Alassane Oumar

Mohamed Barro

Olivier Himdi

Member, IEEE Lafond

Reconfigurable Patch Antenna Radiations Using Plasma Faraday Shield Effect

Keywords:

This letter presents a new reconfigurable antenna associated with a plasma Faraday shield effect. The Faraday shield effect is realized by using a fluorescent lamp. A patch antenna operating at 2.45 GHz is placed inside the lamp. The performance of the reconfigurable system is observed in terms of S11, gain and radiation patterns by simulation and measurement. It is shown that by switching ON the fluorescent lamp, the gain of the antenna decreases and the antenna system (patch+lamp) keeps a good matching at the operating frequency. This reconfigurable antenna can be used to avoid coupling with other communications or radar systems working in the same frequency band.

I. INTRODUCTION

P LASMA is the fourth state of the matter with complex permittivity that can be exploited as a metal. When the plasma inside a container (tube in our case) is energized (state ON), the media performs like a conductive element capable to reflect radio signal like a metal [START_REF] Inan | Principles of plasma physics for engineers and scientists[END_REF], [START_REF] Laroussi | Numerical calculation of the reflection, absorption, and transmission of microwaves by nonuniform plasma slab[END_REF]. But, when the tube is de-energized (state OFF), the plasma is non-conductor and transparent to electromagnetic radiations. The main advantage of plasma reflector or plasma antenna compared to metallic element resides in the possibility to use an electrical control rather than a mechanical one. In [START_REF] Alexeff | Experimental and theoretical results with plasma antennas[END_REF], [START_REF] Anderson | Smart plasma antenna[END_REF], the authors proposed plasma reflector antenna in order to steer the beam in certain directions. More recently, reconfigurable reflector plasma antennas have been realized by using low cost commercial fluorescent lamps (CFL), refer [START_REF] Jusoh | Performance of a reconfigurable reflector antenna with scanning capability using low cost plasma elements[END_REF], [START_REF] Jusoh | Performance and radiation patterns of a reconfigurable plasma corner-reflector antenna[END_REF]. On the other hand, a monopole fluorescent tube antenna was proposed in [START_REF] Zali | Design monopole antenna with florescent tube at 4.9 GHz[END_REF], [START_REF] Cerri | Measurement of the properties of a plasma column used as a radiated element[END_REF].

In this letter, we present a reconfigurable patch antenna using a plasma Faraday shield effect. In reality, a Faraday cage is an enclosure formed by conductive material or by a mesh of such material. In our case, the Faraday shield is made with a fluorescent lamp which allows to obtain a reconfigurable gain and radiation pattern of a printed antenna by switching ON or OFF the plasma.

The paper is organized as follows: We present the plasma model in section II. In section III, we describe the modeling and simulation of the antenna system. The comparison between simulations and measurements is presented in section IV. A conclusion is given in section V.

Oumar

Alassane Barro (oumar-alassane.barro@univ-rennes1.fr), Olivier Lafond (olivier.lafond@univ-rennes1.fr) and Mohamed Himdi (mohamed.himdi@univ-rennes1.fr) are with the Institute of Electronics and Telecommunications of Rennes, UMR CNRS 6164, University of Rennes 1, Campus de Beaulieu, Rennes Cedex 35042, France.

II. DRUDE MODEL OF PLASMA MEDIUM

The behavior of the plasma is defined by the Drude dispersion model. The expression of the permittivity under low electron-neutral collision is given below (Eq. ( 1)).

r = 1 - ω 2 p ω(ω -jν) ( 1
)
where r is the complex plasma permittivity, ω is the operating angular frequency, and ν is the electron-neutral collision frequency. ω p is the plasma angular frequency and it is proportional to the density of unbound electrons or the amount of ionization in the plasma. The plasma angular frequency is defined as:

ω p = ne 2 m 0 ( 2
)
where n is the electron density, e is the charge of electron, m is the electron mass, and 0 is the free space permittivity. When the operating angular frequency is greater than the plasma angular frequency (ω > ω p ), the plasma acts like a classical dielectric medium and when the opposite is true (ω < ω p ), i.e.

r < 0, plasma acts like a metal. Consequently, depending on the angular frequency, the plasma can transmit or reflect the microwave radiation.

III. MODELING AND SIMULATIONS

We design a circular patch antenna operating at 2.45 GHz which will be enclosed in CFL, used as Faraday shield effect. The geometry of the proposed patch antenna fed by a coaxial line is shown in Figure 1(a). This circular patch with a 31 mm diameter is printed on FR4 substrate with a thickness h = 3.2 mm, r = 4.4 and tan δ = 0.025. The diameter of the substrate is 50 mm. The feed point is located along the y-axis, at a distance d = 5 mm from the center of the patch. The antenna is polarized along the y-axis and the ground plane is on the bottom of the substrate.

The geometry of the spiral-shaped lamp [START_REF] Helitron | V/ 50Hz[END_REF] is shown in Figure 1(b) and Figure 2. The height of the lamp is 134 mm, the inner diameter is 60 mm, the spiral diameter is 19 mm, the outer diameter is 98 mm, and the gap between the turns is 3.64 mm. A ground plane size of 200 × 200 mm 2 is used in the bottom of the lamp in order to mask the electronic devices used to energize the plasma. The patch antenna is put inside the lamp at a height equals to 50 mm from the ground plane. The realized prototypes and measurement setup are shown in Figure 2.

In simulation (performed using CST Microwave studio [START_REF] Cst | Computer Simulation Technology[END_REF]), the tubes containing the gas are made from lossy glass Pyrex with r = 4.82, tan δ = 0.005 and thickness of 0.5 mm. The plasma obeys to the Drude model. At the beginning, we used the same Drude model as in [START_REF] Jusoh | Performance of a reconfigurable reflector antenna with scanning capability using low cost plasma elements[END_REF], with the same parameters (ν = 900 MHz and ω p = 43.9823 10 9 rad/s ). Unfortunately, the simulation results were not in good agreement with measurements. Hence, we tried to match the simulations with the measurement by changing the plasma parameters defined in the Drude model. After retro-simulations, ω p = 62.8318 10 9 rad/s is considered and ν is kept equal to 900 MHz. In the absence of information from the manufacturer, the retro-simulation was necessary in order to have realistic plasma data for this kind of lamp.

IV. RESULTS AND DISCUSSION

The results are separated in two cases in order to understand the interaction between the patch antenna and the lamp. In the first one, the electric field polarization is parallel to the end of the lamp (y-axis), while in the second one the electric field polarization is orthogonal to the end of the lamp (x-axis).

The simulated and measured S 11 parameters are shown in Figure 3 for the patch alone and by switching ON or OFF the fluorescent lamp (Plasma ON / Plasma OFF). The measured results are in a good agreement with the simulated ones. For all configurations (patch alone, plasma OFF, plasma ON), the resonant frequency is close to 2.45 GHz in both simulation and measurement (Fig. 3(a) and 3(b)). The Figure 3(a) shows also the magnitude S 11 parameter when the plasma is replaced by a lamp made of perfect electrical conductor (PEC). It is important to notice that the antenna system (patch + PEC) is not well matching at the operating frequency (-2.89 dB at 2.45 GHz). On the contrary, with the plasma lamp, th results show that the matching of the patch is not significantly affected by the plasma (ON or OFF). The S 11 parameters are the same in both polarization cases. Radiation patterns have been measured in order to validate the simulation results. Measurements have been performed in a SATIMO anechoic chamber (near fields setup) with a peak gain accuracy equals to ±0.8 dBi. The measurement setup with lamp, used as Faraday shield effect, is shown in the Figure 2(d). The Figures 4 and6 show the measured and simulated radiation patterns at 2.45 GHz, for respectively the co-and the cross-polarization. For both simulation and measurement results, each radiation pattern is normalized to the maximum value of the electric-field for the plasma OFF. We can clearly observe that the radiation patterns in measurement and simulation are similar.

• First case: Regarding the gain, we can notice a difference of 12 dB for both simulation and measurement between plasma OFF and plasma ON for θ = 0 in co-polarization (Fig. 4(a) and 4(b)) and a difference of 5 dB for the measured cross-polarization ( Fig. 4(c) and 4(d)). In copolarization, the antenna gain decreases strongly when the plasma is ON. In order to understand well the effect of the plasma, the Figure 5 shows the normalized copolarization radiation patterns when the plasma is replaced by a PEC and for the two principal planes (E and H). The difference of gain between plasma OFF and metal at θ = 0 is 15 dB. This result shows that the PEC is more efficient for shielding but as seeing in Figure 3, the using of plasma lamp allows to keep a good matching for the antenna at the operating frequency and their radiation patterns are also reconfigurable. In both cases, the measurements of cross-polarization give the expected results but the simulation results show the opposite behavior due to the non-perfect model. The results obtained for the first case (polarization of patch along y axis) are more interesting because the decreasing of gain is more significant.

After, we tried to find which part of the lamp affects the radiation patterns. Thus, in the simulations (first case), the lamp is separated in two parts, the end of the lamp (without spiral part) and the spiral part (without the end of the lamp).

Figure 7 shows the co-polarization radiation patterns in Eplane (Fig. 7(a)) and H-plane (Fig. 7(b)) of the end of the lamp and spiral part compared to the plasma OFF and plasma ON. We notice that, the radiation patterns are affected by the combination of both parts and not only by the end of the lamp. In fact, the lamp and the patch are relatively near to each other, so the impact of lamp must be seen in near fields conditions that can explain why the two aprts of the lamp (end and spiral ones) affect the electric field of the patch antenna.

Table I and Table II present respectively the maximum simulated and measured gain at 2.45 GHz for both polarization cases. From these results, it is very interesting to notice that the radiation of the patch can be strongly reduced when the plasma is ON. This means that the lamp acts like a Faraday shield effect.

V. CONCLUSION

In this letter, a Faraday shield effect using commercial Fluorescent Lamp (plasma) was presented. Two cases have been simulated and measured showing the impact of the lamp on the gain of patch antenna put inside it. By switching OFF or ON the plasma, the lamp behaves like a transparent media or a Faraday shield effect respectively and the S 11 parameters keep a good matching at the operating frequency. This reconfigurability could be used to reduce antenna gain when different communication systems, working at the same frequency, are put close to each others. Moreover, the Faraday shield can be used to protect antenna from external high power aggression.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Simulated models. (a) The patch geometry. (b) The fluorescent lamp geometry.

Fig. 3 .

 3 Fig. 3. S 11 magnitude comparison. (a) Simulation. (b) Measurement.

•

  Second case: The difference of gain is 7 dB in simulation and 5 dB in measurement at θ = 0 between plasma OFF and plasma ON in co-polarization (Fig. 6(a) and 6(b)) and almost 15 dB for the measured cross-polarization (Fig. 6(c) and 6(d)). In the Figures 4(c), 4(d), 6(c) and 6(d) the level of simulated plasma OFF cross-polarization are very low in E and H-planes and do not appear in the figures.

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Normalized radiation patterns at 2.45 GHz for plasma OFF and plasma ON in the first case. (a) Co-polarization E-plane. (b) Co-polarization H-plane. (c) Cross-polarization E-plane. (d) Cross-polarization H-plane.

TABLE I REALIZED

 I GAIN MAX IN THE FIRST CASE

	States	Plasma OFF	Plasma ON
	Maximum simulated gain (dBi)	6.4	0.3
	Maximum measured gain (dBi)	5.5	-0.7

TABLE II REALIZED

 II GAIN MAX IN THE SECOND CASE

	States	Plasma OFF	Plasma ON
	Maximum simulated gain (dBi)	6.4	1.4
	Maximum measured gain (dBi)	5.4	0.2

ACKNOWLEDGMENT

The authors would like to acknowledge Laurent Cronier and Jérôme Sol from IETR for their technical support.


O A Barro

O Lafond

H Himdi

Reconfigurable Antennas Radiations Using Plasma Faraday Cage

This letter presents a new reconfigurable plasma antenna associated with a Faraday cage. The Faraday cage is realized using a fluorescent lamp. A patch antenna with a broadside radiation pattern or a monopole antenna with an end-fire radiation pattern, operating at 2.45 GHz, is placed inside Faraday cage. The performance of the reconfigurable system is observed in terms of input reflection coefficient, gain and radiation pattern via simulation and measurement. It is shown that by switching ON the fluorescent lamp, the gain of the antenna decreases. This reconfigurable antenna can be used to avoid coupling with other communications or radar systems working in the same frequency band.

INTRODUCTION

Plasma refers to the fourth state of matter. When the plasma inside a container (tube in our case) is energized (state ON), the media performs like a conductive element capable to reflect radio signals like a metal [START_REF] Laroussi | Numerical calculation of the reflection, absorption, and transmission of microwaves by nonuniform plasma slab[END_REF]. But, when the tube is de-energized (State OFF), the plasma is non-conductor and electromagnetic waves can go through it. In the literature, plasma can be used as radiator to replace metallic radiator or as reflector. The main advantage of plasma reflector or plasma antenna compared to metallic element resides in the possibility to use an electrical control rather than a mechanical one. In [START_REF] Anderson | An operating intelligent plasma antenna[END_REF], the authors proposed plasma reflector antennas in order to steer the beam in certain directions. More recently, reconfigurable reflector plasma antennas have been realized by using lowcost commercial fluorescent lamps (CFL) [START_REF] Jusoh | Performance and radiation patterns of a reconfigurable plasma corner-reflector antenna[END_REF]. On the other hand, a monopole fluorescent tube antenna was proposed in [START_REF] Zali | Study of Monopole plasma antenna in wireless transmission applications[END_REF][START_REF] Cerri | Measurement of the properties of a plasma column used as a radiated element[END_REF].

In this letter, we present reconfigurable antennas using plasma faraday cage. A Faraday cage is an enclosure formed by a conductive material or by a mesh of such material. In our case, the Faraday cage is realized by using a fluorescent lamp which allows to switch ON or OFF the plasma and to obtain reconfigurable gain and radiation patterns.

The paper is organized as follows: in section II, the patch and monopole antennas as well as the Faraday cage modeling and simulations are presented. The comparison between simulation and measurement results is provided in section III. A conclusion is given in section IV.

MODELING AND SIMULATIONS

First, we design two different antennas. A circular patch operating at 2.45 GHz which radiates in broadside direction and a monopole operating also at 2.45 GHz with end-fire radiation. The geometry of the proposed patch antenna fed by coaxial line is shown in Figure 1(a). This circular patch with a diameter of 31 mm is printed on an FR4 substrate with thickness h = 3.2 mm, r = 4.4 and tan δ = 0.025.The diameter of the substrate is 50 mm. The antenna is fed by a 50 Ω coaxial line. The feed point is located along the y-axis, at a distance d = 5 mm from the center of the patch. The antenna is polarized along the y-axis and the ground plane is printed on the bottom side of the substrate.The designed quarter-wavelength monopole has a diameter of 2 mm and a height of 30 mm. This monopole is placed in the center of a ground plane with a diameter of 50 mm (Fig. 1(b)).

Secondly, a spiral shape lamp is modelized (Fig. 1(c)) [START_REF] Helitron | V/ 50Hz[END_REF]. The plasma diameter is 19 mm, the height of the lamp is 134 mm, its inner diameter is 60 mm, while the outer one is 98 mm and the gap between the coils is 3.64 mm. A ground plane of 200 × 200 mm 2 is used in the bottom of the lamp in order to mask the electronic devices used to energize the plasma. The manufacturing prototypes and measurement setup are shown in Figure 2.

In simulation (the simulations are performed using CST Microwave studio [START_REF] Cst | Computer Simulation Technology[END_REF]), the tubes containing the gas are made from lossy glass Pyrex with r = 4.82, tan δ = 0.005 and thickness of 0.5 mm. The plasma obeys to the Drude model defined by the equation [START_REF] Laroussi | Numerical calculation of the reflection, absorption, and transmission of microwaves by nonuniform plasma slab[END_REF].

r = 1 - ω 2 p ω(ω -jν) ( 1
)
where r is the complex plasma permittivity, ω p is the plasma angular frequency, ω is the operating angular frequency and ν is the electron-neutral collision frequency.

At the beginning, we used the same Drude model as in [START_REF] Jusoh | Performance and radiation patterns of a reconfigurable plasma corner-reflector antenna[END_REF], with the same parameters (ν = 900 MHz and ω p = 43.9823 10 9 rad/s ). Unfortunately, the simulation results were not in good agreement with measurements. Hence, we tried to match the simulations with the measurement by changing the plasma parameters defined in the Drude model. After retro-simulations, ω p = 62.8318 10 9 rad/s is considered and ν is kept equal to 900 MHz. In the absence of information from the manufacturer, the retro-simulation was necessary in order to have realistic plasma data for this kind of lamp.

RESULTS AND DISCUSSION

Simulated and measured S 11 parameters are shown in Figure 3 for both patch and monopole cases and by switching ON or OFF the fluorescent lamp (Plasma ON / Plasma OFF). For the patch case and all configurations (patch alone, plasma OFF, plasma ON), the resonant frequency is close to 2.45 GHz and simulation and measurement are in good agreement (Fig. 3(a) and 3(b)). These results show that the matching of patch is not significantly affected by the plasma tube (ON or OFF). In the case of the monopole (Fig. 3(c) and 3(d)), the antenna is not well matched at the operating frequency in ON case. The plasma affects the antenna's resonance. Radiation patterns have been measured in order to validate the simulation results. Measurements have been performed in a SATIMO anechoic chamber (near-fields setup) with peak gain accuracy equal to ±0.8 dBi. Figure 4 shows the measured and simulated radiation patterns at 2.45 GHz. For both simulation and measurements results, each radiation pattern is normalized to the maximum value of plasma OFF. It can be observed that the radiation patterns in measurement and simulation are quite similar. For the patch antenna, in both simulation and measurement the difference of gain between plasma OFF and ON at θ = 0 (broadside) is 12 dB (Fig. 4(a),4(b)). The gain of antenna is slightly decreased when the plasma is ON because the electric field polarization is parallel to the end of the lamp (Fig. 2(a)). For the monopole antenna (Fig. 4(c) and 4(d)), the difference is lower, almost 5dB, because the electric filed polarization of monopole is orthogonal to the spiral part of the lamp. So the electromagnetic waves coming from the monopole are less attenuated.

Table 1 shows the maximum realized gain at 2.45 GHz for the patch and the monopole antenna cases. The simulation and measurement are in good agreement. It is interesting to note that the radiation of the patch can be strongly reduced when the plasma is ON. This means that the lamp acts as a Faraday Cage especially in the broadside direction. This behavior can be suitable if we want to avoid coupling this antenna and other near communication systems or to protect it against external undesirable signal.

CONCLUSION

In this letter, a Faraday cage using commercial Fluorescent Lamp (plasma) was presented. Two types of antennas were considered inside the lamp to show the impact of Faraday Cage on antenna radiation pattern and polarization. By switching OFF or ON the plasma, the lamp behaves like a trans-parent media or Faraday Cage respectively. This reconfigurability could be used to reduce antenna gain when different communication systems working at the same frequency are put close to each others. The results obtained in this paper show that the plasma Faraday cage with patch antenna is more interesting than the plasma Faraday cage with monopole antenna.

Figure 1 :

 1 Figure 1: The designed models. (a) The patch antenna. (b) The monopole antenna. (c) The Fluorescent lamp.

Figure 2 :

 2 Figure 2: Realized model. (a) Dimensions of plasma Faraday cage. (b) Patch antenna inside the plasma Faraday cage. (c) Monopole antenna inside the plasma Faraday cage. (d) Radiation pattern measurement setup (SATIMO)

Figure 3 :

 3 Figure 3: S 11 magnitude parameter comparison. (a) Simulated S 11 patch antenna case. (b) Measured S 11 patch antenna. (c) Simulated S 11 monopole antenna case. (d) Measured S 11 monopole antenna.

Figure 4 :

 4 Figure 4: Normalized radiation patterns at 2.45 GHz. (a)-(b) Patch antenna case in the H-and E-planes respectively. (c)-(d) Monopole antenna case in H-and E-planes respectively.

Table 1 :

 1 Maximum simulated and measured gain for the patch and monopole antennas

	Configurations	Patch antenna	Patch antenna
		Plasma OFF Plasma ON Plasma OFF Plasma ON
	Maximum simulated gain (dBi)	6.4	0.3	3.4	-1.3
	Maximum measured gain (dBi)	5.5	-0.7	2.3	0.5

Acknowledgments

The authors would like to acknowledge Laurent Cronier and Jérôme Sol from IETR for their technical support.


Erik Henriksson

Late Greek Poetry: a Computational Approach

Keywords: Late antiquity, Greek poetry, hexameter, classicism, distant reading, digital humanities

Late antiquity (c. 300-600 CE) saw the rise of classically inspired Greek poetry, leaving behind a large corpus of texts that has hardly received the scholarly attention it merits. This article presents a work in progress that aims to introduce new digital tools in the analysis of Greek poetry. To evaluate the benefits of a computational approach, I have chosen a relevant case study in late Greek literary history: the question whether, and how, explicitly Christian hexameter verses differed from those with non-Christian content in terms of metrics and diction. A major methodological challenge is posed by the fact that few texts from late antiquity are available in open source digital format. This article presents a number of features that may be legally extracted from licensed texts available online, as well as some preliminary remarks on how to make use of the collected datasets in a large-scale statistical analysis.

I INTRODUCTION

Late antiquity (c. 300 -600 CE) witnessed a resurgence of poetry after a less productive period in the first centuries CE. This comeback has been accounted for by the renewed social stability attained by political reforms in the early 4th century [START_REF] Dihle | Greek and Latin literature of the Roman Empire: from Augustus to Justinian[END_REF]) and more recently, by the dynamic interactions between the emerging Christian literary culture and the classical tradition [START_REF] Cameron | Poetry and literary culture in late antiquity[END_REF], [START_REF] Shorrock | The Myth of Paganism: Nonnus, Dionysus and the World of Late Antiquity[END_REF]). Throughout late antiquity, classical poetry -in particular, Homer and Virgil -formed the basis of Roman literary education, imposing strong stylistic and metrical conventions into poetic production (e.g. [START_REF] Agosti | Greek poetry[END_REF]). The normative force of classicism made late antique versification an entirely scholarly affair that was at odds with the phonological developments of spoken language. Despite numerous studies on poetic meters and diction since the nineteenth century [START_REF] Hermann | Elementa doctrinae metricae[END_REF], [START_REF] Ludwich | Hexametrische untersuchungen ii: Ein betonungsgesetz des nonnos und seiner schule[END_REF], [START_REF] Maas | Griechische Metrik[END_REF], [START_REF] West | Greek Metre[END_REF] etc.), a comprehensive account of late Greek poetry is still nonexistent [START_REF] Agosti | Greek poetry[END_REF]).

In this work, I present a new digital "distant reading" [START_REF] Moretti | Distant reading[END_REF]) approach to studying the meters and language of late Greek poetry. As opposed to the traditional process of manual data collection and analysis, which typically focuses on predetermined phenomena in small selections of texts, distant reading involves employing computer algorithms to uncover previously unseen patterns in large textual corpora. As noted by [START_REF] Fusi | An expert system for the classical languages: Metrical analysis components[END_REF], metrical analysis is particularly attractive from a computational perspective. First, collecting metrical data from thousands of poetical units is liable to produce errors when performed manually (e.g. [START_REF] Maas | Griechische Metrik[END_REF] and [START_REF] Maas | Greek Metre[END_REF], with contradictive figures). Second, studying metrics along with other linguistic phenomena, such as phonological processes, is hardly feasible by hand due to the abundance of variables that have to be taken into account.

In order to assess the advantages of using digital methods to trace the evolution of Greek poetry in late antiquity, I have chosen a case study that has a high relevance for an ongoing discussion about the relationship between classicism and religion in this period (e.g. [START_REF] Agosti | Classicism, paideia, religion[END_REF]). Classicism in late antiquity has traditionally been seen as inspired by an active "pagan" (itself a Christian derogatory term) opposition to Christianity. In recent years, however, the pagan/Christian dichotomy is understood to have been completely misleading (e.g. [START_REF] Kahlos | Debate and dialogue: Christian and pagan cultures c[END_REF]), giving way to a more accurate view of a sophisticated dialogue between the two.

1.1 The case of Christian and "pagan" hexameters Classical Greek verses were based on a number of poetic meters, the choice depending on purpose and literary genre. Thus, epic poetry was associated with the dactylic hexameter, drama with the iambic trimeter and lyric poetry with a handful of complex metrical types [START_REF] Golston | Metrics. In Encyclopedia of Ancient Greek Language and Linguistics[END_REF]). In late antiquity, however, hexameter gradually supplanted nearly every other metre, becoming the "generic meter" thought of as proper for any occasion (Miguélez-Cavero [2008]). Consequently, a relatively large number of (several tens of thousands) lines of late antique hexameters survive to this day, showing a wide variety of functions and genres including monumental dedications and philosophical treatises as well as works with a Christian or "pagan" subject matter.

In the light of the current scientific view that emphasizes the common classical ground of all Greek poetry, one is inclined to ask whether there are any stylistic or metric differences between non-Christian and explicitly Christian verses with regard to classical ideals. As regards metrics, an important preliminary study [START_REF] Agosti | Materiali per la storia dell'esametro nei poeti cristiani greci[END_REF]) already indicated that no such division exists (see also Agosti [2004]), and that Christian poetry is in itself rather versatile when it comes to metrical practices. In this project, my aim is to augment and evaluate these results by virtue of introducing new digital tools in the metrical and stylistic analysis of Greek poetry. Furthermore, by incorporating a phonological feature in the dataset, I wish to be able to shed new light on the parallel development of metrics and the spoken language in late antiquity.

II MATERIALS AND METHODS

Practically every published Greek text from antiquity (and beyond) can be found online courtesy of the Thesaurus Linguae Graecae (TLG) project at the University of California, Irvine. TLG's copyright license states, however, that these vast materials can only be used by subscribers through TLG's own web interface and can under no circumstances be downloaded to a remote database, even for purely scholarly use. These restrictions make it difficult to use these texts for any large-scale analysis purposes. Consequently, most existing digital methods dealing with ancient texts have been based on smaller corpora, such as those provided by the Perseus Digital Library (per).

In this project, my aim is to explore the different ways in which TLG's resources, and poetry in particular, might be leveraged in a text mining project. Though an important goal in itself given the untapped potential of all of TLG's materials, it was also dictated by the fact that no other database containing the whole corpus of late Greek poetry currently exists. In order to illustrate the components of the metrical analysis, I first briefly describe the principal parts of a hexameter line.

Greek hexameter in outline

Greek meter, in essence, is based on patterns of light and heavy syllables, where a light syllable ( ˘) contains one so-called mora (a minimal unit of timing) and a heavy syllable ( ¯) two, all syllables except the ones ending in a short vowel being heavy. A dactylic hexameter line consists of six feet (also known as metra), each of which has four morae in one of two patterns: ¯˘( dactyl) or ¯¯(spondee) except for the last foot, which is always a spondee. These alternating patterns alone yield 32 different lines; in addition, the hexameter line tends to break into two DRAFT distinct chunks (colae), the break (caesura) being usually somewhere around the middle of the line. Moreover, there are places (bridges) where word breaks are rarely found. From the hellenistic period (c. 300-BC) onward an increasingly strict system of metrical laws evolved, regulating the positions of caesuras, bridges and even word-accents (e.g. [START_REF] Whitby | From moschus to nonnus: the evolution of the nonnian style[END_REF]).

Data collection

Both the TLG and the Perseus Project provide their materials encoded in Beta Code, a standard format representing Greek characters, diacritics and punctuation using only ASCII characters. For example, consider the following hexameter line from the Dionysiaca by Nonnus, a major late antique (early 5th century) poet: E pË, jeà, Kron-dao diàktoron a"jopoc eOEn®c *EI)PE/, QEA/, *KRONI/DAO DIA/KTORON AI)/QOPOS EU)NH=S A detailed account of the Beta Code format is not possible here, but the above example serves to illustrate the way Beta Code represents texts written in Greek.

Metrical data

The first task is to divide the line into a string of syllables and analyze the metrical weight of each syllable. In the case of public domain materials, this process can be partly automated. To this end, I have developed a script that performs the syllable division (according to, i.a., the criteria outlined in Chapter 2.1) and carries out an analysis of every possible metrical reading of each line, yielding the most probable one. For the example shown above, it would output the following syllable divisions and metrical analysis:

[*EI)], [PE/, ], [QE], [A/, ], [*KRO], [NI/], [DA] ,[O], [DI], [A/], [KTO], [RON], [AI)/], [QO], [POS], [EU)], [NH=S]
¯˘˘¯˘˘¯˘˘¯˘˘¯˘˘¯Ū sing these data, the automatic collection of the positions of caesurae, bridges, punctuation and word-accents is a matter of observing syllables and their positions within the metrical feet. In a variable representation, these data can be summarized as follows:

n Weight Word-start Word-end Foot-start Foot-end Caesura Diaeresis etc. n 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1

Phonetic data

In order to extend the scope of the metrical analysis, a phonological feature is included in the syllable based dataset. Two restrictions apply: first, we have only approximate knowledge of the pronounciation of Greek in late antiquity; and second, as noted earlier, data collection from TLG is limited owing to the copyright license. By virtue of studies such as [START_REF] Allen | Vox Graeca: The Pronunciation of Classical Greek[END_REF] and [START_REF] Horrocks | Greek: A History of the Language and its Speakers[END_REF], however, our approximation of late Greek phonology is now fairly reliable. The copyright issue, on the other hand, effectively means that the phonetic transcription must be performed manually. Just as with the collection of metrical data outlined above, an automatic transformation of the text is only allowed when working with texts other than those provided by the TLG. Using the previous example, a transcription would roughly look as follows:

[i],[pe],[✓e],[a],[kro],[ni],[ a],[o],[ i],[a],[kto],[ron],[e],[✓o],[pos],[ev],[nes]
DRAFT This transcription, though superficially similar to the Beta Code version, can be considered an independent scholarly transformation of the raw text, and therefore may be stored in a local database even when the originals are protected by a license.

Morphological data

A third type of data to be collected from the texts are the morphological analyses of each word. This feature is made up of two components: dictionary headword (lemma) and the description of the morphological features (part of speech, number, gender, etc.) of each word form. The collection can be performed semi-automatically with the open source Morpheus (mor) tool developed as part of the Perseus Project (per). In most cases, however, either the lemma or the morphological interpretation, or both, are ambiguous, making a completely automated analysis difficult to achieve.

A technical note

The TLG license strictly prohibits the use of scripts. Contrarily to what was proposed in an earlier version of this draft, even client-side scripts invisible to the TLG servers (e.g. a JavaScript extension) are forbidden, as TLG's director, professor Maria Pantelia has kindly pointed out to me. As regards public domain texts, however, data collection can be automated in various ways. I am currently in the process of developing several sscripts in JavaScript and Python to speed up the collection of metrical readings, phonetic transcriptions and morphological analyses.

Data analysis methods

A thorough investigation concerning the available methods to analyse the collected data is the subject of further work and will be only very briefly discussed here. Focusing on the case study discussed in chapter 1.1, I have chosen a technique known as the Euclidean distance (see [START_REF] Jockers | Text analysis with R for students of literature[END_REF]) as my starting point. In summary, calculating the Euclidean distance means applying Euclidean metric to discover the closeness or distance between books, determined by a number of variables associated with each book. In the case of analysing Greek hexameters, these variables range from syllable weight to frequencies of parts of speech in a line or sentence. The versatile selection of features should be sufficient enough to yield some interesting results with regard to the discussion about Christian and "pagan" poetry. Another data analysis methodology I will be exploring in the future is based on algorithms known as topic models [START_REF] Blei | Probabilistic topic models[END_REF]), which have proved to be highly useful in finding hidden patterns in text collections.

III CONCLUSIONS

Considering the potentially huge benefits of using digital tools and methods in analysing the meters and language of Greek poetry, surprisingly few such tools exist. This may be in part due to the poor availability of freely downloadable digitized texts, and in part, perhaps, to the common suspicion among classicists that the numerous hand-made statistics from the past centuries have the final word in metrical studies. In this work, I have proposed a new approach to collecting metrical and linguistic data from online databases of Greek texts, whether in the public domain or not. The presented methods demonstrate to what extent computer algorithms can help to analyse Greek verses on the one hand, and the untapped potential of electronic resources on the other. The newly collected datasets can be useful for many purposes, such as scrutinizing old statistics in metrics handbooks. In this project, I will analyse the data specifically with a view to contributing to an ongoing discussion about the relationship between late antique classicism and the emerging Christian literary culture. Future work will show whether a "distant reading" approach will provide the field of late antique literary studies with useful results.

DRAFT