Fast Forward or the metamorphoses of literary studies turning digital

Anne Baillot, lecture held in July 2014, revised in March 2015

Compared to many, I am a newcomer in the community of the Digital Humanities. I am also a (comparatively) technically challenged Digital Humanist. Given these aggravating circumstances, I will rather concentrate on what is often called a "change of paradigm". This paper deals with the way in which my disciplinary field has evolved with the introduction of digital methods, as I have observed it during the last three years.

When I say "my disciplinary field", I mean the domain within which the German Research Foundation is currently funding my work, that is modern German literature. Coming from the French German Studies, I was given the opportunity not to specialize during my B.A., M.A. and Ph.D., but to include (German) literature, philosophy and history in my curriculum.

The first half of my PhD thesis consists of a literary approach to the work of philosopher and philologist Karl Wilhelm Ferdinand Solger (1780-1819) which in the second half of the opus I contextualized historically. 1 Both parts are based on paleographic methods that I learned by myself while discovering the manuscripts that made up the corpus. I borrowed methods from other disciplines. This has always been a part of my scholarly identity; it is a blessing and a curse: a blessing to not stay stuck into a rut, a curse to have the feeling that you belong nowhere. This outsider position also means that I will not deliver to you a lecture on an ideologically kosher "big picture". What I consider the most interesting part of my experience is not so much the fact that I came to join the league of the digital front runners, but rather the fact that this was the consequence of an intrinsic development of my research.

This development is what I will present in the first part of this lecture. In the second part, I will draw consequences from this experience and try to see what this means in terms of disciplinary self-definition. In the conclusion, I will evoke the infrastructural winds that are blowing on this process and see how they influence it.

1. How I turned digital I have been primarily working on letters exchanged by writers and scholars. My primary corpus contains letters exchanged by 7 different persons, some being sent one-to-one, others group-to-one, others two-to-one, etc. (Fig. 1) While trying to figure out how to publish these letters, my irritation kept growing as it became more and more obvious that it would be impossible to give a good account of the different dialogue channels that emerge from the corpus through the linearity of a book. My only two options for a publication in the form of a book were to either isolate single exchanges (first the letters between person x and person y, then the letters between person z and person a, etc.) or I would arrange the material chronologically. Both options were doomed to ruin the dialogue character of the exchange. What is more, it seemed to me that I was in no position to decide for the reader which of the two approaches would fit him or her better. In fact, you can interpret the material very differently depending on the way it is presented. In 2005, I concluded my paper at the Congress of the French German Studies Association by saying that it required a different medium than the book to render and analyze the communication issues that were at stake in this corpus in a satisfying way.2 By that time I was speculating on a historical movie, in part because my career perspectives did not look particularly promising and I envisioned having to give up on Academia. Turning to a more creative job seemed a suitable perspective. When I come to think about it now, I am not sure that I would have been more creative in a so-called creative job than I have been while developing a digital edition in the past three years. Berlin is an interesting setting at the beginning of the 19 th century: a place of government, of nobility representation, of culture, as well as, from 1810 on, a city hosting a major University. 4 Having political and academic activities in one place was completely new in German speaking territories. Most Universities were located in comparatively small cities. It was a generally acknowledged wisdom that it was better for students not to be distracted by normal life and better for everyone else not to be disturbed by the students. 5 Universities had their own jurisdiction, even their own prisons. Opening a University in the capital city and, what is more, locating the University building within the city center was an act of provocation that generated its share of resistance, outrage and more or less philosophically justified rebuttal. 6 It took several years of gestation before the University was finally created. The integration of students as well as of teaching personnel in the urban space did however lead to greater social blending and to the establishment of new forms of sociability in the Prussian capital city. University Professors were state officials in the midst of many others, but state officials who benefited from a unique, albeit relative freedom of speech.

It would yet be erroneous to think of the creation of the University as a great invasion. A large number of professors were recruited among either persons that were already teaching privately in Berlin or scholarly active as members of the Academy of Sciences. In order to reach the expected standing, it would not have sufficed to nominate a couple of obscure provincial teachers, one needed names like Fichte, Friedrich August Wolf, Schleiermacher. The Academy of sciences played an important role in the beginnings of the University in that it provided for these kinds of names. After a few years, the flux between the University and Academy of Sciences changed: it was not primarily the University that recruited Academicians, but the Academy that recruited University professors. This can be regarded as an indication of a successful hiring policy by the Ministry for the University.

The University and the Academy of Sciences were not the only places to exchange ideas in Berlin. While Enlightenment had seen reading circles and small libraries flourish, two other forms of sociability developed in the following period. The first one consists in scholarly societies that brought together scholars and Bildungsbürger. Their exchanges dealt either with very specific themes -in the Graeca, one would translate and discuss Greek texts, for instance -or was based on a common aim of a general culture and educating oneself to a morally and intellectually complete human being, as was the case in the Society of the Friends of the Humanity. 7 Many of these societies excluded women, sometimes also Jews. Contrastly in the other form of sociability that played a major role in that period, where women, and especially Jewish women, were key actors. 8 Art (reading literary texts, playing music) was a structure element of salons. They followed rules of their own and were, for that matter, also closed societies; but they obeyed a logic that was different from that of the learned societies.

Both were places where civil society and scholarship could enter a more or less formalized dialogue. Further public places like theater and opera or, for those who published texts, publishers who invited their home authors, also took on the function of generating communication situations. You could meet people with which it would have been impossible to come in contact without these more or less institutionalized get-togethers. All in all, it was possible -and practiced -not to spend one single evening at home and go through the week society-, theater-and salon-hopping. Some of the societies were named after the day of the week in which they came together, a good way not to miss the meetings.

One element is still missing in this costume picture, the final tinge which will make it all even more fashionable: the French touch.

Around 1800, French cultural domination was certainly declining in Berlin, but its traces were still striking. French remained the official language of the Academy of Sciences until 1810. The Huguenot community still represented a numerically important part of the population of the Prussian capital city. Even if the 2 nd or 3 rd generation of Huguenots, in their adult age by the turn of the century, had switched from French to bilingualism and then to German, they were attached to their original culture. 9 The community had its institution, especially a church and a school that still exist today. This network was inherited from a century-long diaspora which had been favored by the Prussian monarchs, not the least of whom, Frederick the Great, wrote and published philosophical Essays in French. His policy was based on French Classics being the standard for all things cultural, and this state of mind dominated the over 40 years of his reign. younger emigrants joined the Prussian army, as did for instance the young Louis Charles-Adélaïde de Chamisso, who later on changed his French forename to the German "Adelbert". As a result of these emigration and integration strategies, scenes taking place on Prussian territories during the Napoleonian Wars are documented in which both fighting parties address one another in French. Besides this singular case and more generally, the opposition to Napoleon, which was particularly strong in Berlin, grew on a ground that was itself impregnated by French culture.

On the background of such a setting, why speak of "intellectuals"? Let's begin with the reasons why not to work with this concept and then come to why there are good reasons to do so anyways.

Reasons why not: "intellectuals" is anachronistic when referring to the beginning of the 19 th century. It corresponds to no self-understanding whatsoever from the persons that are supposed to be designated by this term and hence brings little legitimacy to generalizing analyses. Furthermore, French Research would say -and it did -that intellectualism characterizes a very specific form of political engagement and cannot be applied to anyone before Zola, before "J'accuse" being printed in the front page of L'Aurore (Fig. 2).11 It is certainly true that the social and political situation of late 19 th century France can hardly be compared or applied to that of Prussia almost a century earlier. What "intellectual" accentuates in both cases though is that people who are not primarily politicians, but belong to the cultural (literary, artistic, scholarly) milieu consider it as their duty to raise their voice, either orally or in print, in a political matter. The Napoleonian Wars gave way to a general reaction in Berlin, all the more so in such circles. The "intellectuals" hence designates the writers, publishers, scholars, publicists, who integrated this political dimension to their selfunderstanding and to their communication strategies. Of course, not everyone would rise to the barricades, go to the front, carry weapons. Due to that multiplicity of manifestations, my main focus of interest lies in the publication strategies -I take here the word "publication" in the sense of "rendering public", which concerns books, monuments, translations, letters given to read to several persons, classes in which students take notes to eventually sell them... Publications and communications strategies are being developed by the University professors and by the poets who meet in salons: even if these strategies are arguably different, they are articulated in a cohesive network structured by political, occasionally religious or social, actuality, but also by a strong circulation of ideas through many paths that cross each other surprisingly often.

"intellectuals" brings together authors -in the sense of persons who publish texts, even if it is anonymously or under a pseudonym -who are usually studied by specific fields of research. The history of literature studies Schlegel, Kleist, Tieck. The history of Classical Philology studies Friedrich August Wolf, Friedrich Schleiermacher. The history of Philosophy studies Fichte, Hegel, Schelling. Everybody studies the Humboldts. Nobody studies with the same intensity the colleagues and friends of all these people, their families, their publishers. And yet they were together all part of a creative synergy. Friends read drafts and made suggestions for improvements, publishers modified manuscripts, wives negotiated with the publishers, daughters copied and translated.

Obviously, it is necessary to break this complex down to key questions that can make it more manageable. When I applied for the funding of my current research group, I defined four axes to shed light on the different aspects that seemed most fruitful to me: one is the University and more specifically the Philosophical Faculty, which consisted in a peculiar disciplinary construction, that also evolved with the emergence of new Humanities disciplines along time; another is on French-speaking learned communication in the Enlightenment period in order to understand the communication structures that prevailed before the turn of the century; the third is the contribution of publishers to the realization of authoritative texts and the fourth aspect consists in the hide-and-seek strategies developed by women who were literary active. All of these aspects were to be explored more bottomup than top-down, light was to be thrown on the contribution of well-known authors through that of the lesser known ones. Letters would not be studied by themselves, but in that they shed light on other published texts. This is how far I had thought when I reached in my application in 2009. I wanted to edit some transcriptions online with a small editor12 in order to make the new texts that were to be unveiled quickly and widely available. I had not the slightest idea what metadata are. I had not the slightest idea what entities are. Ontology had solely to do with philosophy and vocabulary with grammar. The word "authority files" evoked -nothing… at this point, I will simply jump a year and a half ahead, when I had understood the point of tagging entities and working with rich metadata.

In its core, it was the network idea that lead to the conception of a digital edition. With letters being the primary sources, connecting the persons and the publications was logically the best way to bring together the different spheres we were working on in the different work packages (University, publishers, learned societies, and wherever it was that women found time and space to write). Who writes to whom about whom, who comments on this or that publication, who contributes to a draft, how do publications circulate: this is what I wanted to find out. Besides gathering this information to help answer my questions, I wanted to give the reader the opportunity to approach this corpus from different angles. I wanted to give access to unedited manuscripts, but leave the reader, to a certain extent, free to make his or her own reading of them. This meant making the texts accessible to specialists of a potentially wide variety of aspects (language, literature, history of ideas were the ones I had in mind) as well as to "the interested public" in a larger sense. I wanted to complement what was being done on the salons or in the research group Berliner Klassik on theater, learned societies and the Academy of the Arts. 13 That was the ideal, which had to be then scaled down to the bare truth of reality, since I had not applied for funding dedicated to a digital edition -and digital editions are expensive endeavors.

The discovery of Van Gogh-The Letters 14 was a moment of epiphany for the whole research group, but there was no way we would ever be able to afford such a beautiful result. The idea to bring together different types of documents turned out to be one major challenge from the first decision on. This first decision was to present a line-to-line diplomatic transcription opposite or next to a high-quality scan of the manuscript. This works fine for Van Gogh and even leaves room for comments in a third column in the center, since the pages are narrow and all contain about the same amount of text (see Fig. 3).

13 http://www.bbaw.de/forschung/berlinerklassik/uebersicht 14 http://www.vangoghletters.org/ We on the other hand had to adapt from four-word verses in one manuscript to long, very, very long prose lines on others, as well as to the idea that not everyone has a 29 inches monitor. We wanted to make several entry points available for each manuscript, which lead, in the first version of the web interface, to a menu with incoherent categories, some being author-centered, others organized by topics, and redundant ones at that, since some corpora appeared under the author corpus and under the thematic corpus. The latest version has the advantage of being coherent in the entry points it offers: topics, authors, genres, and dates.

Multiplying access and views on the corpus also meant displaying different views of the information we encoded for each single document. Each document can be viewed from 5 points of views, on either one or two columns. All these views are generated from the same XML document. Design was the most important decision in these cases. Design is always a balance between too much and too little information. Our edition is not per se intuitive; it does not associate, like it is traditionally the case, one author and one genre as do Van Gogh-Letters, August Wilhlem Schlegel-Correspondence, Alfred Escher-Letters, Carl Maria von Weber-Complete Works. 15 Because of that, we had to integrate quite a lot of information to our standard document view in order to make it clear for each document where it is situated in terms of author/genre/topic. It seemed more intuitive to integrate the scrolling elements (previous/next page/document) above the text. Also, the header was too important, especially considering the fact that the different entry points do not provide for an overall orientation (author, genre and theme having to be specified for each document), to be dropped to the lower part of the page. This orientation information was so numerous that we had to place the indication regarding the 5 different views at the lower part of the page, despite the fact that it is what makes one the beauty -and, by the time we conceived it, originality -of our edition. We have been considering reducing the header in order to make the document itself take comparatively more space on the page; this is something we are working on. Design improvements seem to never reach a point where everything is satisfying. This has in large part to do with the fact that our corpora are structured so diversely, some in prose, some in verse, some letters and some texts.

Most of the orientation information is available in three languages (or should be, we are still working on translating the last missing bits). Most of the texts that we are editing are in German, this a German research project, so there had to be a German version of the frame text. But part of the corpora is completely and exclusively in French, a case in which it does not make much sense to frame the transcription with explanations primarily in German. The basis version of comments, etc. for the French documents is hence in French. Finally, the encoding itself is in English. What is more, our edition might be of interest to researchers who either don't understand German or French so well or who want to get orientation in order to reuse our data for instance to do data mining. These users are likely to need some information in English, especially metadata. So we have decided to offer as much metadata information as possible in the three languages. At first, we translated manually, then identified elements that could be re-used and automatized their translation. There is still room for improvement on that level, but it requires a lot of energy to translate every relevant piece of information hidden in the frame of each and every page.

Finally, we offer a third layer of access to the information in the form of a search interface, which works fine, but is rather unspectacular, except for 2 features. You can either do a traditional full-text search or browse through our indexes of persons, places, groups, and works. Places more or less reducible to a point (a city, a village) are being associated with geographic coordinates and are displayed on a map, which is mostly helpful for places with ambiguous names like Neudorf or Altstadt rather than for Berlin or Paris. For each place, you can search the name in form of the sign string as it is to be found in the manuscript, the current common sign string if it is different from the first one, the version in the other two languages (two out of French, English, German) if different and finally, for the places that are nowadays located in Poland, the Polish name. For persons too, the different versions of the name are available. Apart from basic biographical information, we record family relationships and are currently adding pupil-teacher relationships. What is more, we are offering additional biographical information via the GND Beacon. This works only for a limited amount of biographical entries -those that are attributed a GND number, e.g. basically men who published -but allows to interact with other repositories and editions. The second neat feature concerns the subproject I will talk about at more length in the second part, namely the Boeckh project. Additionally to the digital edition Letters and texts. Intellectual Berlin around 1800, we have set up a repository that records all known manuscripts by, to and from August Boeckh. The indexes are common to both the edition and the manuscript repository so that a search can lead you to both the manuscript repository and the digital edition. Now let me get to the core of our editorial work. How and what exactly do we tag? 16 Our tagging works on two levels. The first level is that of the entities, which are as far as possible connected to authority files through the indexes. Our indexes are essentially enriched manually, apart from a raw import from kalliope when conceiving the Boeckh platform. Persons are being indexed, but also works by these persons, who interest us especially because they are writing and publishing. Encoding bibliography in TEI is not particularly intuitive and makes it rather complicated to order entries and connect them, for instance in the case of different editions of the same work or translations of a text. Hierarchizing bibliographical information on the fly as it became necessary along project and data growth was a challenge. The output could be better than it currently is, especially if we had implemented a FRBR model from the conception on.

The second layer of tagging concerns textual elements reflecting the genesis of each document. We did not have the time and money necessary to implement Critical Apparatus,17 especially design-wise. We developed a light encoding of our own that reflects text-genesis and responds to our needs.

In order to make the importance of this layer of tagging clear as well as what our needs were, I have to get back to the writing context shortly. When a publisher receives a manuscript he wants to publish, what does he do? First of all, by then, publishers generally intervened in the text that they published much more than what we might expect by today's standards. This is partly due to the fact that spelling and punctuation were not standardized. But publishers also plainly considered it to be their job to adapt texts to their public. What is more, the handwritten copies handed out to publishers for print were often still full of corrections. These were sometimes difficult to decipher, sometimes not placed directly where they belong in the text (in the case of marginalia). In short, there were plenty of reasons for the printed text to deviate from the handwritten text that the author had handed over to the publisher. The history of the 18 th century is full of examples of editions so incorrect that the authors turned to another publisher to realize as quickly as possible a new edition, thus generating a mess of concurrent versions of one text.

As far as letters are concerned, the situation is even trickier. First of all, interesting letters were shown around. Everybody knew this, in particular the author of the interesting letters. A letter could be interesting because of its author (typically: Goethe), of its topic (typically: Goethe) or of its style (typically: Goethe-like). Gossip scored pretty high too on the general scale of interestingness. Anyways: whoever wrote interestingly wrote for a more or less defined larger audience, and thus, they wrote differently than if they would be writing for only one person. What is more, being interesting means being susceptible to being printed. Writing for print also alters the style. But on the other hand, even those who wrote hoping or knowing that their letters would be, at some point, printed, assumed that they would never ever be printed as they were written, but would be copyedited, "redigiert", by an old friend, a good son or an admirer. In that sense, the balance between authenticity and pretense, between private and public information, is always difficult to assess in a letter from that period.

But the old friends, the good sons and the admirers not only paid warm tributes to the deceased they honored and whose texts they edited. These dedicated editors had in fact a completely different understanding of the status of the manuscript from the one we have in our days of materiality cult. When preparing their editions of the letters, they often made their corrections directly on the original, more often in ink than in pencil. I personally see some beauty in this rewriting process. The editors preciously preserved the manuscripts they had first -seen by modern standards -mutilated. To me, it is as if they had expressed their love and admiration by mixing their handwriting in that of their loved ones, paid their respect by making a cherished text readable by their moral and stylistic standards, then allowing the manuscript to return to its iconic status.

In the end, e.g. at our end, it means that the manuscripts we deal with are manuscripts in which several hands contributed: the author, a first editor, a second editor, an archivist, to name those that are identifiable with certitude. Ink variations are usually identifiable although they can also only tell us that the ink holder was empty and the new one was mixed differently. When it comes to pencil, some marks can very well come from different interventions without the difference being seeable. Also, there are cases where the old friend, the good son, the admirer, e.g. the person in charge of editorial functions, is actually the original author, deciding to write his own golden legend, often a few decades later, by re-mixing his own letters. This means that his hand is to be found in at least two temporal occurrences on the manuscript: at the original conception time and at the later editorial time. Distinguishing the hands according to a time factor is a confusing criterion for letters.

In this case, it is more useful to differentiate by function, or else one has to consider encoding any kind of break the writer took during the conception of the letter, be it because he had to mix more ink, to smoke a pipe, to answer a question from his wife... For literary texts on the other hand, novels, dramas for instance, it is precisely that kind of temporal interruption that needs to be encoded, since the different work layers contribute to the progressive construction of the coherence of the text. The requirements in the genetic encoding of the hands hence differ depending on the type of text concerned. It was certainly a great challenge to take all these aspects into consideration in one single set of encoding guidelines.

What I consider the most beautiful aspect of our two-layered tagging -entities on the one hand, text genesis on the other -is that it can really show on a fine-granular as well as middle-sized scale the construction of a literary canon as well as the circulation of ideas. You can connect for instance the information about the books read by an author with the fact that his editor has suppressed this information when he edited the letter that mentions these books, hence erasing traces of intertextuality and emphasizing the originality of an author, as if he had produced his own work independently from his publication environment. This is a way to seize the core of what romanticism is, to show the reality of the tension between the network character of the circulation of ideas and a conception of creativity that is based on the individual genius. The idea of the author as a singular occurrence obviously does not hold water when approached in such a perspective. The embedding of the text-production process in a series of structural as well as accidental factors accentuates the necessity to compare writing practices and strategies of different authors to make the real originalities emerge from what was, in that decade, a meme, or at the very least common practice.

All this we tagged, and can show. Or rather, could show, be it for the design, again. Having tagged all of this is fine, displaying it is another story. First challenge: you can consider yourself lucky if the main text is written in horizontal lines. In fact, written lines sometimes seem only to be there to be written in between, around, vertically to, the other way around, or even on, and this by the same author who has written the main text. The expensiveness of paper explains part of these amazingly condensed manuscripts, but in other cases, it is decidedly an overall conception of writing that leads to a form of page-filling that is per se a declaration of literary intention.

The letters we are dealing with are also multi-layered due to the exterior hands. In order to display the different hands, one would actually need a third dimension to the page, one that would allow isolating from one another elements that appeared on the manuscript along time.

The manuscript we have access to is not the original; it is but the result of the history of the original from its creation until today. Elements have been preserved, elements have been added, elements have disappeared. Temporality is an enemy to materiality from the moment on when the feather reaches the page. Not only do we have to deal with the consequences of acid in 19th century paper. Even the addressee of a letter does not receive what he or she has been sent, since the breaking of the seal necessary to open the letter leads almost ineluctably to text loss. Basically, this contradicts the idea of any possible authorial version. If I transcribe on the basis of the manuscript that I have scanned today, someone going to the archive in 20 years might see something different, even if no one has written anything new on the page or even in the meantime consulted the manuscript. This calls for the attribution of a date not only to the transcription and the assessment of the different hands and text layers, but also to the scans we are working with and which do not display -even independently from the progress that can be made in scanning techniquetoday what they will display in 5, 10 or 20 years from now.

The idea to work with a dynamic time scale and to locate the different hands on that time scale would mean breaking linearity, and transgress the most basic way in which we apprehend texts. Our brains are not used to that -in fact, I don't really know what this could look like once realized. I think that this is one more striking illustration of the fact that we are still conceiving digital editions like books, only with a few additional fancy features and search options. It is immensely difficult to project oneself outside the linearity of edited text as we know it. In that sense, the questions we are confronted with when conceiving a digital edition do not only have to do with establishing quality standards for texts made available online, it has to do with re-thinking text. This insight has not really reached modern literary studies yet, so that the gap between, on the one hand, information sciences, where not only the concept of text, but even the concept of document is being questioned and taken apart, and, on the other hand, literary studies, where the simple idea of going past WYSWYG is still inconceivable for many, still grows wider every day. 18 Compared to these levels of abstract thinking, the result of what we have actually implemented is sober. Each text block is being attributed a hand. When you scroll over the text with the mouse, a window pops up telling you whose hand it is, except for the main text, that is meant to remain undisturbed. This is the coherent and, I think, rather elegant part of our implementation, even if it obstructs text with a pop-up for the time you need to read the content of the pop-up. But there is, additionally to that, the problem of color. In a first step, we envisioned rendering each color appearing on the manuscript. We gave up that option pretty quickly. First, we had to change color to signalize hyperlinks anyway, and that would have made the system incoherent. Second, it would have been difficult to render the many shades of inks, of grey, of red; it was not even sure that all browsers would interpret the color codes correctly. So we decided to use only three colors: black for the main text, orange for the links (fitting to the overall design) and red for the interventions from other hands. This is an interpretation that defines the way the text is to be read, for sure, because not all the text in red has the same status -if several persons intervened in a manuscript additionally to the author, they will all be rendered in the same red. Also, the fact that some elements (those that include graphical information additionally to or instead of text) are being either roughly rendered (lines) or described (stamps) gives a reading orientation. The other option would have been to copy-paste the graphical element, as is being done in numerous editions. 19 The choice we made is conceived to allow the intelligent reader to make his or her own mind based on the fact that the scan is there anyway. (As you know, one tends to conceive one's readership to one's own image) This is not a problem for big, striking elements -a line through the page for instance. It is more complicated for small elements like the ligatures. Confronted with the ligatures, we realized that the most important thing about one's data model is to define the granularity in which one wants to work. Breaking encoding down to the single sign (not character) was a step that we could not afford if we wanted to reach a representative text mass to work with at the end of the project.

The example of the ligatures leading to overarching encoding decisions is typical for the workflow and the results we experienced in the last three years while developing the digital edition. What was initially conceived to bring together different corpora in order to gain insight in what they have in common in terms of circulation of ideas has given way to a literary confrontation with the most basic instruments of our daily work -author, text, literary canon. In that sense, I think that the future of modern literary studies lies in the recognition of the discipline of digital philology. And what I mean by that, I will explain in my second part.

In his presentation of the Open Philology Project, Gregory Crane specifies Boeckh's20 inspirational role as follows:

In this [project] we advance a digital successor to that philology which sees in language a source for what Augustus Boeckh in 1822 termed "the understanding of all antiquity, including the events of both the physical and intellectual world."

[…] From the human perspective philology constitutes a set of language-based critical scholarly skills -not only annotating […] , but also comparing, connecting, interpreting, proving or rejecting hypotheses, finding evidence; critical apparatuses and commentaries often preserve condensed fruits of such reasoning […]. 21 Contrarily to the Open Philology project though, what I want to talk about is not -or at least not only, and certainly not primarily -focused on the knowledge of the ancient world. What interests me is more how Boeckh situates philology within the humanities as a discipline and particularly as an institutionalized discipline. To understand that, we need to get back to the text of his Encyclopaedia and Methodology of Philological Sciences: I. Die Idee der Philologie oder ihr Begriff, Umfang und höchster Zweck. § 1. Der Begriff einer Wissenschaft oder wissenschaftlichen Disciplin wird nicht dadurch gegeben, dass man stückweise aufzählt, was in derselben enthalten sei. Dies scheint sich zwar übermässig von selbst zu verstehen; aber die Philologie sind Viele gewohnt nur als Aggregat zu betrachten und die, welche sie so betrachten, könnten allerdings keinen andern Begriff derselben geben als den, welcher in der Aufzählung der Theile läge, d. h. im Grunde gar keinen. […] Die gesammte Wissenschaft als ein Ganzes ist Philosophie, Wissenschaft der Ideen. Aber je nach der Betrachtungsweise, ob das All von materieller oder ideeller Seite genommen wird, als Natur oder Geist, als Nothwendigkeit oder Freiheit, ergeben sich, abgesehen von formalen Disciplinen, zwei Wissenschaften, die wir Physik und Ethik nennen. In welche gehört nun die Philologie? Sie umfasst gewissermassen beide und ist doch keine von beiden.[…] Hiernach scheint die eigentliche Aufgabe der Philologie das Erkennen des vom menschlichen Geist Producirten, d.h. des Erkannten zu sein. Es wird überall von der Philologie ein gegebenes Wissen vorausgesetzt, welches sie wiederzuerkennen hat. Die Geschichte aller Wissenschaften ist also philologisch. Allein hiermit ist der Begriff der Philologie nicht erschöpft, vielmehr fällt er mit dem der Geschichte im weitesten Sinne zusammen. Geschichte und Philologie sind nach allgemeiner Ansicht eng verwandt. 22 Allow me to comment on the conception of the humanities that is expressed here. 23 Boeckh defines the humanities as a whole that should not be sliced up in disciplines depending on their content. On the contrary, to him, the content of philosophy, philology and history (to take the ones that are named in this passage) is the same; what constitutes the difference between them is the method, the point of view. What characterizes the philological approach specifically -the ominous "Erkenntnis des Erkannten" dear to hermeneutists -is that it deals with produced, human knowledge. Now produced knowledge can be a text and is often a text, but still: in that conception, text is only one type of documentation of human knowledge among others susceptible to be explored. This is certainly the greatest originality of Boeckh in his time and what Gregory Crane emphasizes in the quote, namely that the totality of a civilization cannot be explored only through text, but also requires to take into account architecture, economy, measure system, weather, etc. Also, "recognition of the recognized" does not presume of its own medial shape. Of course, a science is mostly transmitted in written form. But Boeckh's philology, as an approach of the products of human mind, did not find its sole expression in books. It was also transmitted orally, especially to students.

When you would go to the University back then, it was mainly to sit on a bench and hear what the professors had to say. Fichte or Hegel were known for having troops of students, more aficionados really, following them everywhere on campus. You can measure the importance of this magisterial discourse -and particularly in the field of Classics -by taking a look at US University libraries.24 When they were founded at the end of the 19 th century, they imported in delirious amounts dissertations and handwritten lecture notes, which could be bought from German booksellers. There was a real market for such handwritten lecture notes. Some professors agreed to students making their lecture notes into real books and publishing them, and some professors left the university because they disagreed with that, as did Schelling.

Boeckh founded in 1812 the so-called Philological Seminar at the University of Berlin. At that exact same time, Schleiermacher founded the Theological Seminar. In both, the idea was to teach more intensely, more personally the best possible students. Boeckh directed the Berlin Philological Seminar until his death in 1867. Buttmann took care of Latin exercises, but 22 August Boeckh, Encyklopädie und Methodologie der philologischen Wissenschaften, ed. by Ernst Bratuschek, Leipzig, 1877, here p. 3 and 9-10. 23 I have developed this in some more length (and in German) in my working paper: ""Digitale Philologie" -Versuch einer Einordnung, mithilfe August Boeckhs" (https://halshs.archives-ouvertes.fr/halshs-01132263 ). 24 Some elements on that topic are to be found in my working paper: "The University Library and the Humanities: Historical and Contemporary Perspectives" (https://halshs.archives-ouvertes.fr/hal-00676073 ) Boeckh did all the rest personally. Now which conception of philology was practiced in the Philological Seminar? Boeckh presented a plan to the Ministry, with 3 objectives. Those were: teaching Classics, preparing the future teachers, bringing philological methods to other disciplines. The ministry saw things differently and set as an aim for the seminar solely the formation of Classical Philologists. This did not prevent Boeckh to do pretty much what he wanted in his Seminar. 25 Members of the Philological Seminar received money if they worked well, but they had to work a lot. Critic, interpretation, disputation were the three pillars of their activities. They did not dispute on abstract, content-less theses as taught by the medieval tradition. They prepared in advance a text (often an essay commenting on a passage of a classical author) which they gave to their co-students and to director Boeckh. This was the basis for the discussion; everyone was to have read the essay well in advance and the discussion had to be lively. This illustrates the general principle of the Seminar: teaching the students autonomous research was a key aim of Boeckh's.

The Seminar students were not only intensely trained, they were also institutionally coached. Boeckh helped them find good positions by recommending them to the Ministry when there were openings in good High schools. He helped them conceive their Seminar essays in such a way that they would then have a solid basis for a dissertation. Except for one philosopher and one chemist, all successful PhDs of the 10 first years at the Philosophical Faculty of the Berlin University were former Seminar students -and not all of them got a PhD in Philology. This overall strategy allowed Boeckh to bring philological methods into other disciplines, like Philosophy or History, a field that was only beginning to become an Academic discipline. 26 My point with this detour is to learn from the way Boeckh modernized his discipline. First, he did amazing, groundbreaking research. He got into epic scholarly fights, especially with the Leipzigan Hermann. He built bridges between teaching and research. He developed new learning methods and formats. He had a vision of what philology is. He engaged in a huge, justly and strongly criticized Academy project, the first one ever: the Greek inscriptions project, still unfinished to date. And although he disapproved of considering fractionized aspects of his discipline rather than the whole, he also acknowledged his own limits.

Inspired by the idea that you can reach interesting results on your way to something that may (or may not) be too big, I divided our own Boeckh project into three work packages. I have to say that I found the Boeckh manuscript corpus almost untouched when I turned to it in 2011 -in fact, the corpus was so big that nobody had dared confronting all of it. I admit it was a little bit naive of me to consider "all Boeckh". But I did not know what would be the richest aspect when I first approached this huge mass of manuscripts. So we set up an online catalogue of the manuscripts by, from and to Boeckh in order to get some orientation.27 I mentioned it before, it is connected to the digital edition Letters and texts via the indexes. The second part is the reconstruction of his book collection on the basis of the volumes and the list he donated to the University Library of the then-Berlin University. 28 All the biographical and bibliographical data collected in these two work steps, which are well advanced but still being enriched, will be usable for the "big" one which I am still missing funding for: a digital edition of Boeckh's own notes for his lecture on the Encyclopaedia and Methodology of the philological sciences. This manuscript has 270 pages and was enriched by Boeckh during 56 years (he gave the class 26 times between 1809 and 1865), occasionally changing his mind on some scholarly matters as new results were published that refuted his first opinion.

Because, as paradoxical as it may seem, the Encyclopaedia as it has been edited by Ernst Bratuschek, who was a student of the old Boeckh, and reedited since 1877, this reference work for any philologist, is the epitome of bad editorial philology. 29 It consists of a compilation of Boeckh's own notes with those that some of his students (primarily Bratuschek, but not only) took in the Encyclopaedia class as well as in some other classes he gave towards the end of his career. This is explained in the foreword, but the text itself contains no indication whatsoever of the original source each passage comes from. What is more, the only version of the class considered is the final one, as if there had been no inbetweens, no changes, no questions: Digital philology can do better than that, it can be more Boeckhian than that. This allows me to get back to what I first mentioned about text as the basis of literary studies being radically questioned by the digital approach. The double genesis-centered and entitycentered approach of text in our digital edition has shown me, if nothing else, how much the digital approach renews the importance of text genesis (which questions, again, such concepts as author or authorial text). So -what is text, what is text genesis?

If you take the creative process of text genesis as generally as possible, it basically consists in combining existing linguistic elements in a new order. Texts only vary from one another in how radically they re-order the linguistic elements they are using. In literary texts, this means combining recognition effects, alienation effects; in scientific texts, ordering ideas anew: all of which can be read as expressions of a more general intertextuality. Digital philology makes it possible to connect all of these phenomena.

It would be an illusion to think, however, that because it is digital, rendering everything, connecting everything is possible. Filtering information and gathering insight would not be possible but for considering these phenomena within a conceptual frame. Digital philology works out such concepts, makes choices, and manages the deficits that inevitably come along with a selection process.

But digital philology does not only manage deficits, it also reflects on them, something that cannot be done by the computer, but has to be done by us and that makes us digital philologists. This means asking ourselves what we want to do with the mass of text information that is available. This means confronting us with that of which we know that we will never be able to give account of, either because it is gone forever or because we won't have time, money, room to deal with it. As I mentioned in the first part, this is also what happens on the scale of fine granularity. Encoding does not go without interpretation, and by interpretation I mean a reflection of the selection process when giving access to a text. Encoding forces us not to take the source for granted, but to question how it reached us and how we will make it reach others. In that sense, I think that text genesis and the epistemology of text genesis are the two pillars of digital philology.

This -or that?

The development of our digital edition and the epistemological approaches that I have presented here took three years and a half from the moment on when I had understood what metadata are. The time needed to formulate, implement, adapt, enrich, adapt, implement and reformulate a digital edition is simply a long time in terms of German Research Foundation project funding. It takes at the very least its four, five years.

To my eyes, this work process can be compared to training deep muscles, like our abdominal or our back muscles, the ones from which the rest of the body can stand, sit, move, those that make the real strength. How do you institutionalize that kind of research? I will not say that Boeckh had it easy. But he had a professorship from his 26 th year on, he managed to get the first Academy project funding ever and one of his best friends was working at a decisive position at the Ministry. What do we have?

We have for instance calls for DH centers and a basic situation where promises of big money sound like a fountain in the middle of the desert. Rushing to the water, every humanist can think of a database he or she could set up for the good of science. Let the digital money flow!

20

We have big infrastructures which nobody really knows what they do. We have little coordination between projects because the goal remains to put one's name on a result. And we have universities and infrastructures offering no solid long-term access to digital sources. This generalization probably makes things look worse than they really are, but this is still the overall feeling of the DH community. All of this stimulates our superficial muscles, those that try to go with the wind, because going against it would be suicidal.

But both movements are contradictory. You cannot train your deep muscles by permanently soliciting your superficial muscles. You cannot interrogate your methods and questions by writing applications and living by call deadlines. I don't see any solution to that problem right now. It has in great part to do with a much wider structural problem in the German Research System, which will not be solved lightly. But it takes extreme forms in the case of Digital Humanities. 30 Digital Humanities have to comply with two requirements. First, they don't really exist as a discipline, but there are a few DH professorships, and they are still pushed to the infrastructural side (computers are much less scary when they are infrastructure). Second, there is a lot of money offered in calls for DH projects (or infrastructures, for that matter), but not only do the projects cost a lot, the infrastructure they require tends to suck up most of the money. It would be necessary, for instance in the literary studies, to go beyond "the thing with the computer" and start seeing it as a chance to renew our hermeneutical practice and maybe, along way, the theory as well.

Fig. 1 :

 1 Fig. 1: Schematic representation of letter exchanges within the "Friday Society" (fig. by @Melanie Siemund)

  Between 2005 and 2009, I explored what would become my main field of research: Berlin intellectuals at the beginning of the 19 th century. 3

  Fig. 2: Cover of the Journal "L'Aurore" of Jan. 13 th , 1898 (source: http://fr.wikisource.org/wiki/J%E2%80%99accuse%E2%80%A6!)

Fig. 3 :

 3 Fig. 3: Screenshot from Van Gogh-The Letters displaying the basis 2 columns and a commentary in the central column (http://vangoghletters.org/vg/letters/let706/letter.html).

See https://halshs.archives-ouvertes.fr/tel-00783069.

"Wie rehabilitiert man einen Schriftsteller und wozu? Das Beispiel unerschlossener Briefwechsel aus dem Umfeld des Dichters Ludwig Tieck, des Philosophen Karl Solger und des Historikers Friedrich von Raumer", in: Dokument/Monument. Textvarianz in den verschiedenen Disziplinen der europäischen Germanistik. Akten des

Kongresses des französischen Hochschulgermanistikverbandes A.G.E.S., hg v. F. Lartillot u. A. Gellhaus, Peter Lang Verlag, Bern/etc. 2007, S. 103-126

S. for instance Netzwerke des Wissens. Das intellektuelle Berlin um 1800 (Hg.), Berliner Wissenschaftsverlag, Berlin, 2011.

S. Theodore Ziolkowski, Berlin: Aufstieg einer Kulturmetropole um 1810,Göttingen, 2002.

S. William Clark, Academic Charisma and the Origins of the Research University, Chicago, 2007.

Even in French research, the episode is considered as founding moment for Western History of Science, see Luc Ferry (ed, et al.), Philosophies de l'université: l'idéalisme allemand et la question de l'Université,Paris, 1979.

See Kirill Abrosimov, "Die Genese des Intellektuellen im Prozeß der Kommunikation, in: Geschichte und Gesellschaft 33/2007

Vgl. Björn Märtin, Christian Thomas: "Das Wuchern der Archive. Die digitale Edition des Nachlasses Franz Brümmer mit dem Refine!Editor", in: editio 22, 2008, p. 204-212.

http://vangoghletters.org/, http://august-wilhelm-schlegel.de/briefedigital/, http://www.briefedition.alfredescher.ch/,http://www.weber-gesamtausgabe.de/de/Index .

Our encoding guidelines are downloadable from there: http://tei.ibi.hu-berlin.de/berlinerintellektuelle/about?de

17 http://www.tei-c.org/release/doc/tei-p5-doc/en/html/TC.html

I have developed these aspects in a paper written with Markus Schnöpf in February 2015: "Von wissenschaftlichen Editionen als interoperable Projekte, oder: Was können eigentlich digitale Editionen?" (to appear in: Historische Mitteilungen der Ranke-Gesellschaft, Beiheft "Zukunft der Digital Humanities", April 2015).

What is digital Philology?19 Like for instance the Deutsches Textarchiv (http://www.deutschestextarchiv.de/).

On Boeckh and his work, see: Christiane Hackel and Sabine Seifert (dirs.), August Boeckh. Philologie, Hermeneutik und Wissenschaftsgeschichte, Berlin, 2013.

http://sites.tufts.edu/perseusupdates/2013/04/04/the-open-philology-project-and-humboldt-chairof-digital-humanities-at-leipzig/.

This and the following is largely inspired by the work of Sabine Seifert, especially her paper "August Boeckh und die Gründung des Berliner philologischen Seminars. Wissenschaftlerausbildung und Beziehungen zum Ministerium" in the volume mentioned in FN20.

For more details on this, see my paper " Die Entwicklung der Philosophischen Fakultät der Berliner Universität in den Jahren 1813-1817 -oder wie Boeckh seinen Schülern zur Promotion verhalf" in the volume mentioned in FN 20.

http://tei.ibi.hu-berlin.de/boeckh/.

http://tei.ibi.hu-berlin.de/berliner-intellektuelle/manuscript?Boeckh_Buchkatalog+de.

See FN 22.

As was suggested in the manifesto of young researchers in DH: http://dhdhi.hypotheses.org/1855.


Mohammed H A Hamid

Romain Postoyan

Jamal Daafouz

Local observers design for a class of neural mass models

We present a model-based approach to estimate the mean membrane potentials (and their time-derivatives) of populations of neurons within cortical columns. We consider a general class of neural mass models for which we design local state observers. The synthesis relies on linear parametervarying systems techniques and the observer gains are obtained by solving linear matrix inequalities. Simulations results are presented to illustrate the efficiency of the approach.

I. INTRODUCTION

Cortical mechanisms involved in epilepsy remain largely unknown nowadays. In this context, measurements of the cortical activity are essential to improve our understanding of the underlying processes. Among the different available methodologies, electroencephalograms (EEG) provide the best time resolution, and is therefore often favoured by the clinicians to investigate seizure generation and propagation. EEG recordings reflect membrane potential variations of pyramidal neurons grouped into populations within cortical columns. These cortical columns are also composed of excitatory interneurons and inhibitory interneurons (see Figure 1 for an illustration), which are also expected to contain important electrophysiological information but which are not measurable today. The purpose of this study is to estimate the mean membrane potential of all the populations of given cortical columns using (simulated) EEG signals and a model of the cortical columns dynamics.

Fig. 1: Functional relationship between neural populations for the model in [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF].

Several works have investigated this problem in the recent years. Nonlinear Kalman filters are constructed in [START_REF] Freestone | A data-driven framework for neural field modeling[END_REF], [START_REF] Rigatos | Estimation of wave-type dynamics in neurons' membrane with the use of the Derivative-free nonlinear Kalman Filter[END_REF], [START_REF] Schiff | Kalman filter control of a model of spatiotemporal cortical dynamics[END_REF], [START_REF] Ullah | Assimilating seizure dynamics[END_REF] mainly for models of the type of [START_REF] Wilson | Excitatory and inhibitory interactions in localized populations of model neurons[END_REF], [START_REF] Wilson | A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue[END_REF]. On the The authors are with the Université de Lorraine, CRAN, UMR 7039 and the CNRS, CRAN, UMR 7039, France, {mohammed.hamid, romain.postoyan,jamal.daafouz}@univ-lorraine.fr.

J. Daafouz is also with the Institut Universitaire de France (IUF). Their work was partially supported by the ANR under the grant JCJC SEPICOT (ANR-12-JS03-004-01).

other hand, deterministic global observers with guaranteed convergence are designed in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] for a class of neural mass models which covers the models in [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF], [START_REF] Stam | Dynamics of the human alpha rhythm: evidence for non-linearity[END_REF], [START_REF] Wendling | Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition[END_REF] as particular cases. We focus in this paper on the same class of models as in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF]. The objective is to go a step further towards the implementation of state observers for neural mass models. The models considered in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] generate outputs which are assumed to model EEG recordings. However, these output signals are not centered at the origin in general, contrary to real EEG signals, which a priori prevents the application of the observers of [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] on real data. We therefore first revisit the models considered in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] so that they generate output signals with zero means, by using high-pass filters. It appears that the results in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF] are no longer applicable in this case, and that those in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] can only be used for some specific model parameters as we show. To overcome those issues, we design local observers, i.e. observers which are ensured to converge when they are initialized sufficiently close to the initial condition of the system (see e.g., [START_REF] Hammouri | Local observer for infinitesimally observable nonlinear systems[END_REF], [START_REF] Reif | An EKF-based nonlinear observer with a prescribed degree of stability[END_REF], [START_REF] Sundarapandian | Local observer design for nonlinear systems[END_REF], [START_REF] Xia | On exponential observers for nonlinear systems[END_REF]). The design of local observers is expected to be more amenable compared to the synthesis of global observers. Indeed, in this case we are only interested in the behaviour of the estimation error around the origin where we can use first order approximations to analyse it. This leads to a linear time-varying systems which usually facilitates the design of the observer gains.

The originality of our work compared to existing local observer designs is that we apply tools from linear parameter varying (LPV) systems to construct the observer gains. We use the properties of the considered models to write the linearized estimation error as a LPV system, where the 'parameter' corresponds to a known bounded function of the state estimate which lies in a known hyper-rectangle. We then resort to standard analytical tools for LPV systems to design the local observer gains. We provide linear matrix inequalities (LMIs) to construct the observer gains at the vertices of the hyper-rectangle mentioned above. We then use the interpolation technique (see [START_REF] Bara | Parameter-dependent state observer design for affine LPV systems[END_REF] for instance) to obtain the observer gain, which is therefore nonlinear in the state estimate. Contrary to [START_REF] Hammouri | Local observer for infinitesimally observable nonlinear systems[END_REF], [START_REF] Reif | An EKF-based nonlinear observer with a prescribed degree of stability[END_REF] where local observers are designed for general nonlinear systems, the proposed conditions can be verified a priori as they do not involve properties of the system trajectories which are unknown. Furthermore, we do not linearize the system around an equilibrium point to construct the observer, as it is done in [START_REF] Sundarapandian | Local observer design for nonlinear systems[END_REF], [START_REF] Xia | On exponential observers for nonlinear systems[END_REF], only the state estimation error system is linearized at the origin, which is different. Simulation results are provided for a model of neural mass models inspired by the one in [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF] and we characterize the set of model parameters for which the required LMIs hold.

The paper is organized as follows. We present the considered class of neural mass models in Section II. The design of the local observers is addressed in Section III and simulation results are proposed in Section IV. Finally, Section V concludes the paper.

Notations. Let R := (-∞, ∞), R ≥0 := [0, ∞ ), R >0 := (0, ∞), Z >0 := {1, 2, . . .}. For (x, y) ∈ R n+m , the notation (x, y) stands for [x T , y T ]
T . The identity matrix is denoted by I. For a vector x ∈ R nx , |x| denotes the Euclidean norm of x.

The notation L ∞ stands for the set of piecewise continuous functions f :

R ≥0 → R n , n ∈ Z >0 , such that f ∞ := sup τ ≥0
|f (τ )| < r, for some r ∈ R ≥0 .

II. NEURAL MASS MODELS

It is shown in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF] that the models in [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF], [START_REF] Stam | Dynamics of the human alpha rhythm: evidence for non-linearity[END_REF], [START_REF] Wendling | Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition[END_REF] can all be described by the following state-space model

ẋ = Āx + Φ(x, θ) + σ1 (u, θ) + σ2 ( C x, θ) ȳ = C x, (1)
where x ∈ R nx is the state which represents the mean membrane potential of different populations of neurons and, potentially, their time-derivatives, u ∈ R nu is a vector of inputs, which represents the external influences from the afferent neural populations and which is assumed to be known, θ ∈ R n θ is a known vector of parameters and ȳ ∈ R ny is the output. The matrix A is Hurwitz, Φ is smooth, bounded and globally Lipschitz, σ1 and σ2 are smooth functions. An example of such a model is provided in Section IV.

In [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF], the output ȳ of ( 1) is assumed to represent EEG signals. However, the output signals generated by [START_REF] Bara | Parameter-dependent state observer design for affine LPV systems[END_REF] are not necessarily centered at the origin contrary to real EEG recordings, see for instance Figure 2. To overcome this issue, we add a high-pass filter to model [START_REF] Bara | Parameter-dependent state observer design for affine LPV systems[END_REF]. In particular, we consider the multi-dimensional filter below

ẋf = -f 0 x f + w f y f = -f 0 x f + w f , (2)
where x f := (x f1 , . . . , x fn y ) is the filter state, w f is the vector of inputs to the filter and f 0 is the cutoff frequency.

Since we want to remove the offset from the signals ȳ generated by [START_REF] Bara | Parameter-dependent state observer design for affine LPV systems[END_REF], f 0 will be taken sufficiently small. In view of ( 1) and ( 2), we obtain the augmented model below

ẋ = Āx + Φ(x, θ) + σ1 (u, θ) + σ2 ( C x, θ) ẋf = -f 0 x f + C x y f = -f 0 x f + C x, (3)
which we rewrite as

ẋ = Ax + Φ(x, θ) + σ(u, θ) y f = Cx, (4)
where x := (x, x f ) ∈ R nx is the augmented state, y f ∈ R ny is the new output which represents the EEG signals and

A := Ā 0 C -f 0 I , C := C -f 0 I , Φ(x, θ) := ȳ(t), y f (t) time(s) 0 0 0.5
Fig. 2: Outputs of system (1) (solid blue line) and system (4) (dashed red line) for the neural mass model considered in Section IV with parameters values of Table I.

Φ(x, θ) + σ2 ( C x, θ), 0 and σ(u, θ) := σ1 (u, θ), 0 . System (4) generates outputs whose mean values tend to zero as time grows, see for an example Figure 2. The first difference we note between ( 1) and ( 4) is that we no longer have an output injection term in the dynamics as ȳ is no longer measured in (4). As a consequence, the results in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF] cannot be applied to (4) (the compensation of the output injection term plays a key role in the analysis of [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF]). On the other hand, it can be noticed that the matrix A is Hurwitz and that Φ is still smooth, globally Lipschitz and bounded. We could therefore potentially apply the results in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] to construct a global observer for system (4). Simulation results show that the required LMI condition in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] is only valid for a restrictive set of model parameters for the model we consider in Section IV. We consequently have to provide an alternative solution to estimate the state x using the output y f , the input u and model (4).

III. LOCAL OBSERVER SYNTHESIS

The objective of this section is to design a local observer for system (4), i.e. an observer whose convergence is ensured when its initial condition is sufficiently close to the initial condition of system (4) (a formal definition is provided below). For that purpose, we compute a first order approximation of the vector field of system (4) in the neighborhood of x ∈ R nx using Taylor's theorem. We obtain

ẋ = Ax + Φ(x, θ) + σ(u, θ) + A(x -x) + ∂Φ(x,θ) ∂x x (x -x).
(5) We concatenate each non-zero component of the matrix ∂Φ(x,θ) ∂x

x to form the vector α(x) ∈ R nα , where n α ∈ {1, . . . , n 2

x }. As a consequence, we can rewrite (5) as

ẋ = Ax + Φ(x, θ) + σ(u, θ) + A α(x) (x -x). (6) with A α(x) := A+ ∂Φ(x,θ) ∂x x. Notice that each component α i of α evolves in a compact set, i.e. α i (x) ∈ [α i , α i ] for all x ∈ R nx , with known constants α i , α i ∈ R ≥0 , i ∈ {1, . . . , n α }.
This comes from the fact that Φ is globally Lipschitz. Hence, α(x) lies in the hyper-rectangle whose vertices are defined by

V := {(ω 1 , . . . , ω nα ) | ω i ∈ {α i , α i }}. (7)
We consider the following observer candidate

ẋ = Ax + Φ(x, θ) + σ(u, θ) + K α(x) (y f -C x), (8)
where x ∈ R nx is the estimated state and K α(x) is the correction term to be designed. Our objective is to ensure that ( 8) is a local (exponential) observer for system (4) as defined below.

Definition 1: System ( 8) is a local observer of system (4) if there exists a neighborhood W of the origin of R nx such that for any initial condition x 0 and x0 of system ( 4) and ( 8) respectively, for any u ∈ L ∞ , if x 0 -x0 ∈ W , then the corresponding solutions to (4) and ( 8) are such that x(t) -x(t) decays asymptotically to zero. We say that it is a local exponential observer to system (4) if x(t) -x(t) exponentially converges to zero.

We define the estimation error as x := x -x. The dynamics of the estimation error system is, in view of ( 6) and ( 8),

ẋ = A α(x) x -K α(x) (y f -C x) = A α(x) -K α(x) C x. (9)
We can interpret system (9) as a LPV system where α(x) plays the role of parameters. Thus, the design of the local observer (8) reduces to the computation of the parameter dependent gain K α(x) such that the origin is asymptotically or exponentially stable for system [START_REF] Khalil | Nonlinear Systems[END_REF]. Tractable conditions, expressed in terms of LMIs, can be obtained using quadratic Lyapunov functions [START_REF] Barmish | Necessary and sufficient conditions for quadratic stabilizability of an uncertain system[END_REF]. In order to check the stability property of the LPV system (9) using a quadratic Lyapunov function V (x) := xT P x with P a real, symmetric, positive definite matrix, one has to solve the following parameter dependent Lyapunov inequality

A(α) T P + P A(α) -C T K(α) T P -P K(α)C + εI ≤ 0, ∀α ∈ V, (10)
where ε ∈ R >0 . Condition ( 10) is difficult to check in practice because there is an infinite combination of the parameters and it is nonlinear as it involves both P and P K(α(x)) as unknowns. A way to overcome this issue consists in rewriting the LPV approximate error system (9) in a polytopic form and to use a change of variables to tackle the nonlinear term P K(α(x)). Numerically tractable conditions are then derived in terms of LMIs by evaluating the condition [START_REF] Reif | An EKF-based nonlinear observer with a prescribed degree of stability[END_REF] on the vertices of the polytope. To this end, the terms A α(x) and K α(x) of ( 9) are rewritten as follows (as in [START_REF] Bara | Parameter-dependent state observer design for affine LPV systems[END_REF])

A α(x) = 2 nα -1 i=0 µ i (α(x))A [i] K α(x) = 2 nα -1 i=0 µ i (α(x))K [i] , (11)
where A [i] and K [i] are the corners of the polytopes and µ i (α(x)) are interpolation functions. The terms A α(x) and K α(x) are obtained by linear interpolation of each component α i (x), i ∈ {1, . . . , n α }. As the vector α(x) belongs to a hyper-rectangle defined by the vertices set V, then A α(x) and K α(x) are respectively delimited by polytopes of R nx×nx and R nx×1 . These polytopes are defined by the sets of vertices

A := {A [0] , . . . , A [2 nα ] } K := {K [0] , . . . , K [2 nα ] }. (12)
Each corner A [i] of A and K [i] of K corresponds to a corner of V. Let b i nα . . . b i 1 be the binary representation of the index i with b i 1 the least significant bit and b i nα the most significant bit. Then the parameter box corner corresponding to

A [i] , K [i] is (α 1 , . . . , αnα ) where αj := α j when b i j = 0 α j when b i j = 1. (13)
Furthermore, the interpolation functions are given by

µ i (α(x)) := nα j=1 γij αj (x)+βij α j -αj (14)
with

γ ij := 1 when b i j = 0 -1 when b i j = 1 (15)
and

β ij := -α j when b i j = 0 α j when b i j = 1. (16)
It has to be noted that the following holds

0 ≤ µ i (α(x)) ≤ 1 ∀i ∈ {0, . . . , 2 nα-1 } ∀x ∈ R nx , 2 nα -1 i=0 µ i (α(x)) = 1.
(17) We now state the main result based on the use of a quadratic Lyapunov function that allows us to compute the local observer gains.

Proposition 1: If there exist a real, symmetric, and positive definite matrix P , R [i] for i ∈ {1, . . . , 2 nα-1 }, and ε ∈ R >0 such that the following LMIs are satisfied

A [i] T P + P A [i] -C T R [i] T -R [i] C + εI ≤ 0, ∀i ∈ {0, . . . , 2 nα-1 }, (18)
then system [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF] with K(α(x)) given by [START_REF] Rigatos | Estimation of wave-type dynamics in neurons' membrane with the use of the Derivative-free nonlinear Kalman Filter[END_REF] and

K [i] = P -1 R [i]
is a local exponential observer for system (4).

Proof. As mentioned above, to check the stability of the LPV system (9) using a quadratic Lyapunov function V (x) = xT P x with P a real, symmetric, and positive definite matrix, reduces to solve the parameter dependent Lyapunov inequality [START_REF] Reif | An EKF-based nonlinear observer with a prescribed degree of stability[END_REF]. Using the polytopic formulation, it suffices to check that

2 nα -1 i=0 µi(α(x))A [i] T P + P 2 nα -1 i=0 µi(α(x))A [i] -C T × 2 nα -1 i=0 µi(α(x))K [i] T P -P 2 nα -1 i=0 µi(α(x))K [i] C + εI ≤ 0, ∀i ∈ {0, . . . , 2 nα-1 }, ∀x ∈ R nx , (19)
Using the change of variable R [i] = P K [i] , we obtain

2 nα -1 i=0 µi(α(x)) A [i] T P + P A [i] -C T R [i] T -R [i] C + εI ≤ 0, ∀i ∈ {0, . . . , 2 nα-1 }, ∀x ∈ R nx , (20)
which can be verified by considering the vertices of the polytope, that is the LMIs [START_REF] Wilson | Excitatory and inhibitory interactions in localized populations of model neurons[END_REF]. Since ( 18) is assumed to hold, the origin of system ( 9) is exponentially stable according to standard Lyapunov analysis. Now, let us consider the nonapproximated estimation error system

ẋ = (A -K(α(x))C)x + Φ(x, θ) -Φ(x, θ) =: f (x, x, θ). ( 21
)
By considering the dependence of f on x as a timedependence, we write f (x, x, θ) =: F (t, x). We note that F is continuously differentiable since so is Φ. Furthermore, the Jacobian matrix of F at x is A(α(x)), which is bounded in view of ( 11) and ( 17) and Lipschitz, uniformly in t on D = {x ∈ R nα : |x| < r} for any r > 0. Indeed, as α is smooth (since Φ is smooth), so are µ i for any i ∈ {0, . . . , 2 nα-1 }, A(α(x)) and K(α(x)) (in view of ( 11) and ( 14)). Hence, A(α(x)) is locally Lipschitz. In addition, we deduce from ( 11) and ( 17) that the Lipschitz constant and the bound of A(α(x)) on D are uniform in and thus in t. As a consequence, we apply Theorem 4.13 in [START_REF] Khalil | Nonlinear Systems[END_REF] to conclude that the origin of system (21) is locally exponentially stable, which means that system (8) is a local exponential observer for system (4) according to Definition1.

IV. APPLICATION TO A NEURAL MASS MODEL

We revisit the model of [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF] which describes the electrophysiological activity of a cortical column composed of three interconnected populations of neurons (see Figure 1). The firing rate captures the average number of action potentials generated within the population of neurons per unit of time [START_REF] Dayan | Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems[END_REF]. The conversion of the firing rate of the afferent populations to either excitatory or inhibitory postsynaptic membrane potential (EPSP) and (IPSP) is modeled, respectively, by using the linear transformation with an impulse response given by, as in [START_REF] Sauer | Data assimilation for heterogeneous networks: the consensus set[END_REF], [START_REF] Wilson | Excitatory and inhibitory interactions in localized populations of model neurons[END_REF], [START_REF] Wilson | A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue[END_REF],

h e (τ ) = A e exp{-a e τ } τ ≥ 0 (22) h i (τ ) = A i exp{-a i τ } τ ≥ 0, (23)
with h e (τ ) = 0 and h i (τ ) = 0 for τ < 0. Parameters A e > 0 and A i > 0 determine the maximum amplitude of the EPSP and IPSP, respectively, a e and a i represent the average time constants of the excitatory loop and inhibitory loop respectively. Contrary to [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF], we consider linear systems of order 1 in ( 22) and (23) (and not of order 2), however our results do apply to linear systems of higher order. This choice is justified by the fact that this simpler structure is still able to generate a wide range of output signals as studied in e.g., [START_REF] Sauer | Data assimilation for heterogeneous networks: the consensus set[END_REF], [START_REF] Wilson | Excitatory and inhibitory interactions in localized populations of model neurons[END_REF], [START_REF] Wilson | A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue[END_REF]. The mean membrane potential of a population is converted into the average firing rate of the population using the sigmoid function S(v) = 2e 0 /[1 + e r(v0-v) ] for v ∈ R, where e o > 0 determines the maximum firing rate of the neural population, v o > 0 is the postsynaptic membrane potential (PSP) for which a 50% firing rate is achieved, and r the steepness of S (see [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF] for more details). Using the state space representation of ( 22), (23) and by following similar lines as in [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF], the resulting model is

ẋ1 = -a e x1 + A e S(x 2 -x3 ) ẋ2 = -a e x2 + A e u(t) + C 1 S(x 1 ) ẋ3 = -a i x3 + A i C 2 S(x 1 ) ȳ = x2 -x3 , ( 24
)
where x1 is the membrane potential contribution from the pyramidal neurons to the excitatory and inhibitory interneurons, x2 is the membrane potential contribution from the pulse density u and the excitatory interneurons to the pyramidal neurons and x3 is the membrane potential contribution of the inhibitory interneurons to the pyramidal interneurons. The neural populations are connected with connectivity strengths C 1 and C 2 which account for the total number of synapses established by interneurons onto the axons and dendrites of the neurons constituting the cortical column. The pulse density u is typically taken as a white noise function. For our simulations, the input u is a continuous white Gaussian noise of mean 90 and of variance 900. We apply the filter (2) to the output of system (24) and we obtain the system below ẋ1 = -a e x 1 + A e S(x 2 -x 3 ) ẋ2 = -a e x 2 + A e u(t)

+ C 1 S(x 1 ) ẋ3 = -a i x 3 + A i C 2 S(x 1 ) ẋ4 = -f 0 x 4 + x 2 -x 3 y f = -f 0 x 4 + x 2 -x 3 , (25)
which corresponds to (4) with

A =     -a e 0 0 0 0 -a e 0 0 0 0 -a i 0 0 1 -1 -f 0     C = 0 1 -1 -f 0 σ(u, θ) = (0, A e u(t), 0, 0) Φ(x, θ) = (A e S(x 2 -x 3 ), A e C 1 S(x 1 ), A i C 2 S(x 1 ), 0).
(26) We see in Figure 2, system (25) generates output signals with no offset after a transient time as desired. As in [START_REF] Chong | Estimating the unmeasured membrane potential of neuronal populations from the eeg using a class of deterministic nonlinear filters[END_REF], we consider the parameter values presented in Table I. We envision an observer of the form [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF] obtain an approximate estimation error system (9) with

A α(x) =    -ae Aeα1(x) -Aeα1(x) 0 AeC1α2(x) -ae 0 0 AiC2α2(x) 0 -ai 0 0 1 -1 -f0    , (27)
where α(x) = (α 1 (x), α 2 (x)), and

α 1 (x) = ∂S(x 2 -x 3 ) ∂x 2 x2,x3 , α 2 (x) = ∂S(x 1 ) ∂x 1 x1 .
Each α i evolves in [0, 1 2 e 0 r], with 1 2 e 0 r being the Lipschitz constant of the sigmoid function. The particular structure of Φ leads to a vector α of dimension n α = 2. Hence, the matrix A(α(x)) lives in a hyper-rectangle with 2 2 vertices. We compute a gain K [i] for each vertex A [i] by solving LMIs [START_REF] Wilson | Excitatory and inhibitory interactions in localized populations of model neurons[END_REF] as explained in Section III. The gain values are

K [0] = -1, 35 -1, 43 -1, 16 -0, 57
K [1] = -0, 16 -1, 63 -2, 13 0, 17

K [2] = -1, 34 -1, 45 -1, 34 -0, 57
K [3] = -0, 14 -1, 64 -2, 30 0, 17 .

Figure 3 presents simulations results for the initial conditions x(0) = (0.14, 19, 12.5, 7) and x(0) = (0.24, 19.4, 12.9, 7.4).

We see that the estimation error decays to zero as expected. Figure 4 depicts the variations of α 1 (x) and α 2 (x). We note that these variables, which we consider as parameters in the design, are indeed time-varying. It has to be noticed that we could not design a global observer using [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] as the required LMI does not hold for the considered set of parameters. Nevertheless, we have varied the values of A e , A i and C within the set Θ := [2.6, 9.75]× [17.6, 110]×[108, 675] to identify feasible values for the results in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF]. Those parameters are known to play an important role in the dynamics of (24) (see [START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF], [START_REF] Wendling | Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition[END_REF]) and are expected to lie Θ. We have sampled the set Θ with a step of 0.5 for A e , 5 for A i and 30 for C to this purpose. We have tested the LMI in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] for these values. shows the feasible set of model parameters. We have also plotted the feasible set of parameters for our design, see Figure 5. We see that the range of parameters where LMIs (18) is verified is wider than the one for which the LMI in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] holds. More precisely, LMI ( 18) is verified for 90% of the tested parameters values, while the LMI in [START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] holds for 49% of the values.

V. CONCLUSIONS

We have presented a local observer design for a class of neural mass models which relies on LPV techniques. The observer gains are nonlinear in the state estimates and are constructed by solving LMIs. The results apply to neural mass models for which the outputs are centered at the origin as with real EEG recordings.

A drawback of local observers is that they need to be initialized sufficiently close to the true system state to converge. We will present in future work a hybrid estimation scheme that relies on the results of this study to ensure the global convergence of the state estimation error.

Figure 6

 6 Figure3presents simulations results for the initial conditions x(0) = (0.14, 19, 12.5, 7) and x(0) = (0.24, 19.4, 12.9, 7.4). We see that the estimation error decays to zero as expected. Figure4depicts the variations of α 1 (x) and α 2 (x). We note that these variables, which we consider as parameters in the design, are indeed time-varying.It has to be noticed that we could not design a global observer using[START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] as the required LMI does not hold for the considered set of parameters. Nevertheless, we have varied the values of A e , A i and C within the set Θ := [2.6, 9.75]×[17.6, 110]×[108, 675] to identify feasible values for the results in[START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF]. Those parameters are known to play an important role in the dynamics of (24) (see[START_REF] Jansen | Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns[END_REF],[START_REF] Wendling | Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition[END_REF]) and are expected to lie Θ. We have sampled the set Θ with a step of 0.5 for A e , 5 for A i and 30 for C to this purpose. We have tested the LMI in[START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] for these values. Figure6

Fig. 3 :

 3 Fig. 3: Simulation results: true state (red), estimated state (blue).

Fig. 4 :

 4 Fig. 4: Evolution of: α 1 (x) (red dashed line), α 2 (x) (blue line).

Fig. 5 :

 5 Fig. 5: Model parameters for which (18) is verified.

Fig. 6 :

 6 Fig.6: Model parameters for which the LMI in[START_REF] Chong | A robust circle criterion observer with application to neural mass models[END_REF] is verified.

TABLE I :

 I Parameter values.

	Parameter Value
	e 0	2.5
	v 0	6
	a e	100
	a i	50
	A e	3.25
	A i	22
	C	135
	C 1	0.8C
	C 2	0.25C
	f 0	10
		for system (25) and we