of any Greek city. In the second century BCE, the number of Roman citizens already approximated 300 000. By 14 CE, it is said to have exceeded four million, and Myles Lavan suggests in his article in this volume that it could even have reached six million -but this number included women and children; and it extended throughout the entire Italian peninsula, the Roman colonies and Cisapline Gaul, and individual cities in the provinces.

It is clear from Miles Lavan's survey of the history of Roman citizenship here, "The Foundation of Empire? The Spread of Roman Citizenship from the Fourth Century BCE to the Third Century CE," 6 that roughly four periods have to be distinguished in the history of Roman citizenship. 1) The period of the Republic before the Social War of 91-88 BCE, during which, in the earliest phases of Roman imperialism, enfranchisement was actually imposed on conquered populations as a means of regulation and control; but eventually, especially after the Second Punic War, Rome's expanding power enhanced the advantages of Roman citizenship, so that they began using citizenship-grants not as a punishment but as a reward. Near the end of this period, several sources actually testify to a growing stinginess and reluctance on the part of the Romans to grant full citizenship to their Latin allies, leading to expulsions from Rome. 2) The period running from the end of the Social War and the lex Plautia Papiria up to the beginning of the Principate, which saw an enormous increase in the number of citizens and a significant transformation in what Lavan calls "the geography of citizenship". 3) The period from 27 BCE to the edict of Caracalla in 212 CE, when the citizen body was expanded mostly through army service and patronage of both individuals and whole communities. 4) From 212 onward, when the edict of Caracalla granted universal citizenship to all free persons in the Roman Empire. According to Aristotle's analysis in the Politics (VII.4, 1726 a-b), even in the 2 nd century BCE the Romans would never have been 6

In addition, see his article, "The Spread of Roman Citizenship, 14-212 CE: Quantification in the Face of High Uncertainty," Past and Present 230 (2016): 3-46.

100668_Berthelot_ISACR21_01_Intro.indd 4 23/10/18 08:31 considered a polis, but rather an ethnos. 7 They were, however, by their own definition, a populus and a civitas. What did Roman citizenship imply for the citizens? More than the active participation in the political institutions of Rome, which very much depended upon one's wealth, social status, etc., and from the beginning of the Principate progressively came to an end, Roman citizenship implied three things: 1) the participation in the maiestas of the Roman people; 2) the enjoyment of specific rights -conubium, commercium, provocatio (first ad populum and then ad imperatorem), as well as a better legal protection than that of the peregrini; and 3) administrative, military, fiscal and religious duties. Some of the rights of the Roman citizens became less effective with the passage of time and the growth in the number of citizens, whereas from the period of the Antonine dynasty onward, only religious duties and some particular taxes were still incumbent upon the citizens. According to Cassius Dio, the aim of Caracalla's decision to extend Roman citizenship to all free men in the empire (with the exception of the dediticii) was to increase the number of tax-payers and thus alleviate the fiscal burden connected to the inheritance tax (which was paid by Roman citizens alone). Although its exact relationship to the edict of 212 is still debated, the papyrus Giessen 40 makes clear that religious aspects were involved as well. 8 To increase the number of Roman citizens meant to increase the number of those who worshipped the Roman gods, and therefore to increase the honours paid to the gods. Lavan, in his article here, favors "the very contingent and personal concerns of Caracalla in 212-13" as the main motivation for the decree.

Before 212, and at least from the 2 nd century BCE onward, Roman citizenship was generally considered an honour and a privilege. According to Cicero, who famously spoke about the two patriae, the patria of origin and the communis patria, no status or membership 7 See Gauthier, "La citoyenneté en Grèce et à Rome," 169. could be more prestigious than Roman citizenship, and "loyalty toward Rome occupied a superordinate position". 9 Cicero viewed the promise of Roman citizenship as a powerful tool to extend Rome's authority throughout the world, and indeed the standard view agrees with this, crediting citizenship as an important imperial instrument used to integrate provincial populations into the "hegemonic superstructure," as Lavan puts it. Obviously, participation in the Roman world far exceeded participation in the Roman civitas, as Clifford Ando in particular has emphasized. 10 The primary purpose of the present book, however, is not to analyse the different ways people could participate in the Romanitas (to use a late term), 11 but, rather, to study something far less well understood, namely, the impact of the Roman model of citizenship and of the Roman policy of citizenship grants upon other groups and upon their own ways of defining their modes of belonging, be it a local citizenship, an affiliation with an ethnos, a membership in a voluntary association, a philosophical school, a mystery cult or a sect of some sort, and so forth. What kind of an impact did the Roman civitas have upon the ways people defined themselves and reflected upon the groups they belonged to?

While asking this question, one should bear in mind that Roman citizenship had both institutional and ideological aspects, which made it a powerful tool for Roman imperialism. On the one hand it helped to integrate people into the empire and thus to extend its domination, especially in the West, and on the other hand it was an important theme of Roman imperial propaganda, found in Roman and pro-Roman discourses. 12 Those of Dionysus of Halicarnassus and Aelius Aristides are particularly well-known, so let us quote Dio Chrysostom for a change (and see Adam Kemezis' article, summarized below). 9 Ando, Imperial Ideology, 10. See Cicero, De Legibus 2.5. 10 See note 2 above. 11 On this issue, see Hervé Inglebert, Histoire de la civilisation romaine (Paris: PUF, 2005), 451-82.

12 Several ancient sources formulate the idea that the Romans' "generosity" in granting citizenship played an important role in the successful establishment of their domination. See for instance SIG 543 (Philip V of Macedon writing to the Larisaeans); Cicero, Pro Balbo 31; Dionysus of Halicarnassus, Roman Antiquities 2.16-17; etc.

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In his forty-first discourse "To the Apameians, On Concord," Dio writes:

That city (Rome), while so superior to the rest of mankind in good fortune and power, has proved to be even more superior in fairness and benevolence, bestowing ungrudgingly both citizenship (politeia) and laws and offices, believing no man of worth to be an alien, and at the same time safeguarding justice for all alike. 13 What needs to be emphasized is that Roman citizenship was at one and the same time an effective instrument of Roman imperialism and a significant challenge for the peoples and the communities that came under Rome's domination, even if Roman citizenship per se was not the only way to belong to the Roman oikoumenē and to participate in the Romanitas.

The nuances of this phenomenon are illuminated in this volume by Lavan. It is true, as he comments in a recent article, that "It is a commonplace of Roman history that Rome's generosity with its citizenship distinguished it from other ancient city states and played an important role in its success as an imperial power". 14 But here he shows that the full picture was more complex than what blithe ancient assessments or even some modern reconstructions have posited. Citizenship was not shared universally by local elites; the enfranchisement of discharged soldiers, freed slaves, and communities en masse, diffused citizenship broadly across the lower strata of society. Citizenship was just one factor -neither necessary nor sufficient in itself -in the integration of local elites and the stability of different areas of the Empire. In fact, while the imagined community of the populus Romanus was conceptually distinct from the undifferentiated non-citizens, this community was itself highly stratified so that the upper class (honestiores) eventually had a different juridical status from the lower (humiliores), and there were meaningful geographical and cultural and linguistic differences between Roman citizens, as well. That is to say, a conceptual center of Roman citizenship, if not an actual one, defined by Italian origin, Roman ethnic origin and Latinity, retained its force, giving a different practical and abstract significance to "citizenship" in the periphery and the center. This practical and abstract significance can be seen, first, by viewing the provincial Greeks in their own terms. Anna Heller, in her contribution to this volume, "Greek Citizenship in the Roman Empire: Political Participation, Social Status and Identities," explicates the complexities of integration and its profound but uneven impact on the civic and social structures in the Greek poleis in different regions from the Roman conquest in the second century BCE through the period of High Empire. Under the influence of the Roman model and the advantages that Roman citizenship accorded elites in their local contexts, the cities underwent a gradual process of aristocratization, so that, for instance, the boulē became an oligarchical stronghold, even if it was not a directly imitative model of the Roman Senate. Epigraphical evidence testifies to an ever more rigid social hierarchy with legal and political implications, compromising the equal rights and privileges of citizens; politeia in honorific texts shifted from political rights to social prestige. This shift in meaning reflects a subtle but crucial distinction between a grant of citizenship, integrating the person into the political and civic institutions of the city, and the possession of citizenship as one coveted honor among many, whose main importance is to enhance the prestige of the possessor. Social hierarchization -which is expressed in sometimes new Greek terminology for classes of citizens -was enhanced by the grants of Roman citizenship to local elites.

But these grants were not evenly dispersed throughout the Greek cities, nor even universally desired by local elites in every city or region (a phenomenon which also changed over time). It was a dynamic situation, not reducible to a single model or uniform conclusion. Even as Roman domination had a measurable effect on the social hierarchy, political structures and signs of status within poleis, the idea of Greek community persisted, and arguably was even strengthened internally by the external pressure of the Empire. Individuals' involvement in the civic life of their city remained crucial to their identity and their idea of citizenship and belonging. Moreover, the possession of Roman citizenship by Greeks in neighboring cities could in some cases reinforce mutual ties and create a kind of Greek micro-region. Local attachments remained strong even for Greeks who became active in the Roman administration. Thus the introduction of Roman citizenship into the Greek world did not engender a total shift from the "structure de participation" by which Greek 100668_Berthelot_ISACR21_01_Intro.indd 8 23/10/18 08:31

citizenship is characterized (according to Gauthier) to the "structure d'intégration" which is the essential nature of Roman citizenship. Roman citizenship enhanced individuals' status and strengthened local elites but did not create a coherent political community of Roman citizens in the Greek East.

The notion of Roman citizenship as a new essential component in a culturally and socially elite ruling class in the Empire, lies at the base of attempts by Greek intellectuals to come to grips with the challenge of Roman citizenship and the fact of the Roman Empire. Isocrates had attempted to transform Hellenic identity from ethnic (based on physis) to cultural (based on paideusis), and indeed Sylvie Honigman has argued that the shift from ethnicity to paideia as an essential criterion in the attribution of local Greek citizenships, during the Hellenistic period, was in part a consequence of the integration of the Greek world in the sphere of Roman influence. 15 The Isocratean idea informed the constructions of identity and belonging in Greek orators and writers of the second and third centuries CE, as Adam Kemezis, in his article here, "Beyond City Limits: Citizenship and Authorship in Imperial Greek Literature," explains in an interpretation of three authors of the period: Dio Chrysostom, Aelius Aristides and Cassius Dio. Through these authors, Kemezis takes us beyond the confines of the actual poleis or any civic body existing in reality to an imagined community. For each of the Greek authors, Roman citizenship was both an affirmation and an enactment of class privilege and what they viewed as their personal virtue and responsibility to the larger community.

Dio Chrysostom, in a series of city-speeches which relate very little to their specific urban settings, describes an idealized city in which homonoia prevails and the elite citizens are bound not by legal or political obligation nor by their shared ethnic identity but by their own demonstrated virtue. The elite in existing Greek cities create a kind of trans-polis in which they are citizens, and in which actual Roman citizenship functions merely as "the paradigmatic example of the key concept of citizenship as recognition of ethical worth" which in turn legitimates their social status and privilege; the main purpose 15 Sylvie Honigman, "Permanence des stratégies culturelles grecques à l'oeuvre dans les rencontres inter-ethniques, de l'époque archaïque à l'époque hellénistique," Pallas 73 (2007): 125-40.

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of their exclusive citizenship was to ensure social harmony. A similar community which does not originate in or is defined by Roman citizenship but includes it as a component of personal worth, is imagined by Aelius Aristides in his Roman Oration. Aristides' community is more Roman than Dio's -after all, his speech is supposed to have been given in Rome -but still defines citizenship as a degree of excellence which is appropriately awarded and utilized. Thus "in Aristides' implicit aristocratic worldview, the virtues by which the Romans define the citizen community are closely tied to elite social class". In both of these conceptions, Roman citizenship has a different essence and function from the reality in which the authors actually lived. Both Dio Chrysostom and Aelius Aristides would have been horrified by Caracalla's universal grant of Roman citizenship in 212, which eliminated the exclusivity in the privilege together with the opportunity to philosophize about it as a symbol of virtue unifying the ruling elite. The historian Cassius Dio, whose life and professional career were the fulfillment of the ideals in the oratory of Dio and Aristides, did live through that pivotal moment and dismissed the empire-wide enfranchisement as a ploy for increasing revenues by an emperor whom he clearly despised. Cassius Dio had his own notion of the ideal Roman citizenship, reflecting what he thought was an essentially Augustan ideal, which rigidified traditional social hierarchy, ensuring both the status, privileges and responsibilities of narrow the ruling class, on the one hand, and internal peace and harmony, on the other. In Dio's view, this loyal ruling elite had been created in the East through judicious extension of Roman citizenship, and Caracalla's single act brought that whole structure down.

So much for Greeks. The challenge of and reaction to Roman citizenship were different for other groups in the Empire who had little chance, and sometimes little desire, to become Roman citizens before 212. In the case of the Jews, from their first direct contact with Rome as an independent civic body in the second century BCE and continuing through the first century CE, the question is the influence that Roman models had on the their conception and practice of citizenship. This is the question taken up by Katell Berthelot in her paper, "Judaism as 'Citizenship' and the Question of the Impact of Rome". She rejects the idea that the Hasmoneans created a state for which "citizenship" was a relevant concept, and therefore they did not -could not -enroll the Judaized Idumeans as "Judean citizens" 100668_Berthelot_ISACR21_01_Intro.indd 10 23/10/18 08:31

(a phrase which is merely a metaphor); nevertheless, integrating defeated enemies into the polity was new and has to be accounted for.

Morton Smith argued in an article published in 1978 that the conversion of the Idumeans and the Itureans under the Hasmoneans is to be explained by the impact, upon the leaders of Judea, of the Roman policy of granting citizenship to Rome's former enemies. Berthelot points out the serious chronological problem in this theory, since the Rome that the Hasmoneans knew had practically reversed its policy of integrating the conquered, exhibiting a political stinginess that would soon lead to the Social War (and see again Lavan's article here). Yet in a later period, when Rome had established its power absolutely over Judea and the former Hellenistic kingdoms, Philo and Josephus were both so inspired by the discourse about the "generous" Roman policy of integrating foreigners into the Roman polity that they used this kind of discourse to describe the Jewish attitude towards proselytes. These two important Jewish Greek writers described Jewish "citizenship" as reflecting, aside from the essential notion of ancestry, virtue and piety as expressed in the observance of common laws. Thus, to return to the two basic patterns of citizenship as construed by Gauthier, both Philo and Josephus conceived of Jewish affiliation in Roman terms, as a polity of integration rather than participation. This is sensible for several reasons: Jews were scattered throughout the Roman world, so that the Mosaic politeia could not require or imply common political procedure; both authors were responding to the pro-Roman discourse current in their time, as evidenced e.g. in Dionysius of Halicarnassus; and Philo and Josephus lived in an vivid and immediate Roman reality, they had inter alia Roman audiences in mind.

It is instructive, at this point, to consider "one specifically Jewish conceptualization of boundary-crossing, affiliation, and communal identity," as Paula Fredriksen puts it in her paper, "How Do the Nations Relate to Israel? Family, Ethnicity, and Eschatological Inclusion in the Apostle Paul". Paul of course was a Roman citizen by birth, according to Acts, and knew how to use his rights, for instance by appealing to the emperor (provocatio ad imperatorem). His participation in the Roman civitas was through his local civic inscription in the city of Tarsus, and he certainly had a good knowledge of Greek culture. He also belonged to the ethnos of the Ioudaioi, and ultimately became one of the leading members of a Jewish sect which turned into a new "religion". Despite his contentious reference to a Christian politeuma (see below), Paul in general avoids the language of citizenship when speaking of Gentiles converting to Christianity but rather uses the Roman concept of adoption to describe their attachment to the community, in order to legitimize them as heirs to the kingdom of heaven. The adopting father is none other than God himself, which not only usurps other lines of inheritance and binds cult members together, but also further unifies the Christian family by the spiritual bond of common worship. This Roman metaphor sits side by side in Paul's thought with a more strictly biblical idea of descent from Noah that distinguishes Israel and the Gentiles within the same eschatological community. Still, Paul claimed, in a singular passage, that Christians had a "politeuma in heaven" (Philippians 3:20). The puzzle of this expression is unraveled by Peter Oakes in his article here, "The Christians and their Politeuma in Heaven: Philippians 3:20 and the Herakleopolis Papyri". Oakes rejects, in turn, previous solutions which propose to blur the specificity of politeuma and translate it as "citizenship" or a large-scale "commonwealth". Significantly, he also points out the difficulty of interpreting Paul's expression as a deliberate counterpoise to the Jewish politeuma in Philippi, in parallel to the politeuma of Herakleopolis in Egypt, documented in the papyri. It is true that from the Hellenistic period onwards, many Jews, both in Judea and in the Diaspora, were attracted to the Greek civic model, and either tried to adopt it for themselves -as illustrated by the creation of Antiocheia in Jerusalem at the beginning of the 2 nd century BCE, before the Maccabean uprising, or indeed by the creation of politeumata in the Diaspora such as that in Herakleopolis 16 -or used the vocabulary of citizenship to speak about membership with the people of Israel. But as Oakes contends, this is not a useful model to 16

The exact number and nature of Jewish politeumata is hotly disputed, and in any case membership in a politeuma was not a citizenship, but rather a membership in an association. Nevertheless, the constitution of Jewish politeumata should be included in the analysis of the ways Jews interacted with Greek civic institutions and political realities. Oakes cites recent bibliography, as well as Gilles Dorival (notes 48 and 49) in the present volume.

100668_Berthelot_ISACR21_01_Intro.indd 12 23/10/18 08:31 understand Paul's expression. Rather, the politeuma referred to by Paul is a central governmental institution with wide influence and authority over a population beyond defined borders. This insight enables Oakes to argue that Paul meant to create in the minds of his listeners an innovative idea of heavenly citizenship, unrestricted by earthly impediments, thus uniting an otherwise differentiated Christian community: without earthbound distinctions of Roman citizenship or social status in Philippi, all Christians could serve the Christian community on equal footing and stand strong against hostile pressures from within Philippi itself.

Yet if Philo was the first explicitly to define the Jewish community or the Jewish people as a politeia, and if Paul offered a revised version of heavenly citizenship, how, before 212 CE, did Jews in the Diaspora who were not Roman citizens define their collective identity? Or how, after 70 CE, did Jews who were Romans articulate such conflicting affiliations? Or finally, how, after 212 CE, did Jews react to the imposition of Roman citizenship on all free men (with the exception of the dediticii)? In particular, one wonders whether it affected the rabbis, and what their response to the new Roman policy was. These questions are approached from two entirely different angles in the papers by Oded Irshai and by Yair Furstenberg.

In an innovative argument, Irshai, in his piece, "How do the nations relate to Israel? Rabbis, the conversion of goyim, and the Constitutio Antoniniana," demonstrates that the rabbis of the second to fourth centuries CE, while sharply distinguishing between Jews and Gentiles, and between the Jewish community and Roman custom and culture, drew heavily on it for the idea of an all-inclusive community well adapted to accepting foreigners. That is, the earlier generations of the rabbis used a Roman model to conceptualize and deal practically with Gentiles, even if they viewed themselves as an oppressed minority rather than a hopeful apocalyptic community. The rabbis' model was universal inclusion inspired by Caracalla's universal enfranchisement and the real relief and calm it brought to Jews under Roman rule. They sharply distinguished between Jews and non-Jews (goyim) but still devised ways, inspired by Rome's inclusive policy, to bring them into the community.

Roman policies and practices regarding citizenship also had an impact on rabbinic halakhah regarding the definition of insider/outsider in 100668_Berthelot_ISACR21_01_Intro.indd 13 23/10/18 08:31

another, more specific context, as shown by Yair Furstenberg in his article, "The Rabbis and the Roman Citizenship Model: The Case of the Samaritans". The inveterate, ethnic enmity that Jews felt against Samaritans in the Second Temple period, and that has biblical roots, was modified in early rabbinic texts to a form and procedure of acceptance in the community, with certain legal restrictions. Furstenberg argues that by (re-)conceiving the Jewish community as a legal community, according to Roman definitions and norms, the rabbis created a process by which Samaritans could be given an intermediate legal status, with a prohibition on marriage and severe restrictions on commercial transactions with Jews and acquiring land in the Land of Israel -i.e., very much like the restrictions on conubium and commercium for partial citizens in the Roman system. Thus the rabbis abandoned a strict ontological distinction between Jews and others and adopted rather a more subtle and gradated system for classifying others, and as Furstenberg suggests, they used the Roman concept of different levels of participation in the legal community while retaining dominance and control in their own hands. The Jewish communities in both the foreground and background in rabbinic literature are by and large fairly insular and inward-looking, self-sufficient, managing their own legal, social and administrative affairs. This impression stems as well from exemptions of civil service claimed by Jews in the Theodosian Code, and some Jewish communities known from other non-rabbinic evidence certainly can be described as divorced from the civic life of the Empire around them. Two extreme instances are seen in archaeological and epigraphic remains of the synagogal communities at Ein Gedi and Reḥov, which testify to remote Jewish communities entirely focused on their own laws and business -in the case of Ein Gedi, the by-laws of the community, and in the case of Reḥov, Jewish agricultural laws in the Land of Israel -and for whom Roman citizenship and participation in the Roman Empire do not seem to have been important to their identity or internal functions. 17 Other synagogues, even in Israel (such as those 17 For Ein Gedi, see Corpus Inscriptionum Iudaeae/Palaestinae IV, 3851; for Reḥov, J. Naveh, On Stone and Mosaic (Tel Aviv: Israel Exploration Society, 1978), 79-85 (Hebr.), and for a detailed discussion of the halakhic inscription, dealing primarily with agricultural laws, Y. Sussman, "The Halachic Inscription from the Beth She'an Valley," Tarbiz 43 (1973-74): 87-158 and Tarbiz 44 (1974-75): 100668_Berthelot_ISACR21_01_Intro.indd 14 23/10/18 08:31

along the coast, in Caesarea, Ashkelon and Gaza), appear from their physical remains and art to have been more cosmopolitan, but close study of inscriptions, especially the large number of Jews advertising their civic titles, indicates that Jewish participation in municipalities throughout the Empire was more willing and energetic than the legal sources have led us to believe. This is the thesis argued by Capucine Nemo-Pekelman, "The involvement of the Jews in municipal life during the Late Roman Empire". By re-reading, against epigraphical evidence of Jews serving in the imperial administration, the seven imperial constitutions which deal with Jews' asking for exemption from curial duties, Nemo-Pekelman shows that in a significant number of cases, Jews performed civic functions in parallel to their responsibilities in the synagogue, and used election as decurion for advancement to higher honors, including the highest offices in the municipality. It is possible to conclude that there were clear benefits of parallel and mutually strengthening careers in the municipality and synagogue, since "ascending through the ranks of one helped their chances of success in the other". There were even cases of Jews who requested exemption from serving in their local curia in order to pursue careers in the senatorial order and imperial bureaucracy. Naturally, there are attested cases of Jews asking for exemptions from local curial service by claiming the privileged status as clergy, for the privilege of the status and also in order not to impair their standing within the synagogal community, but by the fourth century, the Christian imperial administration in the West had stopped granting these exemptions to Jews (in contrast to a more generous policy in the East). In Late Antiquity, Christian authorities in the West imposed on Jews and Jewish communities in another way, as well. One of the main claims by Samuele Rocca in his article, "From Collegium to Ecclesia: The Changing Outer Framework of the Jewish Communities in Roman Italy," is that later Roman law compelled the Jews to adopt "a communitarian organization, molded on that of the Christian Church". This marked a shift from the period of the early empire, according to Rocca, when the form of Jewish communities in Italy resembled that of the collegia licita and were formally under the patronage of the Roman emperor (or in some cases, a Herodian prince with Roman citizenship).

Similar and yet different questions arise in connection with the Christians: how did Christians who were Roman citizens articulate their different affiliations? From the very beginnings of Christianity, some Christians appropriated the vocabulary of citizenship to speak about membership in the Church. The role played by the imperial context and by Paul's own Roman citizenship in the writings of the apostle is disputed and many-faceted; some idea of the complexity of this topic is displayed in the articles by Paula Fredriksen and by Peter Oakes, as we have already seen.

Unlike the case of some Jews, the Christians who were Romans were not exempted from their religious duties towards the gods of Rome until Galerius's edict in 311 CE. Moreover, Caracalla's policy particularly emphasized these religious duties, which were then the main element that defined Roman citizenship (together with taxes). 18 Only from 311 and above all 313 CE onward would the Christian faith become compatible with one's religious duties as a Roman citizen. Both before and after this turning point, one may ask in which ways Christian authors both opposed the Roman model of citizenship or communis patria and remained indebted to it.

The use of civic vocabulary, in metaphors or by way of analogy, becomes especially important only in later Christian writings, such as the Epistle to Diognetus, the work of Origen and that of Augustine. These authors tend to consider Christians as "citizens" of the heavenly Jerusalem or of the City of God rather than as citizens of local communities. Gilles Dorival, in his close linguistic study here, "Christian Redefinitions of Citizenship," outlines the development of political vocabulary in both Jewish and Christian lexica, showing how the polity gained strong religious connotations, so that Christians were envisioned as citizens of a heavenly city that is superior to and supersedes earthly cities. Similarly, Hervé Inglebert explores the question posed in the title of his article, "How to Define the Citizenship of the City of God: An Augustinian Problem" -a question made especially 18 See Hervé Inglebert, "Citoyenneté romaine, Romanités et identités romaines sous l'empire," in Idéologies et valeurs civiques dans le monde romain : Hommage à Claude Lepelley (Paris: Picard, 2002), 241-60, esp. at 242-45. 100668_Berthelot_ISACR21_01_Intro.indd 16 23/10/18 08:31

difficult by the crumbling of the political structures in Augustine's time, when the meaning of actual citizenship was dwindling accordingly. Earlier, when the Roman Empire was stable, Christians had truly valued the possession of Roman citizenship and the "generous" Roman policy in granting citizenship to numerous inhabitants of the Empire, as Inglebert has already demonstrated elsewhere. 19 But Roman citizenship and its connection to Christian identity became more problematic with the dismantling of the Empire. Augustine's solution was to redefine citizenship in the city of God as Christian ethics. This concept transcended the dismal reality, allowing Christians to feel a sense of belonging to a timeless Christian ideal. By grounding the citizenship of the City of God in ethos rather than in law, Augustine succeeded in making the Church autonomous vis-à-vis the evolution and the ultimately unhappy fate of the Christianized but still earthly Roman empire.

8

  See Peter Alois Kuhlmann, Die Giessener literarischen papyri und die Caracalla-Erlasse: Edition, Übersetzung und Kommentar, Berichte und Arbeiten aus der Universitätsbibliothek und dem Universitätsarchiv Giessen 46 (Giessen:Universitäts- bibliothek, 1994). For a recent analysis of the text as artifact, see Ari Z. Bryen, "Reading the Citizenship Papyrus (P.Giss. 40)," in Citizenship and Empire inEurope 200-1900: The Antonine Constitution after 1800 years, ed. Clifford Ando, Potsdamer Altertumswissenschaftliche Beiträge 54(Stuttgart: Franz Steiner Verlag, 2016

13

  To the Apameians, On Concord §9, trans. by H. Lamar Crosby, LCL, 159, slightly modified. 14 Lavan, "The Spread of Roman Citizenship, 14-212 CE," 4. 100668_Berthelot_ISACR21_01_Intro.indd 7 23/10/18 08:31

  19 See Hervé Inglebert, "Christian Reflections on Roman Citizenship (200-430)," in Clifford Ando (ed.), Citizenship and Empire in Europe 200-1900: The Antonine Constitution after 1800 years, Potsdamer Altertumswissenschaftliche Beiträge 54 (Stuttgart: Franz Steiner Verlag, 2016), 99-112.

100668_Berthelot_ISACR21_01_Intro.indd 17 23/10/18 08:31 100668_Berthelot_ISACR21_01_Intro.indd 18 23/10/18 08:31

On the institutional and political differences between Greek and Roman citizenships, see Philippe Gauthier, "La citoyenneté en Grèce et à Rome : participation et intégration," Ktèma 6 (1981): 167-79.

4

See Gauthier, "'Générosité' romaine et 'avarice' grecque : sur l'octroi du droit de cité," in Mélanges d'histoire ancienne offerts à William Seston, Publications de la Sorbonne, série Etudes 9 (Paris: De Boccard, 1974), 207-15.100668_Berthelot_ISACR21_01_Intro.indd 3 23/10/18 08:31

k. Berthelot aNd j. PriCe


domain: spi phys math info

text:
Albena Tchamova
email: tchamova@bas.bg

Jean Dezert
email: jean.dezert@onera.fr

Pavlina Konstantinova
email: pavlina.konstantinova@gmail.com

Nadejda Bocheva
email: nbbocheva@hotmail.com

Biliana Genova
email: b.genova@abv.bg

Miroslava Stefanova

Human Heading Perception Based on Form and Motion Combination

Keywords: Vision, Heading Perception, Form cue, Motion cue, Cues Combination, DSmT, probabilistic Proportional Redistribution rule no.5, Normalized Conjunctive rule

This paper presents a study on human perception of the heading on the base of motion and form visual cues integration. The authors examine how human age influences this process. Because the visual stimuli are in general uncertain, or in some cases even conflicting, the process of combination is estimated on the base on the well known Normalized Conjunctive Consensus fusion rule, as well as on the base of the more efficient Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning, and more precisely on the probabilistic Proportional Conflict Redistribution rule no.5 defined within it. The main goal is focused on how these fusion rules succeed to model consistent and adequate predictions about both individuals' behavior, and age-contingent groups of individuals 1 .

I. INTRODUCTION

Form and motion information are closely linked and continuously interacting in the human visual system, which takes the advantage to utilize both of these visual characteristics (or so called cues) to make decisions about human heading perception [START_REF] Kourtzi | Linking form and motion in the primate brain[END_REF] described via the respective rapid eye movement (so called saccades) towards the object of interest position. The cooperation between the form and motion cues becomes very useful and even necessary, when: (i) each cue (motion, form) alone does not supply sufficient information to estimate the proper and accurate heading, or/and, (ii) the uncertainty, associated with the utilized visual cues and the possible conflicts between them influence negatively the process of decision making. The last case relates closely to the effect of the age-related changes throughout the life cycle and to deterioration in the cognitive processes, and consequently in visual information processing due to a variety of factors like cell death, cognitive dedifferentiation, increase of internal noise in the visual system.

As a result, the contrast sensitivity, self-motion perception, as well as eye movement characteristics are deteriorated in the elderly [START_REF] Pardhan | Contrast sensitivity loss with aging: sampling efficiency and equivalent noise at different spatial frequencies[END_REF], [START_REF] Dowiasch | Effects of aging on eye movements in the real world[END_REF], [START_REF] Lich | Self-Motion perception in the elderly[END_REF]. To overcome all these difficulties one needs to combine and utilize in an effective way both of cues in order to achieve inferences, more informative and potentially more accurate than if they were obtained by means of a single cue. Integration of information from multiple sources (cues) in a single modality increases the precision of perceptual performance. Such a claim recently has been supported by a list of neurobiological studies, like [START_REF] Pavan | Distinct position assignment mechanisms revealed by cross-order motion[END_REF], [START_REF] Barlow | Convergent evidence for the visual analysis of optic flow through anisotropic attenuation of high spatial frequencies[END_REF], [START_REF] Edwards | Motion streaks improve motion detection[END_REF], and also neurophysiological findings exist about neurons responding to both form and motion in some cortical sites (including early visual areas and extrastriate areas) [START_REF] Jancke | Orientation formed by a spots trajectory: A two-dimensional population approach in primary visual cortex[END_REF], [START_REF] Albright | Direction and orientation selectivity of neurons in visual area MT of the macaque[END_REF].

Inspired and based on these important biological findings of the cue combination effectiveness, the aim of this paper is to investigate how humans integrate motion and form information in the process of decision making about heading direction. The authors will focus on how the human age influences this process, and also whether the human visual system is enable to adapt during the life cycle in order to exploit all available information, providing a sensible and meaningful decision about the problem under concern. In our study we simulate only the directional flow occurring during the forward motion of the observer and not the changes in speed or size of the moving objects that accompanied it. The researcher team will compare human cue combination performance with modelled combination performance, based on particular fusion rules. In the presented study the authors will apply and compare the performances of the following fusion rules: the Normalized Conjunctive Consensus (NCC), and the very recent probabilistic Proportional Conflict Redistribution rule no.5 (pPCR5) defined within DSmT. The novelty of our study consists in applying especially this novel pPCR5 fusion rule to model the human process of form and motion cues integration. This paper is organized as follows. In section II we briefly present the form and motion combination process, and the principles of the used fusion rules, applied to model the human cue integration. Section III is devoted to the experimental strategy, methods, procedures, stimulus, apparatus, and also subjects participating in the experiments. The results obtained are described and analysed in Section IV. Conclusions are made in Section V.

II. FUSION RULES FOR MODELLING VISUAL CUE COMBINATION

Various fusion rules exist in the literature to deal with uncertain or even conflicting evidence based on different mathematical models and on different methods for transferring the conflicting mass onto the sensible hypotheses about the problem under consideration. The classical one is Bayesian inference [START_REF] Bayes | An Essay towards solving a Problem in the Doctrine of Chances[END_REF], [START_REF] Sivia | Data Analysis, a Bayesian Tutorial[END_REF] which deals with probabilistic information. The main idea of Bayesian inference is to obtain the most reliable estimate of the state of the world on the base of independent cues combination, i.e. the estimate in which the variance of the resulting combined cue is minimized. But being very sensitive to the sources with the bigger means, it could neglect part of available information, which is not adequate and reliable behavior in cases of conflicting visual cues combination. Bayesian inference has some difficulties to apply, related to the requirements of measurements' statistics and knowledge about the a priori information. Dempster-Shafer Theory (DST) [START_REF] Dempster | A generalization of Bayesian inference[END_REF], [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF] was the first theory for combining uncertain information expressed as basic belief assignments with Dempster's rule. Although appealing in modelling the epistemic uncertainty this theory shows very questionable and controversial results in cases of high (and even low) conflicting sources of evidence [START_REF] Zadeh | A Mathematical Theory of Evidence (book review)[END_REF], [START_REF] Voorbraak | On the justification of Dempster's rule of combination[END_REF], [START_REF] Wang | A defect in Dempster-Shafer theory[END_REF], [START_REF] Dezert | On the validity of Dempster's fusion rule and its interpretation as a generalization of Bayesian fusion rule[END_REF].

To overcome all these limitations of DST, Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning was developed [START_REF] Smarandache | Advances and applications of DSmT for information fusion[END_REF].

DSmT works for any model, which fits adequately with the true nature of the fusion problem under consideration. It is a general mathematical framework for managing and solving problems of uncertain, highly conflicting, imprecise knowledge representation and fusion, and decision making procedures, based on vague, imprecise models for a wide class of static or dynamic fusion problems.

A. Normalized Conjunctive Consensus rule

The Normalized Conjunctive Consensus (NCC) rule is used to combine simultaneously assumed independent visual cues. In the case considered in our paper, the information obtained by the available form and motion cues is characterized by Gaussian likelihood functions with given means μ i , i = 1, 2, .. and standard deviations σ i , i = 1, 2, .., defining the uncertainty encountered in data. In case of two independent cues with one-dimensional Gaussian distributions p 1 (x) =

1 σ1 √ 2π exp -1 2 ( x-μ1 σ1 ) 2 and p 2 (x) = 1 σ2 √ 2π exp -1 2 ( x-μ2 σ2 ) 2
, the combined distribution based on NCC rule becomes:

p NCC (x) = 1 σ NCC √ 2π exp - 1 2 ( x -μ NCC σ NCC ) 2 (1)
where

σ 2 NCC = σ 2 1 σ 2 2 σ 2 1 +σ 2 2 and μ NCC = σ 2 NCC ( μ1 σ 2 1 + μ2 σ 2 2
).

It is characterized with a mean, biased toward the function with the bigger of the two means, similarly to Bayesian estimator. It is optimal, i.e. minimizes the variance of the error estimation, when the original distributions have close mean values. When both cues are in conflict, however, (characterized with distant distributions), NCC rule leads to neglecting part of the available information, because the source with the bigger mean is weighted more heavily. In this case it is reasonable to keep the original distributions in the fused probability density function until it is possible to make reliable decision. This has been done by pPCR5 fusion rule defined in DSmT.

B. Probabilistic Proportional Conflict Redistribution rule no.5

The general principle of all Proportional Conflict Redistribution rules [START_REF] Smarandache | Advances and applications of DSmT for information fusion[END_REF], Vol.3 is to: 1 ) calculate the conjunctive consensus between sources of evidence (different visual cues) 2 ) calculate the total or partial conflicting masses; 3 ) redistribute the conflicting mass (total or partial) proportionally on non-empty sets involved in the model according to all integrity constraints. The recently proposed non-Bayesian probabilistic Proportional Conflict Redistribution rule no.5 (pPCR5) [START_REF] Smarandache | Advances and applications of DSmT for information fusion[END_REF] is based on the discrete Proportional Conflict Redistribution rule no.5 [START_REF] Smarandache | Advances and applications of DSmT for information fusion[END_REF], Vol.3, for combining discrete basic belief assignments. For completeness, we will discuss in brief the main idea behind the discrete PCR5. It comes from the necessity to deal with both uncertain and conflicting information, transferring partial or total conflicting masses proportionally only to non-empty sets involved in the particular conflict and proportionally to their individual masses. Basic belief assignment (bba) represents the knowledge, provided by particular source of information about its belief in the true state of the problem under consideration. Given a frame of hypotheses Θ = {θ 1 , ..., θ n }, and the so called power set

2 Θ = {∅, θ 1 , ..., θ n , θ 1 ∪ θ 2 , ..., θ 1 ∪ θ 2 ∪ ... ∪ θ n },
on which the combination is defined, the general basic belief assignment is defined as a mapping m s (.) : 2 Θ → [0, 1], associated with the given source of information s, such that: m s (∅) = 0 and X∈2 Θ m s (X) = 1. The quantity m s (X) represents the mass of belief exactly committed to X. Under Shafer's model assumption of the frame Θ (requiring all the hypotheses to be exclusive and exhaustive), the PCR5 combination rule for only two sources of information is defined as:

m P CR5 (∅) = 0 and ∀X ∈ 2 Θ \ {∅} m P CR5 (X) = m 12 (X)+ Y ∈2 Θ \{X} X∩Y =∅ [ m 1 (X) 2 m 2 (Y ) m 1 (X) + m 2 (Y ) + m 2 (X) 2 m 1 (Y ) m 2 (X) + m 1 (Y ) ] (2)
All sets involved in the formula are in canonical form. The quantity m 12 (X) corresponds to the conjunctive consensus,

i.e:

m 12 (X) = X1,X2∈2 Θ X1∩X2=X m 1 (X 1 )m 2 (X 2 ).
All denominators are different from zero. If a denominator is zero, that fraction is discarded. No matter how big or small the conflicting mass is, PCR5 mathematically does a proper redistribution of the conflicting mass. It is because PCR5 goes backwards on the tracks of the conjunctive rule and redistributes the partial conflicting masses only to the sets involved in the conflict and proportionally to their masses put in the conflict, considering the conjunctive normal form of the partial conflict. PCR5 is quasi-associative and preserves the neutral impact of the vacuous belief assignment. The probabilistic PCR5 (pPCR5) is an extension of discrete PCR5 version to its continuous probabilistic counterpart. Basic belief assignment, involved in discrete PCR5 rule is extended to densities of probabilities of random variables. For two independent sources of information with given Gaussian distributions p 1 (x) and p 2 (x), the obtained combined result becomes [START_REF] Smarandache | Advances and applications of DSmT for information fusion[END_REF]:

p pP CR5 (x) = p 1 (x) p 1 (x)p 2 (y) p 1 (x) + p 2 (y) dy+ p 2 (x) p 2 (x)p 1 (y) p 2 (x) + p 1 (y) dy (3)
The behavior of pPCR5 fusion rule in comparison to NCC rule (1) could be characterized by two cases below: Case 1: both densities p 1 (x) and p 2 (x) are close (Fig. 1case 1). The combined density acts as an amplifier of the information by reducing the variance. Here pPCR5 acts as NCC fusion rule.

Case 2: the densities p 1 (x) and p 2 (x) are distant (Fig. 1-case 2). Then the combined density keeps both original densities (not merging both densities into only one unimodal Gaussian density as NCC rule does), avoiding to neglect a part of the available information. This new (from a theoretical point of view) property is very interesting and it presents advantages for practical applications as it will be shown in our particular research. Application of pPCR5 fusion rule assures robustness to the potential errors and allows taking more reliable and adequate decisions in the process of integration of different cues in visual perception.

III. EXPERIMENTS

A. Stimuli

The stimuli consisted of 50 dots. The dot patterns occupied an area of 15 angular degrees. The stimuli were generated beforehand and contained 100 frames (except the static condition). Each frame lasted 33 msec. The lifetime of the dots was 3 frames, thus on every frame one-third of the dots were randomly re-positioned. For the motion and the combined condition the velocity of the dots was 4 degrees of arc/sec. The stimuli were radial patterns with a focus (center) positioned eccentrically to the middle of the screen. The center of the patterns defined by the orientation of the pairs or the trajectories of the dots could take 7 values to the left or to the right of the midpoint of the screen: 0.67 to 4.67 degrees of arc in steps of 0.67 degrees of arc. Ten different exemplars of patterns for each center and condition were generated. The dots subtended 0.2 degrees of arc.

B. Experimental conditions

Four different experimental conditions were performed:

• Static (form) condition The experimental stimuli (Fig. 2) consist of dots pairs separated by 2 degrees of arc. The orientation of the virtual lines connecting the dots in 18 pairs intersected in a common point considered the center of the patterns, while the rest 7 pairs had random orientation. • Motion condition In this experiment (Fig. 3) 36 points had trajectories that intersected at a common point, while the rest 14 dots had random trajectories. • Flicker condition In this condition (Fig. 4) a sequence of random static patterns was presented. As in the static condition the orientation of 18 pairs of dots, separated by 2 degrees of arc pointed to a common center while the rest 7 pairs had different orientation. The sequential presentation of the static patterns created illusory motion, but the trajectories of the apparent motion were random. • Combined condition In this experiment (Fig. 5) 18 pairs of dots moved along trajectories towards a common center. The orientation of these pairs was along the motion trajectory. The rest 7 pairs had random trajectories, but again, the orientation defined by the pairs was along the trajectory of motion. The figures 2-5 correspond to a single frame from the four experimental conditions. The four conditions of the experiment differ by the relative contribution and the order of temporal and spatial integration. In the static conditions the observers needed to find the correspondence of the dots to a pair and to globally integrate this information in order to find the focus of the radial pattern. In the flicker condition on every frame the observers had to integrate the spatial information from the pairs of dots but they could benefit from temporal integration of the sequential patterns that would be equivalent to the presence of a larger number of dot pairs. In the motion conditions the observers had to temporally integrate the displacement of dots in the sequential frames in order to determine their trajectory of motion and to integrate this information in space to determine the focus of the radial pattern. In the combined condition the observers had redundant information as both the trajectory of dot motion and the orientation of the dot pairs provided similar information.

C. Experimental Procedure

The subject sat at 57 cm from the monitor screen. The stimuli were presented on a gray screen with mean luminance 50 cd/m2. Each stimulus presentation was preceded by a warning signal. A red fixation point with size of 0.8 degrees of arc appeared in the center of the screen for 500 msec. The stimuli were presented simultaneously with the disappearance of the fixation point. The Subjects performed a single-stimulus two-alternative force choice task. They had to continue looking at the position where the fixation point was presented until making a decision where the center of the pattern was (left or right relative to the fixation point). At this moment the subject had to move his/her eyes towards the position of the perceived center and to press the left or the right mouse button depending on whether the perceived center appeared to the left or to the right from the fixation point. If the subject could not make a decision during the 3.3 sec of the stimulus presentation (100 frames), the stimulus disappeared and the screen remained gray until the subject made a response.

D. Method

The method of constant stimuli was used. Each condition was presented in a separate block consisting of 10 presentations for each position of the pattern center (a total of 140 presentations, 7 positions for a center shifted to the left and 7 positions for a center shifted to the right). The order of stimulus presentation was random. Each Subject took part in at least two experiments with 4 blocks for each of the 4 experimental conditions. All conditions were presented in a random order in a single day. The duration of each block depended on the subject performance, but the experiment did not exceed 1 hour. The eye movements of the subjects were registered with Jazz-novo multisensor measurement system (Ober Consulting Sp. z o.o) [20].

E. Apparatus

The stimuli were presented on a 20.1 inch NEC MultiSync LCD monitor with NvidiaQuadro 900XGL graphic board at a refresh rate of 60 Hz and screen resolution 1280/1024 pixels. The experiments were controlled by a custom program developed under Visual C++ and OpenGl.

F. Subjects

The subjects participating in the experiments are divided in three age groups: young (aged from 20 to 34 years), middle (aged 35 to 55 years) and elderly (aged 57 to 84 years). They did not have a whole training session, but they were given examples of stimuli to check whether they understood the task and to get an idea of the stimuli in a given condition.

IV. PERFORMANCE EVALUATION OF AGE-RELATED OBSERVERS GROUPS

The experimental goal of our study is directed to characterize the human heading perception influenced by: (i) form information only (ii) motion information only (iii) flicker information, i.e temporal integration of form information (iv) combined form and motion information. The question is if people rely and base their responses on a single source of information, or on combined one, and also which type of information utilized is more informative in the decision process. The participants belong to three age groups: Young, Middle aged, and Old. Hence, also the influence of human age on the assessment of heading perception will be evaluated. The evaluation is made on the base of experimental psychometric functions, obtained for all different experimental conditions and for each subject in all age-contingent groups. The psychometric function reflects the dependence between a given physical quantity (in this case, the pattern shift from the middle of the screen) and the proportion of subjects responses of a given type, in our case the proportion of responses the pattern center is to the right".

• Evaluation of heading perception in Young observers group

The comparison of the performance in the static, motion and flicker conditions show that in Young group only 2 out of 10 observers have best performance for the static condition, 4 observers effectively utilized the motion information showing best performance in this case, and 4 out of 10 observers show best performance in the flicker condition. For 4 out of 10 observers the null hypothesis of equal psychometric functions for both motion and flicker information could not be rejected, i.e they could be considered as equivalent. These results suggest that the young observers effectively integrate the available information in time. The contribution of the information available in each of these three conditions to the performance of the combined condition differs. Only 1 out of 10 subjects relies mainly on motion, 1 -on the information available in the flicker condition, while 7 out 10 combined effectively the independent sources of information available in the static and motion condition.

The performance of averaged (on the base of 10 subjects in the group) young subject is shown on Fig. 6.

For the averaged young subject the psychometric curves associated with static, motion, and flicker information are not distant and the null hypothesis that they do not differ could not be rejected.

• Evaluation of heading perception in Middle aged observers group

In this age-related group only 1 out of 6 subjects shows better performance in the static condition and 1 out of 6 observers -in the flicker condition. For 1 out of 6 observers the null hypotheses of equal psychometric functions for both motion and static information could not be rejected. For 4 out of 6 observers the null hypothesis for equal psychometric functions for motion and flicker conditions could not be rejected too. As general, the results suggest a small effect of the static information.

The results for 4 out of 6 observers show that the results in the combined condition could be successfully predicted based on the performance of the static and motion conditions. The performance of averaged middle aged subject is shown on Fig. 7. The averaged middle aged observer does not rely mainly on the static information. For him the combined and flicker condition do not differ significantly.

• Evaluation of heading perception in Old observers group

The obtained results in Old-age group show that 3 out of 10 observers show best performance in the static, 3 out of 10 -in motion, and 4 out of 10 in the flicker condition. The null hypothesis for equal psychometric functions is valid for: 1 out of 10 for motion and static condition, and for 2 out of 10 -for motion and flicker condition. Six out of 10 subjects utilize combined static and motion information to make their final decision in the combined condition. The performance of averaged old subject is shown on Fig. 8. For averaged old subject the null hypotheses that the static and flicker cases do not differ is valid. The averaged old observer relies more on motion information.

V. PPCR5 AND NCC RULES PERFORMANCE FOR PREDICTING HUMAN'S WAY OF FORM AND MOTION COMBINATION

The main question here is which fusion rule -pPCR5 or NCC used to combine available static and motion information predicts more adequately human cue integration? In order to answer this question we need to make a comparison between experimentally obtained and predicted (via pPCR5 and NCC rules) psychometric functions for combined condition (static and motion), for the three age contingent groups. This comparison is provided on the base of goodness-of-fit test [START_REF] Matre | Statistics for Business and Economics[END_REF], one important application of chi-squared criteria:

χ 2 = J j=1 (Oj -Ej ) 2 Ej
where χ 2 is an index of the agreement between an observed(O)/experimental and expected(E)/predicted via particular fusion rule sample values of psychometric function. For our case J = 14 represents the number of pattern's shifts from the middle of the screen. The critical value of the test for ν = J -1 = 13 degrees of freedom at assumed p = 0.1 is χ 2 = 19.81 [START_REF] Matre | Statistics for Business and Economics[END_REF]. The respective results are given in Table I -for young group, in Table II -for middle aged group, and in Table III -for old persons' group.

In general, the results show that the pPCR5 fusion rule predicts more adequately than NCC rule human performance for the three age groups.

For young and for middle aged persons (Tables I andII) both fusion rules predict psychometric functions that do not differ significantly from the experimental ones, but the differences in the fits are smaller in case of pPCR5 rule than in case of NCC rule application. The same findings are valid for old people (Table III), but in this group NCC rule show worse performance for subject no.4 (put in bold in Table III) showing the exceeded critical value of χ 2 = 19.81. The reason for this result reflects the situations, when the experimentally obtained psychometric functions, associated with single static and single motion conditions are characterized with distant underlying Gaussian distributions. In this case pPCR5 makes prediction, which models more correctly and adequately human combination behavior. Using NCC rule however, part of available information has been neglected, because the cue with bigger mean was weighted more heavily than the cue with a smaller one (as it was described in Section II).

VI. COMMON TRENDS OF AGE RELATED OBSERVER

GROUPS

The goal here is to find the common trend, concerning the performance of the three groups. In order to achieve it, we consider each group as a set of different sources of evidence, associated with each person in the group. That way young group consists of 10 (middle aged of 6, old aged of 10) sources (subjects) of evidence, which should be combined all together via pPCR5 and NCC fusion rules.

The combined individual behaviors in particular group are estimated, reveling its intrinsic behavior as a whole, reducing uncertainties associated with individual performances. All the tested subjects in age groups are considered as independent and equally reliable sources of information, because each subject provides his/her own psychometric function, associated In order to compare the performance of both fusion rules in estimating common trends' prediction the city-block errors between the corresponding triples young/middle/old group experimental form and motion combination) -young/middle/old group estimated (via pPCR5 and NCC) form and motion combination are given in Table IV. Results show ultimately that experimentally obtained and those, based on pPCR5 fusion rule are closer and for the three age-contingent groups are more than two times less than those, obtained via NCC fusion rule. pPCR5 fusion rule predicts more correctly the human model of decision making, than NCC rule, utilizing all the available information (Form and Motion), even in case of conflict. NCC based trends are very sensitive to the sources (different subjects' psychometric functions) with the bigger means, neglecting that way part of the available information and acting as an amplifier of the information by reducing the variances.

VII. CONCLUSIONS

This paper presented a study on human heading perception obtained on the base of motion and form visual cues integration. The influence of human age on this process was evaluated. The results obtained show age-related difference in the performance of the subjects in estimating the heading direction based on the combined static (form) and motion information.

Our experimentally obtained data for young observers suggest smaller effect of the static information case and provides indirect evidence that their performance is based more on the temporal integration of information in the motion and flicker conditions. The experimental results for Middle-aged group suggest less effect of the static information and an effect of the order of temporal and spatial integration. The old subjects used to rely more on the motion information. All age-related groups rely on combined (motion and form) information to take their final decisions for heading perception.

A comparison between experimentally obtained and predicted (via pPCR5 and NCC rules) psychometric functions for combined condition (static and motion), for the three age contingent groups was made and estimated on the base of goodness-of-fit test, one important application of chi-squared criteria. Results proved that pPCR5 makes prediction, which models more correctly and adequately human combination behavior than NCC, especially in cases of conflicts between the different visual cues.

The combined individual behaviors (the trends) in particular age groups were estimated, reveling its intrinsic behavior as a whole, reducing uncertainties associated with individual observers performance. Results show ultimately that pPCR5 fusion rule, utilizing all the available information -static (form) and motion, even in case of conflict, predicts more correctly the human model of decision making, than NCC rule. That way pPCR5 fusion rule assures preserving the richness of cues data in the process of visual stimuli combination and assures improvement of decision accuracy. pPCR5 describes better the characteristics of the different age groups in decision making based on the motion and form information in heading perception.

VIII. ACKNOWLEDGEMENT

The reported work is partially supported by the project DN02/3/2016 'Modelling of voluntary saccadic eye movements during decision making' funded by the Bulgarian Science Fund.

Fig. 1 .

 1 Fig. 1. Performance of pPCR5 fusion rule vs. NCC rule.

Fig. 2 .

 2 Fig. 2. Static Condition.

Fig. 3 .

 3 Fig. 3. Motion Condition.

Fig. 4 .

 4 Fig. 4. Flicker Condition.

Fig. 5 .

 5 Fig. 5. Combined Condition.

Fig. 6 .

 6 Fig. 6. Psychometric Curves of Averaged Young Subject.

Fig. 7 .

 7 Fig. 7. Psychometric Curves of Averaged Middle aged Subject.

Fig. 8 .

 8 Fig. 8. Psychometric Curves of Averaged Old Subject.

Fig. 9 .

 9 Fig. 9. Trends of Young Subjects Group.

Fig. 10 .

 10 Fig. 10. Trends of Middle aged Subjects Group.

Fig. 11 .

 11 Fig. 11. Trends of Old Subjects Group.

  able to model correctly and adequately such human age-contingent group trends in the process of decision making. The results obtained for experimental and estimated (via the fusion rules) trends, concerning the cues combination groups' performance are presented inFigures 9,[START_REF] Bayes | An Essay towards solving a Problem in the Doctrine of Chances[END_REF][START_REF] Sivia | Data Analysis, a Bayesian Tutorial[END_REF]

		TABLE III
		CHI-SQUARED VALUES FOR OLD SUBJECTS.
	Subject	(Form and Motion) pPCR5	(Form and Motion) NCC
	1	0.3751	0.7693
	2	0.2762	0.5721
	3	0.3691	0.4078
	4	2.9287	21.0845
	5	0.5418	0.8592
	6	0.1652	0.3021
	7	0.2013	0.3103
	8	0.3984	0.5932
	9	0.6712	1.6964
	10	0.7152	1.8598
	with the static and motion condition and should be taken into
	account with equal weights to derive these trends.
	Our goal is to find out which combinational rule (pPCR5 or
	NCC) is

TABLE IV CITY

 IV BLOCK ERRORS BETWEEN EXPERIMENTAL AND PREDICTED TRENDS.

		PCR5	NCC
	FM Young	0.03	0.10
	FM Middle	0.06	0.13
	FM Old	0.04	0.12